The DOI matches its Crossref record; 88 of the 88 references it cites were found in a registry or an index; 40 of the 49 sources its claims cite were checked for support.
Non-Gaussianities in two-field inflation
Open accessAbstract
We study the bispectrum of the curvature perturbation on uniform energy density hypersurfaces in models of inflation with two scalar fields evolving simultaneously. In the case of a separable potential, it is possible to compute the curvature perturbation up to second order in the perturbations, generated on large scales due to the presence of non-adiabatic perturbations, by employing the δ N -formalism, in the slow-roll approximation. In this case, we provide an analytic formula for the nonlinear parameter f NL . We apply this formula to double inflation with two massive fields, showing that it does not generate significant non-Gaussianity; the nonlinear parameter at the end of inflation is slow-roll suppressed. Finally, we develop a numerical method for generic two-field models of inflation, which allows us to go beyond the slow-roll approximation and confirms our analytic results for double inflation.
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TL;DR
The paper computes the bispectrum and nonlinear parameter \(f_{\rm NL}\) for two-field inflation using the \(\delta N\)-formalism up to second order, providing an analytic formula for separable potentials in slow roll. It finds that double quadratic inflation does not generate significant non-Gaussianity, with \(f_{\rm NL}\) slow-roll suppressed and numerically confirmed.
Key findings
- For two-field inflation with a separable potential, the authors derive an analytic expression for the nonlinear parameter \(f_{\rm NL}\), Eq. (68), in terms of the potential and slow-roll parameters.
- In double quadratic inflation with two massive fields, they conclude that non-Gaussianity is slow-roll suppressed: \(|f_{\rm NL}|\ll 1\).
- For the specific numerical example with mass ratio \(R=1/9\) and initial condition \(\phi=\chi=13\,m_P\), at the end of inflation they find \(-(6/5)f^{(4)}_{\rm NL}=0.008\), \(-(6/5)f^{(3)}_{\rm NL}=0.008\), and \(-(6/5)f_{\rm NL}=0.016\simeq 1/60\).
- Their numerical calculation agrees remarkably well with the analytic results and confirms that nonlinear evolution on super-Hubble scales during double quadratic inflation does not produce detectable non-Gaussianity; they disagree with Rigopoulos et al. and agree with Alabidi and Lyth.
Methods
- Uses the \(\delta N\)-formalism to compute the curvature perturbation \(\zeta\) on uniform density hypersurfaces up to second order in perturbations, assuming slow roll at Hubble exit.
- Specializes to two scalar fields with canonical kinetic terms and a separable potential \(W=U(\phi)+V(\chi)\), deriving analytic expressions for the power spectrum, spectral index, and \(f_{\rm NL}\).
- Develops a numerical method that solves the full background field and Friedmann equations and computes first and second derivatives of \(N\) by finite differences, allowing slow roll to be relaxed after Hubble exit; applies it to double quadratic inflation.
Limitations
- The analytic formula assumes slow-roll conditions for all fields from Hubble exit until the end of inflation; the numerical method still assumes slow roll at Hubble exit.
- The analytic treatment is restricted to two fields with a separable potential, though the numerical method is stated to be extendable to any two-field model.
- The authors state they are unable to explain the discrepancy with Rigopoulos et al., who found large non-Gaussianity in the same double quadratic model.
- They leave to future work the investigation of models where the quantity \(A\), and thus \(f_{\rm NL}\), can be large.
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Claims the paper makes
18 Own interpretation · 17 No basis given · 11 Own result · 10 Partly supported · 7 Couldn’t confirm · 4 Own method · 3 Supported · 3 Sources not found · 2 Supported so far · 2 No full text of the sources · 1 Not supported · accuracy not yet measured
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“In particular, the δN -formalism is equivalent to integrate the evolution of ζ on super-Hubble scales from Hubble exit until t c .”
What the sources say
- Partly supportedcites [20] sourceExperimental — accuracy not yet measured
The paper’s discussion of Eqs. (19), (23), and (32) addresses the evolution and conservation of ζ on super-Hubble scales. It does not state that the δN formalism is equivalent to integrating that evolution from Hubble exit to tc. (LLM, conf=0.80)
plainstates an association- Asserted: passes — The authors put it forward as true.
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- Partly supported
Every source the paper cites for this claim was checked and supports it.
In the paper
“Note that, using Eqs. (62) and (28) for the adiabatic case, this can be expressed as a consistency relation between observables [5],”
What the sources say
- Supportedcites [5] Maldacena J, 2003, J. High Energy Phys. source
In the discussion around Eq. (4.9) (JHEP05(2003)013; page not provided), Maldacena expresses a k-dependent nonlinear parameter in terms of the scalar and tensor spectral tilts, which are observables. The paper cautions that its full result cannot be recast as a single, momentum-independent f_NL; the consistency relation is shape-dependent. (LLM, conf=0.91)
plainstates an association- Asserted: passes — The authors put it forward as true.
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- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
- Supported
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“Furthermore, non-adiabatic perturbations produced during multi-field inflation can certainly generate detectable non-Gaussianity in the density field after inflation, in models such as the curvaton scenario [10] (see also [11]) or reheating [12, 13, 14, 15].”
What the sources say
- Supportedcites [10] source
The Introduction (p. 1) says the curvaton scenario generates an adiabatic density perturbation after inflation from an initially isocurvature perturbation and can produce significant non-Gaussianity. The Conclusions (p. 11) say that non-Gaussianity can be large and detectable in a regime where the curvaton does not dominate before decay. The separate reheating claim is cited to other sources, not this paper. (LLM, conf=0.92)
- Partly supportedcites [11] sourceExperimental — accuracy not yet measured
The Abstract and Conclusions support the central point: non-Gaussian isocurvature perturbations in multifield inflation can transfer to adiabatic perturbations and produce significant primordial non-Gaussianity. But Section III says the paper's transfer mechanism is effective only during inflation; it does not establish the curvaton or post-inflation reheating examples attached to this citation. (LLM, conf=0.88)
- Partly supportedcites [12] sourceExperimental — accuracy not yet measured
The introduction (p. 1) says multifield inflation can produce non-Gaussian isocurvature fluctuations that are transferred to curvature fluctuations, and discusses prospects for detecting primordial non-Gaussianity. But the paper’s models transfer those fluctuations during inflation; it does not establish the cited curvaton or reheating examples as mechanisms producing non-Gaussianity after inflation. (LLM, conf=0.87)
- Supportedcites [13] source
For the reheating part of the citing sentence, the paper describes density perturbations arising from fluctuations in the inflaton’s decay rate and says the resulting non-Gaussianities may be observable (title passage, p. 1). The Introduction (p. 1) places this mechanism among scenarios involving other light fields during inflation, while the Summary (p. 7) says its predicted non-Gaussianity could reach the sensitivity of future CMB experiments. (LLM, conf=0.91)
- Supportedcites [14] source
The citation to this paper is attached to the reheating example, not the curvaton scenario. The Abstract describes a two-field inflation model in which preheating amplifies perturbations and enhances non-Gaussianity; the discussion on p. 3 says the resulting signal could be observable. (LLM, conf=0.90)
- Not matchedcites [15] Barnaby N Cline J M, 2006
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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- Supported
The sources with a verdict support this claim; the rest weren’t checked yet, have no full text we could read, or their verdicts aren’t rated yet.
In the paper
“For multi-field inflation, the expression for the scalar spectral index has been given, for instance, in [31, 1]. At lowest order in slow-roll one has [2]”
What the sources say
- Could not verifycites [31] Malik K A, 2005, J. Cosmol. Astropart. Phys. sourceExperimental — accuracy not yet measured
The Introduction mentions calculating the spectral index, but gives no expression for it. Section 8 applies slow roll to a two-field model to calculate the second-order curvature perturbation, not the lowest-order scalar spectral index. A search for “spectral index” found no formula in our copy that could verify the attribution to Eq. (15). (LLM, conf=0.76)
- Supportedcites [1] source
Section 4.4 (p. 32) derives an expression for the scalar spectral index in the multi-component case as Eq. (115). The citing paper’s Eq. (15) is not reproduced here, so its exact algebraic match cannot be checked, but the attributed claim that this source gives the multi-field expression is supported. (LLM, conf=0.88)
- Not checked — no full text of the sourcecites [2] Liddle A R, 2000, Cosmological Inflation and Large-scale Structure source
plain- Asserted: passes — The authors put it forward as true.
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- Could not verify
The cited sources that could be checked couldn’t confirm or dispute this claim.
In the paper
“However, Seery and Lidsey [35] have found that during slow-roll inflation the field three-point correlation functions do not vanish and read”
What the sources say
- Could not verifycites [35] sourceExperimental — accuracy not yet measured
Section 4 (p. 6) discusses scalar-field perturbations and the spectral index under slow-roll conditions, but does not address whether field three-point correlations vanish. Searches for three-point correlations and the bispectrum found no passage supporting the claim. The citing sentence names Seery and Lidsey, but that does not establish a source from this paper's text. (LLM, conf=0.76)
plain- Asserted: passes — The authors put it forward as true.
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- The authors state this as an assumption: All k_i are of the same order of magnitude so that they cross the Hubble radius approximately at the same time.
- Could not verify
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“which coincides with the single field case result [5, 36].”
What the sources say
- Supportedcites [5] Maldacena J, 2003, J. High Energy Phys. source
The cited paper gives a single-field result for a momentum-dependent nonlinear parameter in its discussion of equation (4.9). The citation supplies the single-field result used for comparison; it does not need to establish the citing paper’s two-field limit. (LLM, conf=0.88)
- Could not verifycites [36] sourceExperimental — accuracy not yet measured
Section 3 (pp. 12–15) develops a quasi-nonlinear treatment of multi-scalar perturbations, but the readable passages do not state a result for a nonlinear parameter in the limit t_c → t_*. Searches for that limit, a two-field adiabatic comparison, and f_NL found no passage establishing the claimed agreement with the single-field result; relevant formulas in our copy are undecoded. (LLM, conf=0.72)
plain- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
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- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
- Supported
Every source the paper cites for this claim was checked and supports it.
In the paper
“Indeed, the particular combination of second derivatives, ˙ ϕ J N ,IJ , that appears in the spectral index (15) can be eliminated in favor of second derivatives of the potential using the slow-roll approximation to give [1]”
What the sources say
- Supportedcites [1] source
Section 4.4 (p. 32) differentiates the slow-roll relation for N to obtain Eq. (114), which replaces a potential-gradient contraction of N’s second derivatives with a term involving V,ab. The resulting spectral-index formula, Eq. (115), contains second derivatives of the potential instead. (LLM, conf=0.92)
plainstates a cause- Asserted: passes — The authors put it forward as true.
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In the paper
“In Ref. [1] it is argued that N in Eq. (42) is dominated by the field values at Hubble exit and hence one can neglect the dependence of N upon the field values at the final time, t c . This is not in general true when evaluating the perturbation ζ during inflation.”
What the sources say
- Partly supportedcites [1] sourceExperimental — accuracy not yet measured
Section 4.6 (p. 34, Eqs. 120–121) says that each integral for N is dominated by its horizon-exit endpoint and derives a result that neglects the final-field contribution. But it makes this argument under specified conditions, including that every field at horizon exit is much larger than its value at the end of inflation. It does not establish the same neglect for an arbitrary final time during inflation; the citing authors’ statement that this is not generally true is their own assessment. (LLM, conf=0.87)
plain- Asserted: passes — The authors put it forward as true.
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- Partly supported
The cited sources that could be checked couldn’t confirm or dispute this claim.
In the paper
“Our results disagree with those of Rigopoulos et al. [22] who found that double quadratic inflation, in particular the model studied in Sec. 5.2, can generate large non-Gaussianity.”
What the sources say
- Could not verifycites [22] sourceExperimental — accuracy not yet measured
The discussion on p. 4 says that non-Gaussianity can evolve on large scales when more than one field is present, but it does not discuss double quadratic inflation or a large non-Gaussianity result for that model. The references on p. 4 list Rigopoulos and Shellard, without reporting the finding attributed to them. Searches for the model and the alleged disagreement found no passage addressing either point. (LLM, conf=0.73)
plain- Asserted: passes — The authors put it forward as true.
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- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: The potential is separable into the sum of two potentials, each of which is dependent on only one of the two fields.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
- Could not verify
The cited sources that could be checked couldn’t confirm or dispute this claim.
In the paper
“These results coincide with the estimate of Ref. [23].”
What the sources say
- Could not verifycites [23] sourceExperimental — accuracy not yet measured
The Introduction (p. 2) and the discussion of second-order perturbations (p. 12) describe the paper’s cosmological-perturbation formalism, but do not report a double-inflation estimate or compare results with one. Searches for “double inflation” and “estimate coincide” found no passage addressing the claimed agreement; the identity of Ref. [23] in the citing paper is not established by this source’s reference list. (LLM, conf=0.74)
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: The potential is separable into the sum of two potentials, each of which is dependent on only one of the two fields.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
- Could not verify
The cited sources that could be checked couldn’t confirm or dispute this claim.
In the paper
“The δN -formalism assumes that the fields are in slow-roll at Hubble exit, Eq. (8) (see [48] for a development of the δN -formalism applicable to more general situations).”
What the sources say
- Could not verifycites [48] sourceExperimental — accuracy not yet measured
The citation is attached to the parenthetical claim that this paper develops the δN formalism for more general situations. Sections 2.2 and 2.3 discuss slow-roll inflation and perturbations at horizon crossing, but the passages found by searching for δN and separate-universe methods do not describe such a development. (LLM, conf=0.74)
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- Could not verify
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“Our results agree with a previous discussion of non-Gaussianity in a double quadratic potential by Alabidi and Lyth [23], based on an estimate of δN given in [1] using the integral (42).”
What the sources say
- Could not verifycites [23] sourceExperimental — accuracy not yet measured
The agreement with Alabidi and Lyth is attributed to [23] in the citing sentence, not to this source, [1]. Our copy discusses a local number of e-folds (Abstract, p. 1), but its discussion of equation (42) concerns a linear perturbation equation (Section 4, p. 10); the passages found do not establish an estimate of δN using an integral (42). (LLM, conf=0.76)
- Supportedcites [1] source
In the citing sentence, [1] is attached to the δN estimate, not to the authors’ statement that their results agree with Alabidi and Lyth [23]. Section 4.3 of the cited paper gives R = δN and defines N as an integral; Section 4.6 gives an integral for N in a two-field quadratic potential. Those passages support its use as the basis for a δN estimate, but do not independently establish the citing authors’ agreement claim. (LLM, conf=0.87)
plainstates an association- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: The potential is separable into the sum of two potentials, each of which is dependent on only one of the two fields.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
- Could not verify
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We apply this formula to double inflation with two massive fields, showing that it does not generate significant non-Gaussianity; the nonlinear parameter at the end of inflation is slow-roll suppressed.”
- Also stated in: § 1 Introduction · p. 2 · plain
“In the case of double inflation with two massive fields, we find no significant non-Gaussianity produced, which confirms a previous discussion by Alabidi and Lyth in Ref. [23].”
boosted- Asserted: passes — The authors put it forward as true.
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- The authors state this as an assumption: The potential of the fields is separable into the sum of two potentials each dependent on only one of the two fields.
- The authors state this as an assumption: The slow-roll conditions are satisfied for both fields during inflation.
- Also stated in: § 1 Introduction · p. 2 · plain
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Finally, we develop a numerical method for generic two-field models of inflation, which allows us to go beyond the slow-roll approximation and confirms our analytic results for double inflation.”
- Also stated in: § 1 Introduction · p. 2 · plain
“Furthermore, we also use numerical solutions to go beyond the slow-roll approximation after Hubble exit, confirming our analytic results.”
plain- Asserted: passes — The authors put it forward as true.
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- The authors state this as an assumption: The potential of the fields is separable into the sum of two potentials each dependent on only one of the two fields.
- The authors state this as an assumption: The slow-roll conditions are satisfied for both fields during inflation.
- Also stated in: § 1 Introduction · p. 2 · plain
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We apply this formula to double inflation with two massive fields, showing that it does not generate significant non-Gaussianity; the nonlinear parameter at the end of inflation is slow-roll suppressed.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: The potential of the fields is separable into the sum of two potentials each dependent on only one of the two fields.
- The authors state this as an assumption: The slow-roll conditions are satisfied for both fields during inflation.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This is the exact expression for the amplitude of the nonlinear parameter for the curvature perturbation ζ during slow-roll inflation in an arbitrary two-field inflation model with separable potential, and represents one of the main results of this paper.”
plain- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
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- The authors state this as an assumption: The potential is separable into the sum of two potentials, each of which is dependent on only one of the two fields.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“We are thus able to give an analytic expression for f (4) NL defined in Eq. (30).”
plain- Asserted: passes — The authors put it forward as true.
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- The authors state this as an assumption: The potential of the fields is separable into the sum of two potentials each dependent on only one of the two fields.
- The authors state this as an assumption: The slow-roll conditions are satisfied for both fields during inflation.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Only the third term, which is of order A ε -2 ∗ , leads to a contribution that is not automatically slow-roll suppressed.”
plainstates a cause- Asserted: passes — The authors put it forward as true.
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- The authors state this as an assumption: The potential is separable into the sum of two potentials, each of which is dependent on only one of the two fields.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“since A does not appear in the expression for the spectral index n ζ , Eq. (61)”
plain- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
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- The authors state this as an assumption: The potential is separable into the sum of two potentials, each of which is dependent on only one of the two fields.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The first two terms in the numerator of Eq. (68) are of order ε -1 ∗ , so their contribution to f (4) NL is of order ε ∗ .”
plainstates a cause- Asserted: passes — The authors put it forward as true.
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- The authors state this as an assumption: The potential is separable into the sum of two potentials, each of which is dependent on only one of the two fields.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Interestingly, for the potential (32), under the slow-roll conditions (38), there exists a dimensionless integral of motion C , using which one can label each slow-roll classical trajectory,”
plainstates an association- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
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- The authors state this as an assumption: The potential of the fields is separable into the sum of two potentials each dependent on only one of the two fields.
- The authors state this as an assumption: The slow-roll conditions are satisfied for both fields during inflation.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In double inflation this contribution can become temporarily large, at most of order unity, at the turn of the trajectory in field space.”
plain- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
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- The authors state this as an assumption: The potential is separable into the sum of two potentials, each of which is dependent on only one of the two fields.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The momentum dependent nonlinear parameter, f (3) NL , defined in Eq. (29), takes a very simple form, derived from Eq. (60),”
plainstates a cause- Asserted: passes — The authors put it forward as true.
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- The authors state this as an assumption: The potential of the fields is separable into the sum of two potentials each dependent on only one of the two fields.
- The authors state this as an assumption: The slow-roll conditions are satisfied for both fields during inflation.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In the expression for the scalar spectral index the derivatives of Z c with respect to the fields contained in these equations mutually cancel.”
plain- Asserted: passes — The authors put it forward as true.
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- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: The potential of the fields is separable into the sum of two potentials each dependent on only one of the two fields.
- The authors state this as an assumption: The slow-roll conditions are satisfied for both fields during inflation.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“As expected, when the heavy field φ dominates the total energy density, for H/m φ > ∼ 0 . 8, the uniform density curvature perturbation ζ remains constant.”
plain- Asserted: passes — The authors put it forward as true.
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A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Note that, as shown in Fig. 4, the curvature perturbation becomes constant after the energy density of the more massive field ( φ in our case) becomes negligible.”
plainstates a cause- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“It starts growing when H drops to 0 . 55 < ∼ H/m φ < ∼ 0 . 8, corresponding to both the light and heavy fields contributing to the total energy density.”
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
In the paper
“During this phase, the large scale total entropy perturbation is non-vanishing, and sources the evolution of ζ [38].”
What the sources say
- Not matchedcites [38] Zaballa I Rodriguez Y Lyth D H, 2006
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Not matched
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In our numerical example we see that the non-linearity parameter does evolve during inflation, especially as the trajectory turns the corner in field space, reflecting its dependence upon the final field values.”
plainstates a causeSingle case- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This growth corresponds to the growth of A defined in Eq. (66).”
plainstates an association- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The evolution of the nonlinear parameter -f (4) NL , however, is non-monotonic. It grows sharply during the intermediate phase 0 . 55 < ∼ H/m φ < ∼ 0 . 8, corresponding to the heavy field leaving slow-roll, but it then decreases.”
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We conclude that f NL in this model is much smaller that unity.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In the case of a separable potential, it is possible to compute the curvature perturbation up to second order in the perturbations, generated on large scales due to the presence of non-adiabatic perturbations, by employing the δN -formalism, in the slow-roll approximation.”
hedgedstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: The potential of the fields is separable into the sum of two potentials each dependent on only one of the two fields.
- The authors state this as an assumption: The slow-roll conditions are satisfied for both fields during inflation.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“During inflation, as explained in Sec. 3.3, f NL can be large only if, in Eq. (68), the contribution proportional to the quantity A defined in Eq. (66) is large.”
plainstates a possible cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: The potential is separable into the sum of two potentials, each of which is dependent on only one of the two fields.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“If this is not the case, since A does not appear in the expression for the spectral index n ζ , Eq. (61), for η ss c /ǫ c ≫ 1 one may have models with large f NL and quasiscale-invariant spectral index, corresponding to large deviations from the consistency relation for purely adiabatic perturbations, Eq. (70).”
hedgedstates a possible cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: The potential is separable into the sum of two potentials, each of which is dependent on only one of the two fields.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“and is thus constrained to be small.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
In the paper
“In single field inflation, perturbations on large scales are adiabatic and hence ζ remains constant during inflation [29].”
What the sources say
- Not checked — no full text of the sourcecites [29] source
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The nonlinear parameter f NL can only be larger than unity if the momentum independent term f (4) NL is large.”
plainstates a possible cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: unclear — It is unclear why the paper says it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The primordial curvature perturbation ζ is then given by the curvature of the end of inflation hypersurface, ζ ( t c ) = δN ( t e , t ∗ ).”
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“However this does not alter the general conclusion that the non-linearity parameter remains small at the end of inflation.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Furthermore, the δN -formalism, on super-Hubble scales, is equivalent to integrating the evolution of ζ .”
plainstates an association- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: unclear — It is unclear why the paper says it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We conclude that double inflation cannot produce large non-Gaussianity - i.e., | f NL |≪ 1 - these being suppressed by the slow-roll conditions on the fields at Hubble exit .”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: The potential is separable into the sum of two potentials, each of which is dependent on only one of the two fields.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We conclude, on the basis of our analysis, that nonlinear evolution on super-Hubble scales during double quadratic inflation does not appear to be capable of generating a detectable level of non-Gaussianity in the bispectrum.”
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: The potential is separable into the sum of two potentials, each of which is dependent on only one of the two fields.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“The two calculations agree remarkably well, within an accuracy that depends on the numerical precision.”
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
- The authors state this as an assumption: The δN-formalism assumes that the fields are in slow-roll at Hubble exit.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“Indeed, this provides an efficient method to compute the non-Gaussianity numerically for any two-field model, also when the field potential is not separable.”
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: The δN-formalism assumes that the fields are in slow-roll at Hubble exit.
- It may state two separate claims as one. 22
- Probably not a substantial claim. 9
- The quote only partly states this claim. 3
At least one cited source doesn’t support this claim or points to a different paper, and none confirmed it — see the verdicts below.
In the paper
“is momentum independent and local in real space, because it is due to the evolution of nonlinearities outside the Hubble radius during inflation.”
What the sources say
- Disputedcites [20] sourceExperimental — accuracy not yet measured
In the discussion following Eq. (6), the paper says that, for single-field inflation, non-Gaussianities in the conserved comoving curvature perturbation can only be generated inside the Hubble radius and are conserved outside it. This is contrary to the claim's explanation that the term arises from evolving nonlinearities outside the Hubble radius. The paper also does not identify a momentum-independent, real-space-local second term. (LLM, conf=0.86)
Checked by a reasoning model — may be wrong.
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: The connected part of the four-point correlation functions is negligible.
- Disputed
The sources with a verdict support this claim; the rest weren’t checked yet, have no full text we could read, or their verdicts aren’t rated yet.
In the paper
“In particular, slow-roll models of inflation generically predict an almost scale-invariant, almost Gaussian distribution of primordial density perturbations [1, 2].”
What the sources say
- Supportedcites [1] source
The Introduction says slow-roll inflation predicts a spectrum with |n−1| well below 1 and that, except in contrived models, the primordial density perturbation is Gaussian. Section 3.2 likewise derives Gaussian primordial perturbations under its stated assumptions about negligible interactions and the initial vacuum state. (LLM, conf=0.94)
- Not checked — no full text of the sourcecites [2] Liddle A R, 2000, Cosmological Inflation and Large-scale Structure source
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
- Supported
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“According to the so called δN -formalism [30, 31, 32], ζ , evaluated at some time t = t c , is equivalent, on large scales , to the perturbation of the number of e -foldings N ( t c , t ∗ , x ) from an initial fl at hypersurface at t = t ∗ , to a final comoving - or, equivalently, uniform density - hypersurface at t = t c .”
What the sources say
- Partly supportedcites [30] sourceExperimental — accuracy not yet measured
In “Two definitions of the curvature perturbation” (p. 2), the paper defines ζ on uniform-density slices and says these practically coincide with comoving slices. In “Single-component inflation” (p. 7), it relates ζ to a difference in e-folds between slicings. The available text does not state the claim’s specific construction from an initial flat hypersurface at t* to a final uniform-density hypersurface at tc. (LLM, conf=0.82)
- Partly supportedcites [31] Malik K A, 2005, J. Cosmol. Astropart. Phys. sourceExperimental — accuracy not yet measured
The introduction says the ΔN formalism relates the comoving curvature perturbation to a perturbation in the number of e-foldings. The discussion around Eq. (4.8) says comoving and uniform-density curvature perturbations coincide on large scales. Our copy does not specify the claimed initial flat and final comoving or uniform-density hypersurfaces for that e-folding calculation. (LLM, conf=0.85)
- Partly supportedcites [32] sourceExperimental — accuracy not yet measured
The Separate Universe Approach (p. 4) relates the large-scale curvature perturbation to differences in integrated expansion between hypersurfaces, supporting the δN part of the claim. But the paper says comoving and uniform-density hypersurfaces coincide for adiabatic perturbations (p. 6) and need not coincide when non-adiabatic pressure perturbations are present (p. 7). The citing sentence omits that qualification when calling the final hypersurfaces equivalent. (LLM, conf=0.88)
plainstates an association- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
- Partly supported
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“The first term on the right hand side of Eq. (26) is momentum dependent and comes from the three-point correlation functions of the fields, Eq. (21), computed by quantizing the perturbations inside the Hubble radius during inflation [35, 37].”
What the sources say
- Partly supportedcites [35] sourceExperimental — accuracy not yet measured
The Introduction (p. 2) describes scalar-field vacuum fluctuations on scales smaller than the Hubble radius, and §4 (p. 6) discusses the momentum dependence of the perturbation spectrum. Our copy does not connect either point to a three-point correlation function or show that such a function produces the cited first term. (LLM, conf=0.82)
- Could not verifycites [37] sourceExperimental — accuracy not yet measured
The Introduction describes vacuum fluctuations of light fields during inflation, and Section II discusses conserving second-order perturbations produced during inflation. Neither passage addresses the claimed momentum-dependent term, its origin in field three-point correlations, or their calculation by quantizing perturbations inside the Hubble radius; searches for those terms found no supporting passage in our copy. (LLM, conf=0.74)
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: All k_i are of the same order of magnitude so that they cross the Hubble radius approximately at the same time.
- Partly supported
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“This definition is not restricted to linear theory but holds also at second or higher order in the cosmological perturbations [32, 33, 18, 21].”
What the sources say
- Partly supportedcites [32] sourceExperimental — accuracy not yet measured
The rate-of-change discussion (p. 3) defines an expansion rate with respect to coordinate time for constant-time hypersurfaces, and the separate-universe discussion (p. 4) defines the integrated expansion N. But the paper frames its treatment in linear perturbation theory and says in the Conclusions (p. 8) that the separate-universe description applies as long as linear perturbation theory is valid. It does not establish that this definition holds at second or higher order. (LLM, conf=0.86)
- Not checked yetcites [33] Starobinsky A A, 1985, Pis. Zh. Eksp. Teor. Fiz.
- Partly supportedcites [18] sourceExperimental — accuracy not yet measured
Section II (p. 4) defines a local scale factor from the spatial-metric determinant, and Section III (p. 6) uses that determinant to construct a nonlinear curvature perturbation. This supports a nonlinear volume-expansion interpretation in the paper’s long-wavelength approximation, but not an unrestricted claim about perturbations at all scales. The paper also calls its symbol N the lapse function, not the volume expansion rate (Section II, p. 2). (LLM, conf=0.83)
- Supportedcites [21] source
On p. 1, the paper defines N as the amount of expansion using a locally defined scale factor tied to spatial volume. On p. 2, it says the underlying expression is non-perturbative and that its second-order expansion is a convenience, supporting the claim that the definition is not limited to linear theory. The paper makes this point in the super-horizon regime. (LLM, conf=0.90)
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
- Partly supported
Every source the paper cites for this claim was checked and supports it.
In the paper
“For instance, it is known that the size of the bispectrum during single-field, slow-roll inflation is related to the spectral tilt of the power spectrum and is thus constrained to be small [5].”
What the sources say
- Supportedcites [5] Maldacena J, 2003, J. High Energy Phys. source
The Introduction and summary of results says non-Gaussian corrections in single-field inflation are expected to be small. Its discussion of equation (1.2) relates the scalar three-point function to the power-spectrum tilt in the squeezed limit and says its size does not change much for other momentum configurations. The paper therefore supports the claim's broad wording, though the direct tilt relation is derived for the squeezed limit. (LLM, conf=0.90)
boostedstates an association- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may state two separate claims as one.
- Supported
The cited sources that could be checked couldn’t confirm or dispute this claim.
In the paper
“Rigopoulos et al. [22] have used numerical simulations of the stochastic dynamics on large scales and found significant non-Gaussianity even in simple two-field models.”
What the sources say
- Could not verifycites [22] sourceExperimental — accuracy not yet measured
The discussion on p. 4 says only that non-Gaussianity can evolve on large scales when more than one field is present. The references on p. 4 name Rigopoulos and Shellard, but our copy does not say they ran numerical simulations of stochastic dynamics or found significant non-Gaussianity in two-field models (searched: numerical, stochastic, two-field). (LLM, conf=0.76)
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
- Could not verify
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“On the other hand, inflationary models with higher derivative operators, such as ghost inflation or inflation based on the Dirac-Born-Infeld action, can produce higher non-Gaussianity [6, 7, 8, 9], possibly detectable.”
What the sources say
- Supportedcites [6] Arkani-Hamed N, 2004, J. Cosmol. Astropart. Phys. source
The paper supports the ghost-inflation example: Section 3 attributes its enhanced non-Gaussianity to higher-dimension derivative interactions, and the introductory JCAP passage says the predicted level is near then-current WMAP constraints. This citation need not establish the separate Dirac–Born–Infeld example in the multiply cited sentence. (LLM, conf=0.91)
- Supportedcites [7] source
The Introduction and Summary (p. 3) explains that expanding the DBI action produces a large contribution to non-Gaussianity and says ghost inflation has a similar magnitude. The Conclusions (p. 25) describe the model’s non-Gaussian signal as observable, supporting the cited sentence’s qualified claim. (LLM, conf=0.93)
- Supportedcites [8] Seery D, 2005, J. Cosmol. Astropart. Phys. source
The introduction identifies models with higher-derivative operators and cites work on ghost inflation and DBI inflation as examples. The Conclusions say relatively large non-Gaussianity could arise when the paper’s slow-roll conditions do not apply, and discuss the possibility of an appreciable CMB signal; they also caution that non-Gaussianity remains small in the slow-roll regime studied. This supports the citing sentence’s qualified claim that such models can produce a possibly detectable signal. (LLM, conf=0.86)
- Partly supportedcites [9] Creminelli P, 2003, J. Cosmol. Astropart. Phys. sourceExperimental — accuracy not yet measured
The Abstract says higher-dimension operators, including a higher-derivative interaction, can strongly enhance non-Gaussianity. The Conclusions say the predicted effect is near the threshold of detectability. Our copy does not identify ghost inflation or Dirac–Born–Infeld inflation as examples, so those specifics are not supported by this source. (LLM, conf=0.86)
hedgedstates a possible cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Supported
The cited sources that could be checked couldn’t confirm or dispute this claim.
In the paper
“Note added: After completing this work we have learnt [50] that our conclusion that f NL is small for the specific double quadratic inflation model investigated in Sec. 5 is in qualitative agreement with an improved numerical calculation by the authors of [22].”
What the sources say
- Could not verifycites [50] sourceExperimental — accuracy not yet measured
The Introduction (p. 2) and Double Inflation section (p. 3) describe a two-field inflation model, but the copy does not report an f_NL calculation or a comparison with an improved numerical calculation. Searches for f_NL and non-Gaussianity found no passage addressing that claimed agreement. (LLM, conf=0.76)
- Could not verifycites [22] sourceExperimental — accuracy not yet measured
The Conclusion (p. 4) discusses the evolution of non-Gaussianity during inflation, but gives no result for f_NL in a double quadratic model. Searches for the model, Sec. 5, and the improved numerical calculation found no passage addressing the claimed agreement. (LLM, conf=0.76)
plainstates an association- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- The authors state this as an assumption: The potential is separable into the sum of two potentials, each of which is dependent on only one of the two fields.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
- Could not verify
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“However, we have explicitly calculated in this model the non-Gaussianity due to the three-point function for the field perturbations at Hubble exit, using the result of Seery and Lidsey [8], and shown that it is small, as previously argued by Lyth and Zaballa [37].”
What the sources say
- Supportedcites [8] Seery D, 2005, J. Cosmol. Astropart. Phys. source
Split into 2 atoms — 2 confirmed, 0 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.
- Partly supportedcites [37] sourceExperimental — accuracy not yet measured
Split into 2 atoms — 0 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 1 unverifiable. Expand the claim to see per-atom verdicts.
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
- Supported
The cited sources that could be checked couldn’t confirm or dispute this claim.
In the paper
“The formalism used by Rigopoulos et al. differs from the δN -formalism in two aspects: First, it takes into account the sub-Hubble evolution of the field perturbations via stochastic terms. Second, it integrates explicitly the coupled evolution of the adiabatic and entropy super-Hubble perturbations.”
What the sources say
- Could not verifycites [22] sourceExperimental — accuracy not yet measured
The paper identifies Rigopoulos and Shellard in its references (p. 4) and notes a related long-wavelength result (p. 2), but does not describe their formalism as using stochastic terms or explicitly integrating coupled adiabatic and entropy perturbations. Its discussion of evolution at all scales concerns the authors’ own formulation (p. 4). Searches for those distinctive features did not find support for the claimed comparison with δN. (LLM, conf=0.76)
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Could not verify
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Note that in the limit t c → t ∗ , using Eq. (59), one finds the spectral index for purely adiabatic perturbations,”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The quote only partly states this claim.
- The authors state this as an assumption: The potential of the fields is separable into the sum of two potentials each dependent on only one of the two fields.
- The authors state this as an assumption: The slow-roll conditions are satisfied for both fields during inflation.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Note that this can never be less than the power spectrum derived by considering only adiabatic perturbations restricted to the background trajectory (at fixed C ). In multi-field inflation there is an additional contribution to the power spectrum due to non-adiabatic perturbations at Hubble exit. Thus one has P ζ ≥ P ζ | C”
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: The potential of the fields is separable into the sum of two potentials each dependent on only one of the two fields.
- The authors state this as an assumption: The slow-roll conditions are satisfied for both fields during inflation.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Consequently, the power spectrum and the spectral index grow monotonically, following the growth of ζ .”
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In this case the dependence on the field values at t = t c in Eq. (57) disappears and we can simply rewrite Eqs. (58), (61), (64) and (68) by using the potential (75) and Eq. (76) with φ c = χ c = 0, as”
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: The potential is separable into the sum of two potentials, each of which is dependent on only one of the two fields.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“However, after inflation, the fields have settled to their minima, which implies Z c = 0 and also A = 0.”
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: The potential is separable into the sum of two potentials, each of which is dependent on only one of the two fields.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“One can compute the value of f NL at the end of inflation, for ǫ e ≃ 1, in the limit where f ( k 1 , k 2 , k 3 ) = 0 ( k 1 ≪ k 2 ≈ k 3 ). One finds -(6 / 5) f (4) NL = 0 . 008 and -(6 / 5) f (3) NL = 0 . 008 which coincide with the analytical result of Eq. (83), -(6 / 5) f NL = 0 . 016 ≃ 1 / 60.”
plainstates an association- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“After few oscillations, the heavy field energy density is red-shifted and the light field dominates the universe while ζ becomes constant in time again.”
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
In the paper
“However, if two fields are present, the phase-space becomes two-dimensional and there is an infinite number of possible classical trajectories in field space. The values of the two fields at the end of inflation will in general depend on the choice of trajectory.”
What the sources say
- Not matchedcites [38] Zaballa I Rodriguez Y Lyth D H, 2006
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Not matched
In the paper
“In single field inflation the slow-roll solution forms a one-dimensional phase space. This means that once the inflationary attractor has been reached, there is a unique trajectory. In particular, the end of inflation takes place at a fixed value of the inflaton field which in turn corresponds to a fixed energy density.”
What the sources say
- Not matchedcites [38] Zaballa I Rodriguez Y Lyth D H, 2006
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In two-field models, however, the large-scale perturbations are not in general adiabatic and ζ evolves during inflation.”
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: The potential of the fields is separable into the sum of two potentials each dependent on only one of the two fields.
- The authors state this as an assumption: The slow-roll conditions are satisfied for both fields during inflation.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Note that in this case A = 0 at the end of inflation and the nonlinear parameter f (4) NL will be small.”
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: The potential is separable into the sum of two potentials, each of which is dependent on only one of the two fields.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In a hybrid-type limit, where the false vacuum dominates the self-interaction energy of the slowly-rolling fields, we can take the effective potential to be almost completely flat (consistent with the slow-roll approximation) so that [ δρ/ρ ] e is negligible and δN ( t c , t e ) ≪ δN ( t e , t ∗ ).”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In single field inflation large-scale perturbations are adiabatic and thus the curvature perturbation on uniform density hypersurfaces remains constant both during and after inflation, independent of the detailed physics occurring at the end of inflation.”
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“If one of the two fields - for instance φ - has stabilized before the end of inflation, so that the end of inflation is dominated by a single field χ , then Z c becomes constant, and the power spectrum, the scalar spectral index and the non-linear parameters after the end of inflation are simply given by Eqs. (58), (61), (64) and (68) with Z c = U c = const.”
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: The potential is separable into the sum of two potentials, each of which is dependent on only one of the two fields.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
In the paper
“This quantity is widely used, especially because it is conserved, on large scales, for adiabatic perturbations [29].”
What the sources say
- Not checked — no full text of the sourcecites [29] source
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The isocurvature perturbations in the massive field are suppressed at the end of inflation and hence the nonlinear parameter that we have calculated is indeed the primordial f NL constrained by observations, unless we have some curvaton-type mechanism which alters the large-scale curvature perturbation after inflation.”
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Thus, the contribution to f NL coming from the super-Hubble evolution should be equally taken into account by both formalisms and we are unable to explain the discrepancy between the results.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Including the dependence of φ c and χ c upon the field values at Hubble exit considerably complicates our analysis, but allows to follow perturbations during inflation.”
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“This method, which can be extended to any two-field model, confirms our analytic results.”
plainstates an association- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The quote only partly states this claim.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
- The authors state this as an assumption: The δN-formalism assumes that the fields are in slow-roll at Hubble exit.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“However, the possibility of producing a large non-Gaussianity is left open in models of two-field inflation where the mass of the isocurvature field orthogonal to the classical trajectory becomes larger than the Hubble rate and both the first slow-roll parameters of the two fields do not vanish at the end of inflation.”
hedgedstates a possible cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In particular, we have shown that a large f NL after inflation requires a large η ss - defined in Eq. (67) at the end of inflation, although a large η ss does not necessarily imply large non-Gaussianity.”
boostedstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: The potential is separable into the sum of two potentials, each of which is dependent on only one of the two fields.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“One can see that assuming slow-roll from t ∗ to t e is well justified.”
boostedSingle case- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The quote only partly states this claim.
- The authors state this as an assumption: Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
The authors state this as an assumption.
The model consists of minimally coupled scalar fields with canonical kinetic terms and potential W.
“For simplicity, we will consider a model of inflation driven by a set of minimally coupled scalar fields with canonical kinetic terms and potential W , described by the action”
The authors state this as an assumption.
Scalar field perturbations are uncorrelated stochastic variables at early times, with a scale-invariant spectrum of massless scalar fields in de-Sitter space.
“Let us now take the scalar field perturbations δϕ I as uncorrelated stochastic variables at early times, with scale invariant spectrum of massless scalar fields in de-Sitter space.”
The authors state this as an assumption.
Correlation functions higher than the four-point are neglected.
“where a star denotes the convolution and we have neglected correlation functions higher than the four-point (see [35, 34]).”
The authors state this as an assumption.
All k_i are of the same order of magnitude so that they cross the Hubble radius approximately at the same time.
“where k t = k 1 + k 2 + k 3 , and it is assumed that all the k i are of the same order of magnitude so that they cross the Hubble radius approximately at the same time.”
The authors state this as an assumption.
The connected part of the four-point correlation functions is negligible.
“To evaluate the second line of Eq. (20), as in [35] we assume that the connected part of the four-point correlation functions is negligible and we make use of Wick's theorem to reduce the four-point functions to products of two-point functions.”
The authors state this as an assumption.
The potential of the fields is separable into the sum of two potentials each dependent on only one of the two fields.
“We assume that the potential of the fields is separable into the sum of two potentials each of which is dependent on only one of the two fields,”
The authors state this as an assumption.
The slow-roll conditions are satisfied for both fields during inflation.
“Here it is assumed that the slow-roll conditions are satisfied for both fields during inflation.”
The authors state this as an assumption.
U' ≥ 0 and V' ≥ 0.
“Note that throughout this paper, for simplicity, we will assume U ′ ≥ 0 and V ′ ≥ 0 so that we may eliminate first derivatives of the potential in favor of the slow-roll parameters √ ǫ φ and √ ǫ χ .”
The authors state this as an assumption.
The potential is separable into the sum of two potentials, each of which is dependent on only one of the two fields.
“We have then specialized to the two-field case, and assumed that the potential is separable into the sum of two potentials, each of which is dependent on only one of the two fields.”
The authors state this as an assumption.
Slow-roll conditions are satisfied by all fields from Hubble exit until the end of inflation, and slow-roll is assumed all along the inflationary evolution from t_* to t_c.
“Furthermore, in deriving Eqs. (58), (61), (64), (68) and the background evolution relation (79), we have assumed slow-roll all along the inflationary evolution, from t ∗ to t c .”
The authors state this as an assumption.
The δN-formalism assumes that the fields are in slow-roll at Hubble exit.
“The δN -formalism assumes that the fields are in slow-roll at Hubble exit, Eq. (8) (see [48] for a development of the δN -formalism applicable to more general situations).”
Citations
Cites
Non-gaussian features of primordial fluctuations in single field inflationary models
Maldacena, J. (2003) · Journal of High Energy Physics · doi:10.1088/1126-6708/2003/05/013 · Cited by 2,906
Gauge-invariant cosmological perturbations
Bardeen, J. M. (1980) · Physical Review D · doi:10.1103/physrevd.22.1882 · Cited by 2,393
Cosmological Inflation and Large-Scale Structure
Liddle, A. R., & Lyth, D. H. (2000) · doi:10.1017/cbo9781139175180 · Cited by 2,317 · cited 2×
“(13) The first equality follows from taking k at Hubble crossing, k = aH ∝ H expN , while the second is a consequence of the definition of N , Eq.”
BackgroundSpontaneous creation of almost scale-free density perturbations in an inflationary universe
Bardeen, J. M., Steinhardt, P. J., & Turner, M. S. (1983) · Physical Review D · doi:10.1103/physrevd.28.679 · Cited by 2,073
Particle physics models of inflation and the cosmological density perturbation
Lyth, D. H., & Riotto, A. (1999) · Physics Reports · doi:10.1016/s0370-1573(98)00128-8 · Cited by 2,064
Linde, A. D. (1994) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.49.748 · Cited by 1,456
Non-Gaussianity from inflation: theory and observations
Bartolo, N., Komatsu, E., Matarrese, S., & Riotto, A. W. (2004) · Physics Reports · doi:10.1016/j.physrep.2004.08.022 · Cited by 1,144
False vacuum inflation with Einstein gravity
Copeland, E. J., Liddle, A. R., Lyth, D. H., Stewart, E. D., & Wands, D. (1994) · Physical Review D · doi:10.1103/physrevd.49.6410 · Cited by 1,077
Self-citationDBI in the sky: Non-Gaussianity from inflation with a speed limit
Alishahiha, M., Silverstein, E., & Tong, D. (2004) · Physical Review D · doi:10.1103/physrevd.70.123505 · Cited by 1,064
Sasaki, M., & Stewart, E. D. (1996) · Progress of Theoretical Physics · doi:10.1143/ptp.95.71 · Cited by 982
Research works printed but not linked: 5
- Starobinsky A A, 1985, Pis. Zh. Eksp. Teor. Fiz., 42, 124
- Starobinsky A A, 1985, JETP Lett., 42, 152
- Lee H C, 2005, J. Cosmol. Astropart. Phys., 2005, 004
- Press W H, 1992, Numerical Recipes in FORTRAN: The Art of Scientific Computing
- 10.1103/physrevd.63.0630xx · DOI
Cited by
Sorted by citations
Cosmology and fundamental physics with the Euclid satellite
The Euclid Theory Working Group, Amendola, L., Appleby, S. A., Avgoustidis, A., Bacon, D., Baker, T., Baldi, M., Bartolo, N., Blanchard, A., Bonvin, C., et al. (2018) · Living Reviews in Relativity · doi:10.1007/s41114-017-0010-3 · Cited by 1,096
Self-citationCosmology and Fundamental Physics with the Euclid Satellite
The Euclid Theory Working Group, Amendola, L., Appleby, S., Bacon, D., Baker, T., Baldi, M., Bartolo, N., Blanchard, A., Bonvin, C., Borgani, S., et al. (2013) · Living Reviews in Relativity · doi:10.12942/lrr-2013-6 · Cited by 899
“In this case, the overall expansion of the universe is affected by each of the field while it is in slow-roll; thus, the final non-Gaussianity is slow-roll suppressed, as in single field inflation (Rigopoulos et al. 2006; Alabidi and Lyth 2006; Vernizzi and Wands 2006).”
BackgroundSelf-citationAkrami, Y., Arroja, F. M. A., Ashdown, M., Aumont, J., Baccigalupi, C., Ballardini, M., Banday, A. J., Barreiro, R. B., Bartolo, N., Basak, S., et al. (2020) · Astronomy and Astrophysics · doi:10.1051/0004-6361/201935891 · Cited by 894
Primordial Non‐Gaussianities from Inflation Models
Chen, X. (2010) · Advances in Astronomy · doi:10.1155/2010/638979 · Cited by 701
“Gaussianities from other directions to the inflaton direction [127–134].”
BackgroundQuasi-single field inflation and non-Gaussianities
Chen, X., & Wang, Y. (2010) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2010/04/027 · Cited by 649
“This is in accordance with the general findings of previous studies that it is very difficult to generate large non-Gaussianities in terms of turning trajectories in multifield slow-roll models [22], essentially because imposing slow-roll conditions in all directions are very restrictive.”
Result
Metadata
- Authors
- Vernizzi, F., & Wands, D.
- Affiliations
- University of Helsinki (FI)
- University of Portsmouth (GB)
- ORCID
- Vernizzi, Filippo
- Venue
- Journal of Cosmology and Astroparticle Physics
- Publisher
- IOP Publishing
- Published
- 2006-05-26
- Volume
- 2006
- Issue
- 05
- Pages
- 019-019
- ISSN
- 1475-7508 (ISSN-L)
- 1475-7516
- OpenAlex
- W2079415417
- Semantic Scholar
- a811ff0416098de3bd4c280dd3a692bdb4b7c4b0
- Cited by
- 274
- References
- 44
- Citations by year
- 2026: 1 · 2025: 6 · 2024: 4 · 2023: 5 · 2022: 5 · 2021: 3 · 2020: 5 · 2019: 4 · 2018: 11 · 2017: 10 · 2016: 14 · 2015: 17 · 2014: 20 · 2013: 19 · 2012: 30
- FWCI
- 13.24
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Cosmology and Astroparticle Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Galaxies: Formation, Evolution, Phenomena
- Keywords
- two-field inflation, non-Gaussianity, bispectrum, curvature perturbations, non-adiabatic perturbations, delta N formalism, slow-roll approximation, double inflation, massive fields, separable potentials, primordial perturbations
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-23, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-23 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Cited sources are checked with a language model’s help (gpt-6-sol).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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