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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“(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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Self-citationDBI in the sky: Non-Gaussianity from inflation with a speed limit
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Cited by
Sorted by citations
Items 101–200 of 273
Bartolo, N., Matarrese, S., & Riotto, A. W. (2012) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2012/02/017 · Cited by 57
Inflationary perturbation theory is geometrical optics in phase space
Seery, D., Mulryne, D. J., Frazer, J., et al. (2012) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2012/09/010 · Cited by 56
Initial clustering and the primordial black hole merger rate
(2309266), S. Y., & (4461769), C. B. (2020) · Figshare · Cited by 54
Non-Gaussianity in Axion N -flation Models
Kim, S. A., Liddle, A. R., & Seery, D. (2010) · Physical Review Letters · doi:10.1103/physrevlett.105.181302 · Cited by 53
Moment transport equations for the primordial curvature perturbation
Mulryne, D. J., Seery, D., & Wesley, D. (2011) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2011/04/030 · Cited by 52
“Our evolution agrees with this discussion, and also the explicit calculations of Vernizzi & Wands [27] and the moment transport method using the spatially flat slicing [1].”
BackgroundMethodInfluentialDimopoulos, K., Kohri, K., Lyth, D. H., et al. (2012) · Lancaster EPrints (Lancaster University) · Cited by 52
Anisotropic Trispectrum of Curvature Perturbations Induced by Primordial Non-Abelian Vector FieldsPreprint
Bartolo, N., Dimastrogiovanni, E., & Riotto, A. W. (2012) · Cited by 51
Inflationary perturbation theory is geometrical optics in phase space
Seery, D., Mulryne, D. J., Frazer, J., et al. (2012) · Figshare · Cited by 50
Numerical evaluation of the bispectrum in multiple field inflation
Dias, M., Frazer, J., Mulryne, D. J., & Seery, D. (2016) · Sussex Research Online (University of Sussex) · Cited by 50
Moment transport equations for the primordial curvature perturbation
Mulryne, D. J., Seery, D., & Wesley, D. (2011) · Figshare · Cited by 49
Large primordial trispectra in general single field inflation
Chen, X., Hu, B., Huang, M.-X., et al. (2009) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2009/08/008 · Cited by 49
Non-Gaussianity for a two component hybrid model of inflation
Alabidi, L. (2006) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2006/10/015 · Cited by 49
“Curvature perturbation 4 4. fNL 5”
On reaching the adiabatic limit in multi-field inflation
Renaux‐Petel, S., & Turzyński, K. (2015) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2015/06/010 · Cited by 48
MULTIMODECODE: an efficient numerical solver for multifield inflation
Price, L. C., Frazer, J., Xu, J., Peiris, H. V., & Easther, R. (2015) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2015/03/005 · Cited by 51
“, it will ignore the contribution to N,I and N,IJ from the end-of-inflation surface via the horizon crossing approximation (HCA) [63, 83].”
BackgroundInfluentialThe Hunt for Primordial Interactions in the Large-Scale Structures of the Universe
Biagetti, M. (2019) · Galaxies · doi:10.3390/galaxies7030071 · Cited by 59
“Nevertheless, there are several mechanisms with which isocurvature perturbations can be converted to curvature ones after inflation and evade CMB constraints [102–109].”
BackgroundOn non-Gaussianities in multi-field inflation (N fields): bi- and tri-spectra beyond slow-roll
Battefeld, D., & Battefeld, T. J. (2009) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2009/11/010 · Cited by 47
Multi-field inflation with random potentials: field dimension, feature scale and non-Gaussianity
Frazer, J., & Liddle, A. R. (2012) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2012/02/039 · Cited by 47
“[15, 16]), the Transport approach has the benefit of being computationally more efficient, as well providing a new means of understanding contributions to fNL by having explicit source terms.”
BackgroundAnisotropic trispectrum of curvature perturbations induced by primordial non-Abelian vector fields
Bartolo, N., Dimastrogiovanni, E., Matarrese, S., et al. (2009) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2009/11/028 · Cited by 47
The persistence of large scale structures. Part I. Primordial non-Gaussianity
Biagetti, M., Cole, A., & Shiu, G. (2021) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2021/04/061 · Cited by 45
“This type of primordial non-Gaussianity is generically realized in multi-field models of inflation [68–75], and the corresponding bispectrum peaks in the squeezed limit, where single-field models necessarily produce very small non-Gaussianity as implied by consistency relations [30, 76].”
BackgroundNonlinear perturbations of cosmological scalar fields with non-standard kinetic terms
Renaux‐Petel, S., & Gianmassimo Tasinato, C. (2009) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2009/01/012 · Cited by 46
Reheating, multifield inflation and the fate of the primordial observables
Leung, G., Tarrant, E. R. M., Byrnes, C. T., & Copeland, E. J. (2012) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2012/09/008 · Cited by 45
Non‐Gaussianity from Particle Production during Inflation
Barnaby, N. (2010) · Advances in Astronomy · doi:10.1155/2010/156180 · Cited by 48
Non-Gaussianity from the hybrid potential
Mulryne, D. J., Orani, S., & Rajantie, A. K. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.84.123527 · Cited by 47
Cosmic shear bispectrum from second-order perturbations in general relativity
Bernardeau, F., Bonvin, C., de Rijt, N. V., & Vernizzi, F. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.86.023001 · Cited by 44
“The most common type of non-Gaussianity considered in the literature is the local type, which is typically generated by multi-field models [54, 55, 56, 57].”
BackgroundSelf-citationComprehensive analysis of the simplest curvaton model
Byrnes, C. T., Cortês, M., & Liddle, A. R. (2014) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.90.023523 · Cited by 44
On the non-Gaussianity from recombination
Bartolo, N., & Riotto, A. W. (2009) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2009/03/017 · Cited by 44
Multi-field inflation with large scalar fluctuations: non-Gaussianity and perturbativity
Iacconi, L., & Mulryne, D. J. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/09/033 · Cited by 43
“The amplitude of scalar non-Gaussianities (more precisely the shape-independent part of f NL ) can be calculated within the δN formalism as (see e.g. [114, 115]) where I = { ϕ, χ, ϕ ′ , χ ′ } .”
BackgroundStrongly scale-dependent non-Gaussianity
Riotto, A. W., & Sloth, M. S. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.83.041301 · Cited by 43
Non-Gaussianities in multifield inflation: Superhorizon evolution, adiabaticity, and the fate of fNL
Meyers, J., & Sivanandam, N. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.83.103517 · Cited by 42
Transport equations for the inflationary spectral index
Dias, M., & Seery, D. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.85.043519 · Cited by 40
Biasing and the search for primordial non-Gaussianity beyond the local type
Gleyzes, J., de Putter, R., Green, D., & Doré, O. (2017) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2017/04/002 · Cited by 40
Rodríguez, Y., & Valenzuela-Toledo, C. A. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.81.023531 · Cited by 66
Perturbative reheating after multiple-field inflation: The impact on primordial observables
Meyers, J., & Tarrant, E. R. M. (2014) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.89.063535 · Cited by 39
Non-Gaussianity in single field models without slow-roll conditions
Noller, J., & Magueijo, J. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.83.103511 · Cited by 39
Constraining the initial conditions of the Universe using large scale structure
Agarwal, N., Ho, S., & Shandera, S. E. (2014) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2014/02/038 · Cited by 38
Squeezed bispectrum in the δ N formalism: local observer effect in field space
Tada, Y., & Vennin, V. (2017) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2017/02/021 · Cited by 37
Byrnes, C. T. (2009) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2009/01/011 · Cited by 37
Gravitational Wave Consistency Relations for Multifield Inflation
Price, L. C., Peiris, H. V., Frazer, J., et al. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.031301 · Cited by 36
Transport equations for the inflationary trispectrum
Anderson, G. J., Mulryne, D. J., & Seery, D. (2012) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2012/10/019 · Cited by 35
“However, its amplitude is small in the canonical models to which we restrict attention in this paper [40, 41].”
BackgroundMethodInfluentialDimopoulos, K., Kohri, K., Lyth, D. H., et al. (2012) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2012/03/022 · Cited by 35
“With such a value it will indeed be a good approximation to ignore the non-gaussianity of δσ [25].”
BackgroundManyfield inflation in random potentials
Bjorkmo, T., & Marsh, M. C. D. (2018) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2018/02/037 · Cited by 35
“Reference [16] derived an analytic formula for fNL in multifield models of inflation with sumseparable potentials (thereby generalising the two-field result of [15]), and found that large non-Gaussianities are very rare in slow-roll models with Nf free fields.”
BackgroundMethodInfluentialPath integral for inflationary perturbations
Prokopec, T., & Rigopoulos, G. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.82.023529 · Cited by 35
“[15–31].”
Modulated perturbations from instant preheating after new ekpyrosis
Battefeld, T. J. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.77.063503 · Cited by 35
“To compute these effects, we use the δN -formalism, first proposed by Starobinsky in [56] and extended by Sasaki and Stewart [57] and others [58, 59, 60, 61, 62, 63, 64, 65, 66].”
BackgroundMethodNon-gaussianity for a Two Component Hybrid Model of Inflation
Alabidi, L. (2006) · CERN Document Server (European Organization for Nuclear Research) · Cited by 35
Simple Emergent Power Spectra from Complex Inflationary Physics
Dias, M., Frazer, J., & Marsh, M. C. D. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.141303 · Cited by 34
The δ N formula is the dynamical renormalization group
Dias, M., Ribeiro, R. H., & Seery, D. (2013) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2013/10/062 · Cited by 34
Seery, D., & Hidalgo, J. C. (2006) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2006/07/008 · Cited by 36
“) This result has since been extended to cover the non-Gaussianity produced during slow-roll inflation with an arbitrary number of fields [40, 41, 48, 49, 50, 51, 52, 53], preheating [54, 55, 56], models where the dominant non-Gaussianity is produced by a light scalar which is a spectator during inflation [57, 58, 39]…”
The δN formula is the dynamical renormalization group
Ribeiro, R. H. (2013) · Sussex Research Online (University of Sussex) · Cited by 32
Separable and non-separable multi-field inflation and large non-Gaussianity
Mazumdar, A., & Wang, L. (2012) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2012/09/005 · Cited by 30
“3 Second order perturbations In certain cases, such as in the case of separable potentials [12, 13], the integrals in Eq.”
BackgroundRelativistic effects and primordial non-Gaussianity in the galaxy bias
Bartolo, N., Matarrese, S., & Riotto, A. W. (2011) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2011/04/011 · Cited by 30
Non-linear curvature perturbation in multi-field inflation models with non-minimal coupling
White, J., Minamitsuji, M., & Sasaki, M. (2013) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2013/09/015 · Cited by 30
“See also [33–36] for considerations of analytically soluble applications of the δN formalism in multi-field inflation.”
BackgroundNon-Gaussianities of single field inflation with nonminimal coupling
Qiu, T., & Yang, K.-C. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.83.084022 · Cited by 33
Note on non-Gaussianities in two-field inflation
Wang, T. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.82.123515 · Cited by 30
δNformalism from superpotential and holography
Garriga, J., Urakawa, Y., & Vernizzi, F. (2016) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2016/02/036 · Cited by 30
“, the case where the background evolution can be described by separable equations [58, 59, 60].”
BackgroundMethodInfluentialSelf-citationde Putter, R., Gleyzes, J., & Doré, O. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.95.123507 · Cited by 29
“Taking the derivative of the power spectrum (8), one can express this quantity in terms of the slow-roll parameters at t [65,83],”
BackgroundMethodInfluentialSingular cosmological evolution using canonical and ghost scalar fields
Nojiri, S., Odintsov, S. D., Oikonomou, V. K., & Saridakis, E. N. (2015) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2015/9/044 · Cited by 29
The effects of a fast-turning trajectory in multiple-field inflation
Konieczka, M., Ribeiro, R. H., & Turzyński, K. (2014) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2014/07/030 · Cited by 29
“Indeed, denoting by vl and vh the perturbations corresponding to the smaller and larger mass eigenvalues, m2l and m 2 h, respectively, we obtain the following equations of motion v′′l + ( k2 + a2m2l − ϑ′2 − a′′ a ) vl − ϑ′′vh − 2ϑ′v′h = 0 (2.24) v′′h + ( k2 + a2m2h − ϑ′2 − a′′ a ) vh + ϑ ′′vl + 2ϑ ′v′l = 0 , (2.25) 4A…”
BackgroundInfluentialThe squeezed limit of the bispectrum in multi-field inflation
Kenton, Z., & Mulryne, D. J. (2015) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2015/10/018 · Cited by 28
“This is that the inflationary potentials are of separable form, either sum or product separable [78, 88, 89], or of the generalised sum-separable form of Ref [90].”
BackgroundδN formalism from superpotential and holography
Garriga, J., Urakawa, Y., & Vernizzi, F. (2016) · RECERCAT (Consorci de Serveis Universitaris de Catalunya) · Cited by 28
Self-citationBounce and cyclic cosmology in new gravitational scalar-tensor theories
Saridakis, E. N., Banerjee, S., & Myrzakulov, R. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.98.063513 · Cited by 29
General formula for the running of local fNL
Byrnes, C. T., & Gong, J.-O. (2012) · Physics Letters B · doi:10.1016/j.physletb.2012.11.052 · Cited by 26
Inflation in a two 3-form fields scenario
Kumar, K. S., Marto, J., Nunes, N. J., et al. (2014) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2014/06/064 · Cited by 26
“This kind of scenarios are known as ‘curvaton’ or ‘spectator’ field behavior [48, 49] and also found in double quadratic inflation [47].”
BackgroundLarge trispectrum in two-field slow-roll inflation
Elliston, J., Alabidi, L., Huston, I., et al. (2012) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2012/09/001 · Cited by 25
“Conversely, if the trajectory turns, the statistics will evolve [18, 24, 25].”
BackgroundInfluentialMultifield dynamics in Higgs-otic inflation
Bielleman, S., Ibáñez, L. E., Pedro, F. G., & Valenzuela, I. (2016) · Journal of High Energy Physics · doi:10.1007/jhep01(2016)128 · Cited by 25
“However, for 2-field models the non-linear fNL are of the order of the slow-roll parameters and hence they are surpressed in our model, see [59], [60].”
General analytic predictions of two-field inflation and perturbative reheating
Elliston, J., Orani, S., & Mulryne, D. J. (2014) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.89.103532 · Cited by 25
Bispectra from two-field inflation using the long-wavelength formalism
Tzavara, E., & Tent, B. V. (2011) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2011/06/026 · Cited by 25
“Vernizzi and Wands studied the double field sum potential [19], while the double product potential was studied in [62].”
BackgroundResultInfluentialReconstructing a model of quintessential inflation
Neupane, I. P. (2007) · Classical and Quantum Gravity · doi:10.1088/0264-9381/25/12/125013 · Cited by 30
Reconstructing a model of quintessential inflationPreprint
Neupane, I. P. (2008) · Cited by 25
Predictions in multifield models of inflation
Frazer, J. (2014) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2014/01/028 · Cited by 28
“[36, 41, 42] for derivations of the expressions.”
BackgroundNon-Gaussianity in axion N -flation models: Detailed predictions and mass spectra
Kim, S. A., Liddle, A. R., & Seery, D. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.85.023532 · Cited by 24
First-order formalism for twinlike models with several real scalar fields
Bazeia, D., Lobão, A. S., Losano, L., et al. (2014) · The European Physical Journal C · doi:10.1140/epjc/s10052-014-2755-0 · Cited by 24
Multi-field effects in a simple extension ofR2inflation
Mori, T., Kohri, K., & WHITE, J. W. (2017) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2017/10/044 · Cited by 24
N-flation: Observable predictions from the random matrix mass spectrum
Kim, S. A., & Liddle, A. R. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.76.063515 · Cited by 24
“Finite” non-Gaussianities and tensor–scalar ratio in large volume Swiss-cheese compactifications
Misra, A., & Shukla, P. (2008) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2008.10.022 · Cited by 24
“09 96 v4 [ he p- th ] 1 1 D ec 1e-mail: aalokfph@iitr.ernet.in 2email: pmathdph@iitr.ernet.in”
Byrnes, C. T. (2009) · PUB – Publications at Bielefeld University (Bielefeld University) · Cited by 24
Modest, H. I., Rath, C. W., Banday, A. J., et al. (2012) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/sts056 · Cited by 23
“…been shown that single field as well as two-/multi-field models (Linde & Mukhanov 1997; Bartolo, Matarrese & Riotto 2002; Bernardeau & Uzan 2002; Vernizzi & Wands 2006) generate a small amount of non-Gaussianity, below our current experimental limits though (Maldacena 2003; Acquaviva et al.…”
BackgroundSeven lessons from manyfield inflation in random potentials
Dias, M., Frazer, J., & Marsh, M. C. D. (2018) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2018/01/036 · Cited by 23
“References [46, 47] compute a very similar object:”
BackgroundThe hemispherical asymmetry from a scale-dependent inflationary bispectrum
Byrnes, C. T., Regan, D., Seery, D., et al. (2016) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2016/06/025 · Cited by 22
“5b) from 〈δφaδφbδφc〉 is known to be negligible unless the fields have nontrivial derivative interactions [54, 55], and we discard it in the following discussion.”
The effect of local non-Gaussianity on the matter bispectrum at small scales
Figueroa, D. G., Sefusatti, E., Riotto, A. W., et al. (2012) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2012/08/036 · Cited by 22
Self-citationThe everpresent η-problem: knowledge of all hidden sectors required
Hardeman, S., Oberreuter, J. M., Palma, G. A., Schalm, K., & van der Aalst, T. (2011) · Journal of High Energy Physics · doi:10.1007/jhep04(2011)009 · Cited by 31
Measuring the duration of inflation with the curvaton
Torrado, J., Byrnes, C. T., Hardwick, R. J., Vennin, V., & Wands, D. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.98.063525 · Cited by 22
Self-citationAdiabaticity and the fate of non-Gaussianities: The trispectrum and beyond
Meyers, J., & Sivanandam, N. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.84.063522 · Cited by 21
Inflation in a two 3-form fields scenario
Kumar, K. S., Marto, J., Nunes, N. J., et al. (2014) · Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT) · Cited by 21
The hemispherical asymmetry from a scale-dependent inflationary bispectrum
Byrnes, C. T., Regan, D., Seery, D., et al. (2016) · Sussex Research Online (University of Sussex) · Cited by 21
Ellis, J. R., Gonzalo, T. E., Harz, J., & Wei-chih Huang, A. (2015) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2015/03/039 · Cited by 19
“8) is actually a two-field inflation model, for which the influence of isocurvature modes could be significant [54, 55],4 unlike the case of single-field inflation.”
BackgroundLocal non-Gaussianity from rapidly varying sound speeds
Emery, J., Gianmassimo Tasinato, C., & Wands, D. (2012) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2012/08/005 · Cited by 20
“Again adopting the notation of [21], the k-independent parameter8 f (4) NL accounts for the super-horizon contribution and is given by 6 5 f (4) NL = ∑ IJ N,IN,JN,IJ ( ∑ K N 2 ,K) 2 .”
BackgroundMethodInfluentialSelf-citationSTOLAS: STOchastic LAttice Simulation of cosmic inflation
Mizuguchi, Y., Murata, T., & Tada, Y. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/12/050 · Cited by 19
“[85–87]).”
Full cosmic microwave background temperature bispectrum from single-field inflation
Huang, Z., & Vernizzi, F. (2014) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.89.021302 · Cited by 19
Self-citationDesigning and testing inflationary models with Bayesian networks
Price, L. C., Peiris, H. V., Frazer, J., & Easther, R. (2016) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2016/02/049 · Cited by 19
“The marginalized probability distribution for the tensor:scalar ratio r in the HCA can be obtained analytically by integrating eq.”
MethodInfluentialCosmological observables in multi-field inflation with a non-flat field space
Gao, X. Q., Li, T., & Shukla, P. (2014) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2014/10/008 · Cited by 19
Primordial curvature perturbation during and at the end of multi-field inflation
Choi, K.-Y., Kim, S. A., & Kyae, B. (2012) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2012.04.004 · Cited by 18
Scale dependence offNLin N-flation
Huang, Q.-G. (2010) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2010/12/017 · Cited by 18
“See some other relevant references in [9, 10, 11, 12, 13, 14, 15, 17, 16, 18].”
Non-Gaussianity in multiple three-form field inflation
Kumar, K. S., Mulryne, D. J., Nunes, N. J., et al. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.94.103504 · Cited by 18
Testing supersymmetric Higgs inflation with non-Gaussianity
Kawai, S., & Kim, J. (2015) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.91.045021 · Cited by 18
Seven lessons from manyfield inflation in random potentials
Dias, M., Frazer, J., & Marsh, M. C. D. (2018) · DESY (CERN, DESY, Fermilab, IHEP, and SLAC) · doi:10.17863/cam.24831 · Cited by 17
Primordial non-Gaussianity in noncanonical warm inflation
Zhang, X.-M., & Zhu, J.-Y. (2015) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.91.063510 · Cited by 16
On non-Gaussianities in two-field poly-instanton inflation
Gao, X., & Shukla, P. (2013) · Journal of High Energy Physics · doi:10.1007/jhep03(2013)061 · Cited by 16
Watanabe, Y. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.85.103505 · Cited by 16
Scale-dependent bias from multiple-field inflation
Dias, M., Ribeiro, R. H., & Seery, D. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.87.107301 · Cited by 16
Primordial non-Gaussianity in warm inflation using δNformalism
Zhang, X.-M., Ma, H.-Y., Chu, P.-C., et al. (2016) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2016/03/059 · Cited by 16
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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