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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Written from the paper’s full text.
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.
Model-written summary. Check it against the paper before relying on it.
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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)
plaincorrelational- 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.
- 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)
plaincorrelational- 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.
- 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.
boosteddirect- 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.
- 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.
- 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.
- 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.
- 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: 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.
- 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.
- 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)
plaindirect- 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.
- Supported
The cited sources support only part of this claim — read each source’s verdict below.
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.
- 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.
- 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.
- 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.
- 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
- 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.
plaindirect- 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
plaindirect- 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)
plaincorrelational- 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)
plaindirect- 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)
boostedcorrelational- 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)
plaindirect- 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)
hedgedconditional- 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)
plaincorrelational- 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”
plaindirect- 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 .”
plaindirect- 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”
plaindirect- 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.”
plaindirect- 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.”
plaincorrelational- 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.”
plaindirect- 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.
plaindirect- 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.
plaindirect- 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.”
plaindirect- 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.”
plaindirect- 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.”
plaindirect- 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.”
plaindirect- 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.”
plaindirect- 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.”
plaindirect- 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.”
plaincorrelational- 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.”
hedgedconditional- 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.”
boosteddirect- 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
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Gauge-invariant cosmological perturbations
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Cosmological Inflation and Large-Scale Structure
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“(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
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Particle physics models of inflation and the cosmological density perturbation
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Non-Gaussianity from inflation: theory and observations
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Self-citationDBI in the sky: Non-Gaussianity from inflation with a speed limit
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Cited by
Sorted by citations
Items 201–273 of 273
Magnetogenesis and the primordial non-gaussianityPreprint
Seery, D. (2009) · Cited by 16
Magnetogenesis and the primordial non-gaussianity
Seery, D. (2009) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2009/08/018 · Cited by 15
“In this paper, I compute corrections to the spectrum and bispectrum generated by a varying electromagnetic coupling during inflation, assuming that the variation in this coupling is mediated by interaction with a collection of light scalar fields.”
MethodInfluence of reheating on the trispectrum and its scale dependence
Leung, G., Tarrant, E. R. M., Byrnes, C. T., et al. (2013) · Sussex Research Online (University of Sussex) · Cited by 15
Non-Gaussianity from false vacuum inflation: old curvaton scenario
Gong, J.-O., Lin, C., & Wang, Y. (2010) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2010/03/004 · Cited by 17
Primordial perturbations in multi-scalar inflation
Abedi, H., & Abbassi, A. M. (2017) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2017/07/049 · Cited by 14
Measuring the energy scale of inflation with large scale structures
Bellomo, N., Bartolo, N., Jimenez, R., Matarrese, S., & Verde, L. (2018) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2018/11/043 · Cited by 14
Many-field inflation: universality or prior dependence?
Christodoulidis, P., Roest, D., & Rosati, R. (2020) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2020/04/021 · Cited by 14
Quadra-spectrum and quint-spectrum from inflation and curvaton models
Lin, C., & Wang, Y. (2010) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2010/07/011 · Cited by 14
“Large bispectrum can be obtained from non-standard kinetic terms [2], non-local inflation [3], features in the Lagrangian [4], curvatons [5], old curvatons [6], multiple inflatons [7], quasisingle field inflation [8], multi-brid inflation [9], bifurcating trajectories [10], thermal components [11] and so on.”
BackgroundNonlinear superhorizon perturbations of non-canonical scalar field
Takamizu, Y.-I., & Shinji Mukohyama, A. (2009) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2009/01/013 · Cited by 14
“Another example is multi-field inflation models, where generation of isocurvature perturbations is generally expected because of the existence of more than one fields in the inflaton sector [17, 18, 19, 20].”
BackgroundOn Non-Gaussianities in Two-Field Poly-Instanton InflationPreprint
Gao, X. Q., & Shukla, P. (2016) · Cited by 14
Cosmology from the kinetic polarized Sunyaev Zel'dovich effect
Hotinli, S. C., Holder, G. P., Johnson, M. C., et al. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/10/026 · Cited by 13
Non-Gaussianities in multifield DBI inflation with a waterfall phase transition
Kidani, T., Koyama, K., & Mizuno, S. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.86.083503 · Cited by 13
α -attractor-type double inflation
Maeda, K.-I., Mizuno, S., & Tozuka, R. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.98.123530 · Cited by 13
Influence of reheating on the trispectrum and its scale dependence
Leung, G., Tarrant, E. R. M., Byrnes, C. T., et al. (2013) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2013/08/006 · Cited by 13
Exploring two-field inflation in the Wess-Zumino model
Ellis, J. R., Mavromatos, N. E., & Mulryne, D. J. (2014) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2014/05/012 · Cited by 12
“Analytical calculations of ns, r and fNL are only possible for models in which slow-roll is an extremely good approximation for the entire observable inflationary phase and moreover for which the potential is of product or sum-separable form [7, 8], which is rarely the case in realistic examples (see e.”
BackgroundModulation of the waterfall by a gauge field
Lyth, D. H., & Karčiauskas, M. (2013) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2013/01/031 · Cited by 14
“Such modulation was first considered in [2] using a scalar field (and further explored in [3, 4, 5, 6]).”
BackgroundMixed non-Gaussianity in multiple-DBI inflation
Emery, J., Gianmassimo Tasinato, C., & Wands, D. (2013) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2013/05/021 · Cited by 12
“(9)As opposed to a sum separable potential V (φ,χ) = V (φ) + V (χ), as was used in the original application of this technique [21].”
MethodSelf-citationLocal scale-dependent non-gaussian curvature perturbations at cubic order
Bramante, J., & Kumar, J. (2011) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2011/09/036 · Cited by 12
Non-Gaussianities in a two-field generalization of natural inflation
Simon Riquelme, M. (2018) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2018/04/027 · Cited by 15
Ambiguity in running spectral index with an extra light field during inflation
Kohri, K., & Matsuda, T. (2015) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2015/02/019 · Cited by 12
“[25–27].”
BackgroundWhat Planck does not tell us about inflation
Elliston, J., Mulryne, D. J., & Tavakol, R. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.88.063533 · Cited by 11
Observational constraints on two-field warm inflation
Wang, Y., Zhu, J.-Y., & Zhang, X.-M. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.99.103529 · Cited by 11
Large tensor spectrum of BICEP2 in the natural supersymmetric hybrid model
Choi, K.-Y., & Kyae, B. (2014) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.90.023536 · Cited by 9
Coupling structure of multi-field primordial perturbations
Gao, X. (2013) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2013/10/039 · Cited by 10
Cosmological perturbations of a quartet of scalar fields with a spatially constant gradient
Koh, S., Kouwn, S., Kwon, O.-K., et al. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.88.043523 · Cited by 10
Non-Gaussianity in two-field inflation beyond the slow-roll approximation
Jung, G., & Tent, B. V. (2017) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2017/05/019 · Cited by 10
“[36]), which is the only contribution on super-horizon scales.”
BackgroundInfluentialBernardis, F. D., Serra, P., Cooray, A. R., et al. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.82.083511 · Cited by 10
Ambiguity in running spectral index with an extra light field during inflation
Kohri, K., & Matsuda, T. (2015) · Institutional Repositories DataBase (IRDB) · Cited by 10
Non-Gaussian Signatures from the Postinflationary Early Universe
Silvestri, A., & Trodden, M. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.251301 · Cited by 10
Supergravity and two-field inflation effects in right-handed sneutrino-modified D-term inflation
Lin, C.-M., & McDonald, J. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.77.063529 · Cited by 11
Natural hybrid inflation model with large non-Gaussianity
Choi, K.-Y., & Kyae, B. (2011) · Physics Letters B · doi:10.1016/j.physletb.2011.11.045 · Cited by 10
Momentum dependence of the bispectrum in two-field inflation
Tzavara, E., & Tent, B. V. (2013) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2013/06/001 · Cited by 9
“[19, 20, 31]) show that there is always a momentum dependence inherited from the horizon-crossing era, which can in principle result in a tilt of fNL.”
BackgroundNon-minimally assisted chaotic inflation
Hyun, S. C., Kim, J., Park, S. C., et al. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/05/045 · Cited by 9
Cosmological perturbations in inflation with multiple sound speeds
Pi, S., & Wang, D. (2012) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2012.04.017 · Cited by 9
Two-field inflation with non-minimal coupling
Kim, J., Kim, Y., & Park, S. C. (2014) · Classical and Quantum Gravity · doi:10.1088/0264-9381/31/13/135004 · Cited by 9
“The action in the Einstein frame, equation (7), is reduced to a well known form [16, 17]:”
BackgroundInfluentialLarge scale power suppression in a multifield landscape
Blanco-Pillado, J. J., Dias, M., Frazer, J., et al. (2015) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2015/08/035 · Cited by 9
“Specifically, the vector ∇N in these models can be written as [75]”
BackgroundPrimordial gravitational wave of BICEP2 from dynamical double hybrid inflation
Choi, K.-Y., & Kyae, B. (2014) · Physics Letters B · doi:10.1016/j.physletb.2014.06.053 · Cited by 12
Cosmological perturbations from a spectator field during inflation
Wang, L., & Mazumdar, A. (2013) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2013/05/012 · Cited by 8
Asymmetric reheating from a symmetric inflationary potential
Cline, J. M., & Roux, J.-S. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.105.043506 · Cited by 8
Multi-chaotic inflation with and without spectator field
Morishita, Y., Takahashi, T., & Yokoyama, S. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/07/042 · Cited by 8
“3When the curvaton has a super-Planckian field value, the second inflation can occur after the inflationary phase driven by the inflaton [39, 46, 64, 65].”
BackgroundGenerically large nongaussianity in small multifield inflation
Bramante, J. (2015) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2015/07/006 · Cited by 8
“For sumseparable scalar potentials in particular it is useful to define the following set of parameters [36],”
BackgroundCovariant second-order perturbations in generalized two-field inflation
Tzavara, E., Mizuno, S., & Tent, B. V. (2014) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2014/07/027 · Cited by 7
“(For related works on non-Gaussianity in multiple-field inflation models with canonical kinetic terms, see [55–80].”
BackgroundTwo-field warm inflation and its scalar perturbations on large scales
Wang, Y., Zhu, J.-Y., & Zhang, X.-M. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.97.063510 · Cited by 7
“First we consider a N -fields model with Lagrangian density [6]: L = −(1) 2 ΣI g ∇μφI∇νφI − V (φ), (2.”
Constraints on primordial non-Gaussianity from Planck PR4 data
Jung, G., Citran, M., Tent, B. V., Dumilly, L., & Aghanim, N. (2025) · Astronomy and Astrophysics · doi:10.1051/0004-6361/202555283 · Cited by 6
“…f NL parameters) and type of non-Gaussianity, once detected, will allow us to distinguish between inflation models with multiple fields (see e.g. Vernizzi & Wands 2006; Rigopoulos et al. 2007; Byrnes & Choi 2010; Jung & van Tent 2017; de Put-ter et al. 2017; Wang et al. 2023), models with…”
Gravity- and non-gravity-mediated couplings in multiple-field inflation
Bernardeau, F. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/12/124004 · Cited by 6
“The form presented here for the function M is the one given in [21] rewritten from the expression given in [27].”
BackgroundIsocurvature modes: joint analysis of the CMB power spectrum and bispectrum
Montandon, T., Patanchon, G., & Tent, B. V. (2021) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2021/01/004 · Cited by 6
“[7–14] or the reviews [15, 16], that might be detectable with future”
BackgroundNon-Gaussianities in generalized non-local R2-like inflation
Koshelev, A. S., Kumar, K. S., & Starobinsky, A. A. (2023) · Journal of High Energy Physics · doi:10.1007/jhep07(2023)094 · Cited by 6
“Due to the presence of isocurvature modes, curvature perturbation, if defined as being tangent to the background trajectory of inflaton fields in the field space, is generically not time-independent on super-Hubble scales6 that leads to violation of the Maldacena consistency relation due to the classical evolution of…”
BackgroundNon-Gaussianities in DBI inflation with angular motion
Kidani, T., & Koyama, K. (2014) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.90.023515 · Cited by 5
Colas, T. (2023) · theses.fr (ABES) · doi:10.70675/c036277dz5795z4dcaz8673z5e60a8568a01 · Cited by 5
Non-Gaussianity in a general kind noncanonical warm inflation
Zhang, X.-M., Li, K., Ma, H., et al. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.100.123521 · Cited by 4
Large number limit of multifield inflation
Guo, Z. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.96.123521 · Cited by 4
New source for light dark matter isocurvature in low scale inflation
Caputo, A., Geller, M., & Rossi, G. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.110.055027 · Cited by 3
Two-Field Quintessential Higgs Model and the Swampland
Es-haghi, M., Zarei, M., & Sheykhi, A. (2024) · Iranian Journal of Science · doi:10.1007/s40995-025-01777-2 · Cited by 2
“To this end, we use a generalized action in the Jordan frame for two scalar fields non-minimally coupled to gravity as follows (Starobinsky et al. 2001; Vernizzi and Wands 2006; Kaiser 2010; Kim et al. 2014) where R is the Ricci scalar and f ð h ; / Þ is a non-minimal coupling term.”
Exactly solvable stochastic spectator
Honda, M., Jinno, R., & Tokeshi, K. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/12/044 · Cited by 3
Primordial non-Gaussianity estimator: The inhomogeneous noise effect
Yu, B., & Lu, T. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.78.063008 · Cited by 3
Primordial non-Gaussianity in noncanonical warm inflation: Three- and four-point correlations
Zhang, X.-M., Ma, H., Chu, P.-C., et al. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.96.043516 · Cited by 3
Primordial correlators from multi-point propagators
Costantini, A., Iacconi, L., & Mulryne, D. J. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/09/077 · Cited by 2
“[56] where non-Gaussianities are studied.”
Large-Scale Structure Formation via Quantum Fluctuations and Gravitational Instability
Porcelli, F., & Scibona, G. (2014) · International Journal of Geosciences · doi:10.4236/ijg.2014.56058 · Cited by 2
“Examples of this class include: single field models with non-Bunch-Davies (NBD) vacuum [61] [65], models with general higher-derivative interactions [68], excited canonical single-field inflation model with modified NBD initial state whose enhanced bispectrum has two leading order shapes [115]: the single-field NBD1 s…”
A proposal for constraining initial vacuum by cosmic microwave background
Chandra, D., & Pal, S. (2017) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aa95f7 · Cited by 2
Isocurvature perturbations during two-field inflation and reheating
Abedi, H., & Abbassi, A. M. (2019) · General Relativity and Gravitation · doi:10.1007/s10714-019-2515-4 · Cited by 2
Felegary, F., Mansoori, S. A. H., Serish, T. F., et al. (2025) · Physics of the Dark Universe · doi:10.1016/j.dark.2025.101924 · Cited by 1
Primordial non-Gaussianity in noncanonical warm inflation with nonminimal derivative coupling
Zhang, X.-M., Zhao, R.-Q., Feng, Y., et al. (2025) · The European Physical Journal C · doi:10.1140/epjc/s10052-025-15059-z · Cited by 1
Remarks on non-Gaussian fluctuations of the inflaton and constancy of ζ outside the horizon
Mahajan, N., & Rangarajan, R. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.83.043510 · Cited by 1
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Dynamics and observational signatures from multi-field inflation
Christodoulidis, P. (2021) · doi:10.33612/diss.173751374
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Inflation in a scalar-vector gravity theory
Gonzalez-Espinoza, M., & Herrera, R. (2024) · Annals of Physics · doi:10.1016/j.aop.2024.169876
An analytic study of hybrid inflationary model with quantum gravity corrections
Moiz, M. A., & Ansari, R. U. H. (2025) · Journal of Physics Communications · doi:10.1088/2399-6528/adb09e
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Second-order cosmological perturbations in two-field inflation and predictions for non-Gaussianity
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“While this additional term is always small for the models we consider and hence numerically insignificant, from an analytical point of view it means we could now compare our results directly to the f (4) NL calculated within the δN formalism [81, 106, 73].”
BackgroundResultInfluentialSarkar, C., Choudhuri, A., & Ghosh, B. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.7239493
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
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