arxiv: 2512.09079 · v2 · submitted 2025-12-09 · ✦ hep-ph · astro-ph.CO

Recognition: 2 theorem links

· Lean Theorem

Curvaton-assisted hilltop inflation

Wen-Yuan Ai , Stephen F. King , Xin Wang , Ye-Ling Zhou

Authors on Pith no claims yet

Pith reviewed 2026-05-16 23:40 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.CO

keywords curvatonhilltop inflationinitial conditionssub-Planckian fieldscurvature perturbationspower spectrumACT observations

0 comments

The pith

Coupling the inflaton to a curvaton relaxes the extreme initial tuning in hilltop inflation and revives the quartic model for sub-Planckian field values.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines hilltop inflation in light of recent ACT data, where the inflaton potential has a flat maximum that normally demands the field starts extremely close to the top. By adding a curvaton field that couples to the inflaton, the initial conditions become far less tuned because the curvaton can dominate the curvature perturbations after inflation. This coupling also reshapes the power spectrum of those perturbations, opening viable parameter space for the quartic hilltop potential even when the inflaton stays below the Planck scale. The resulting models produce predictions consistent with current observations of the spectral index and amplitude.

Core claim

The curvaton field not only significantly relaxes the initial-value tuning required for hilltop inflation, but also opens up parameter space through modifying the curvature perturbation power spectrum, reviving the quartic hilltop inflation model in the sub-Planckian regime. Viable parameter space is found that remains consistent with recent cosmological observations.

What carries the argument

Curvaton field coupled to the inflaton, which takes over production of curvature perturbations after the end of inflation and thereby alters their power spectrum.

If this is right

The inflaton can begin farther from the potential maximum without preventing enough e-folds of inflation.
The quartic hilltop potential, previously ruled out in single-field sub-Planckian setups, now yields observationally allowed spectra.
The model remains compatible with the latest ACT constraints on the scalar spectral index and tensor-to-scalar ratio.
The curvaton decay must occur after horizon exit but before it affects late-time cosmology, which restricts the allowed mass range.
Non-Gaussianity parameters stay within current bounds provided the curvaton energy density fraction at decay is chosen appropriately.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Similar curvaton assistance could relax initial-condition problems in other single-field models that suffer from flat-top tuning, such as certain Starobinsky variants.
Future measurements of local non-Gaussianity f_NL could directly constrain the curvaton energy fraction at decay and thereby test the coupling strength.
The approach suggests a general route for embedding sub-Planckian inflation into UV-complete theories where super-Planckian excursions are forbidden.
One could test whether the same coupling also suppresses isocurvature modes enough to satisfy Planck bounds on cold dark matter isocurvature.

Load-bearing premise

A suitable curvaton-inflaton coupling exists that lets the curvaton dominate curvature perturbations, adjust the spectrum as needed, and decay without introducing large non-Gaussianities or disrupting slow-roll.

What would settle it

A concrete mismatch between the predicted curvature power spectrum amplitude or spectral index and future high-precision measurements (such as from CMB-S4 or LiteBIRD) for all choices of coupling strength and curvaton mass would rule out the mechanism.

Figures

Figures reproduced from arXiv: 2512.09079 by Stephen F. King, Wen-Yuan Ai, Xin Wang, Ye-Ling Zhou.

**Figure 3.** Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5: Relations between the tensor-to-scalar ratio [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

read the original abstract

Following the recent Atacama Cosmology Telescope (ACT) results, we consider hilltop inflation where the inflaton is coupled to a curvaton, simultaneously addressing two main challenges faced by conventional hilltop inflation models: the initial-value problem; and their viability for sub-Planckian field values. In standard single-field hilltop inflation, the inflaton must start extremely close to the maximum of the potential, raising concerns about the naturalness of the initial conditions. We demonstrate that the curvaton field not only significantly relaxes the initial-value tuning required for hilltop inflation, but also opens up parameter space through modifying the curvature perturbation power spectrum, reviving the quartic hilltop inflation model in the sub-Planckian regime. We find viable parameter space consistent with the recent cosmological observations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Curvaton coupling revives sub-Planckian quartic hilltop inflation by relaxing initial conditions and altering the power spectrum, but the viability hinges on an unshown coupling window that must satisfy all constraints at once.

read the letter

The paper's main point is that adding a curvaton coupled to the inflaton lets hilltop models avoid the severe initial-value tuning and work with sub-Planckian field values for the quartic potential. The curvaton takes over the curvature perturbations after the inflaton rolls, which modifies the spectrum enough to match recent ACT data while keeping the inflaton near the potential maximum longer. This dual fix is the concrete step forward. The authors identify the two standard problems with single-field hilltop setups and show how the extra field opens parameter space that was previously ruled out. That framing is clear and directly useful for model builders who want to keep simple potentials alive. The abstract states they locate viable regions consistent with observations, which is the positive result if the numerics check out. The soft spot is the coupling itself. Everything depends on a strength that simultaneously relaxes the initial displacement, sets the right perturbation amplitude after decay, and avoids excess non-Gaussianity or isocurvature. The stress-test note is fair: without explicit derivations of the modified power spectrum from the coupled equations and a scan that closes the window under all bounds, it is hard to know whether the claimed viable space is real or just an artifact of choosing the coupling freely. If the full paper only tunes the parameter to fit without showing the joint constraints, the central claim weakens. This is for people working on multi-field inflation and CMB model constraints. A reader already thinking about curvaton scenarios or ways to loosen fine-tuning in hilltop models will get something concrete from it. It deserves peer review so the derivations and parameter consistency can be checked properly.

Referee Report

2 major / 1 minor

Summary. The paper claims that coupling a curvaton to the inflaton in hilltop inflation relaxes the extreme initial-value tuning near the potential maximum and modifies the curvature perturbation power spectrum, thereby reviving the quartic hilltop model for sub-Planckian field values and yielding viable parameter space consistent with recent ACT observations.

Significance. If the central claims hold after explicit verification, the work would be significant for inflationary model building: it directly addresses the initial-conditions naturalness issue in hilltop inflation and reopens a class of simple quartic potentials that had been disfavored by super-Planckian requirements and tuning, potentially broadening the set of observationally viable single-field-like scenarios.

major comments (2)

[main text (power-spectrum and parameter-space sections)] The central claim that the curvaton modifies the curvature perturbation power spectrum to open viable sub-Planckian parameter space is not supported by any explicit derivation of the modified P_ζ(k) from the coupled inflaton-curvaton equations of motion or from the decay dynamics; without this step the assertion that a suitable coupling window exists remains unverified.
[parameter-space discussion] No simultaneous error budget or exclusion plot is supplied showing that the required curvaton-inflaton coupling strength satisfies the observed amplitude, slow-roll conditions, and current f_NL/isocurvature bounds at the same time; the viability statement therefore rests on an unshown assumption that such a non-empty window exists.

minor comments (1)

The specific form of the curvaton-inflaton coupling (e.g., λ ϕ² σ² or similar) should be stated explicitly at first use, together with the regime in which the curvaton is assumed to dominate the perturbations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We appreciate the feedback highlighting the need for greater explicitness in our derivations and parameter-space analysis. We address each major comment below and will incorporate the suggested improvements in the revised version.

read point-by-point responses

Referee: [main text (power-spectrum and parameter-space sections)] The central claim that the curvaton modifies the curvature perturbation power spectrum to open viable sub-Planckian parameter space is not supported by any explicit derivation of the modified P_ζ(k) from the coupled inflaton-curvaton equations of motion or from the decay dynamics; without this step the assertion that a suitable coupling window exists remains unverified.

Authors: We agree that the manuscript would be strengthened by an explicit step-by-step derivation of the modified P_ζ(k). In the revised version we will add a dedicated subsection that starts from the coupled equations of motion for the inflaton and curvaton, incorporates the decay dynamics, and arrives at the resulting curvature power spectrum. This will explicitly demonstrate the existence of the viable coupling window for sub-Planckian quartic hilltop inflation. revision: yes
Referee: [parameter-space discussion] No simultaneous error budget or exclusion plot is supplied showing that the required curvaton-inflaton coupling strength satisfies the observed amplitude, slow-roll conditions, and current f_NL/isocurvature bounds at the same time; the viability statement therefore rests on an unshown assumption that such a non-empty window exists.

Authors: We acknowledge that a joint error budget and exclusion plot is required to robustly establish viability. The revised manuscript will include a comprehensive parameter-space scan together with exclusion plots that simultaneously enforce the observed amplitude, slow-roll conditions, and current f_NL and isocurvature bounds. These will confirm the existence of a non-empty window for the curvaton-inflaton coupling. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on standard multi-field dynamics and parameter search

full rationale

The paper's core claims rest on introducing a curvaton-inflaton coupling to relax initial conditions for hilltop inflation and to modify the curvature power spectrum, then scanning parameters to identify regions consistent with ACT and other data. No quoted equation or step reduces a 'prediction' to a fitted input by construction, nor does any load-bearing premise collapse to a self-citation or ansatz smuggled from prior work by the same authors. The viability statement is an explicit numerical search over couplings and initial values, which is the standard non-circular procedure for such models; the derivation chain remains self-contained against external cosmological constraints.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The model rests on standard slow-roll and curvaton-decay assumptions plus a new coupling parameter whose value is chosen to fit the observed spectrum; no independent evidence is given for the coupling strength.

free parameters (1)

curvaton-inflaton coupling strength
Adjusted to control the curvaton's contribution to the curvature perturbation spectrum and to open viable regions for the quartic potential.

axioms (2)

standard math Slow-roll approximation governs the inflationary dynamics
Invoked for the hilltop potential evolution.
domain assumption Curvaton decays after inflation and sources the observed curvature perturbations
Core assumption of curvaton models used here to modify the power spectrum.

invented entities (1)

curvaton field with inflaton coupling no independent evidence
purpose: To relax initial conditions and alter the perturbation spectrum
Postulated new interaction not derived from prior literature; no independent falsifiable prediction supplied.

pith-pipeline@v0.9.0 · 5428 in / 1427 out tokens · 36994 ms · 2026-05-16T23:40:43.039196+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

V_HT = Λ⁴(1 − φ^p/(2μ^p))² with p=3,4; V_C = λ²/(2M_Pl²)(φ²σ⁴ + φ⁴σ²); Langevin dφ/dN = −V_φ/(3H²) + (H/2π)ξ_φ(N)
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

R ≡ ρ_σ/ρ_r |_{t_dec} treated as free parameter; posterior on {μ,Λ,λ} from χ² fit to n_s, A_s, r bounds

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

62 extracted references · 62 canonical work pages · 23 internal anchors

[1]

*”, and a uniform-density slice whereδρ= 0 as the final hypersurface, labeled by “f

for thecubicandquartichilltop models, respectively, both of which lie outside the 95% C.L. regions in the latest Planck [2] and ACT [8] results. B. The curvaton mechanism The above picture can change if we introduce a curva- ton fieldσ[36–40]. Sincem σ ≪Hduring inflation, the curvaton is effectively frozen atσ ∗. Its quantum fluctua- tions at the horizon ...

work page 2000
[2]

Planck 2013 results. XXII. Constraints on inflation

P. A. R. Adeet al.(Planck), “Planck 2013 results. XXII. Constraints on inflation,” Astron. Astrophys.571, A22 (2014), arXiv:1303.5082 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2013
[3]

Planck 2018 results. X. Constraints on inflation

Y. Akramiet al.(Planck), “Planck 2018 results. X. Constraints on inflation,” Astron. Astrophys.641, A10 (2020), arXiv:1807.06211 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[4]

Planck 2018 results. IX. Constraints on primordial non-Gaussianity

Y. Akramiet al.(Planck), “Planck 2018 results. IX. Con- straints on primordial non-Gaussianity,” Astron. Astro- phys.641, A9 (2020), arXiv:1905.05697 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[5]

A New Type of Isotropic Cosmo- logical Models Without Singularity,

Alexei A. Starobinsky, “A New Type of Isotropic Cosmo- logical Models Without Singularity,” Phys. Lett. B91, 99–102 (1980)

work page 1980
[6]

The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems,

Alan H. Guth, “The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems,” Phys. Rev. D23, 347–356 (1981)

work page 1981
[7]

A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogene- ity, Isotropy and Primordial Monopole Problems,

Andrei D. Linde, “A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogene- ity, Isotropy and Primordial Monopole Problems,” Phys. Lett. B108, 389–393 (1982)

work page 1982
[8]

Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking,

Andreas Albrecht and Paul J. Steinhardt, “Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking,” Phys. Rev. Lett.48, 1220–1223 (1982)

work page 1982
[9]

The Atacama Cosmology Telescope: DR6 Power Spectra, Likelihoods and $\Lambda$CDM Parameters

Thibaut Louiset al.(ACT), “The Atacama Cosmology Telescope: DR6 Power Spectra, Likelihoods and ΛCDM Parameters,” (2025), arXiv:2503.14452 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2025
[10]

Kallosh, A

Renata Kallosh, Andrei Linde, and Diederik Roest, “ACT, SPT, and chaotic inflation,” (2025), arXiv:2503.21030 [hep-th]

work page arXiv 2025
[11]

Higgs-modular inflation,

Shuntaro Aoki, Hajime Otsuka, and Ryota Yanagita, “Higgs-modular inflation,” Phys. Rev. D112, 043505 (2025), arXiv:2504.01622 [hep-ph]

work page arXiv 2025
[12]

The early universe isACT-ingwarm,

Arjun Berera, Suddhasattwa Brahma, Zizang Qiu, Rud- nei O. Ramos, and Gabriel S. Rodrigues, “The early universe isACT-ingwarm,” (2025), arXiv:2504.02655 [hep-th]

work page arXiv 2025
[13]

Fractional attractors in light of the latest ACT observations,

Christian Dioguardi, Antonio J. Iovino, and Antonio Racioppi, “Fractional attractors in light of the latest ACT observations,” Phys. Lett. B868, 139664 (2025), arXiv:2504.02809 [gr-qc]

work page arXiv 2025
[14]

Has ACT measured ra- diative corrections to the tree-level Higgs-like inflation?

Ioannis D. Gialamas, Alexandros Karam, Antonio Racioppi, and Martti Raidal, “Has ACT measured ra- diative corrections to the tree-level Higgs-like inflation?” (2025), arXiv:2504.06002 [astro-ph.CO]

work page arXiv 2025
[15]

Independent connection in action dur- ing inflation,

Alberto Salvio, “Independent connection in action dur- ing inflation,” Phys. Rev. D112, L061301 (2025), 14 arXiv:2504.10488 [hep-ph]

work page arXiv 2025
[16]

Palatini linear attractors are back in action,

Christian Dioguardi and Alexandros Karam, “Palatini linear attractors are back in action,” Phys. Rev. D111, 123521 (2025), arXiv:2504.12937 [gr-qc]

work page arXiv 2025
[17]

Increase of ns in regularized pole inflation & Einstein-Cartan gravity,

Minxi He, Muzi Hong, and Kyohei Mukaida, “Increase of ns in regularized pole inflation & Einstein-Cartan gravity,” JCAP09, 080 (2025), arXiv:2504.16069 [astro- ph.CO]

work page arXiv 2025
[18]

Refined predictions for Starobinsky inflation and post-inflationary constraints in light of ACT,

Manuel Drees and Yong Xu, “Refined predictions for Starobinsky inflation and post-inflationary constraints in light of ACT,” Phys. Lett. B867, 139612 (2025), arXiv:2504.20757 [astro-ph.CO]

work page arXiv 2025
[19]

Enhancement of primordial curvature perturbations in R 3-corrected Starobinsky-Higgs infla- tion,

Jinsu Kim, Xinpeng Wang, Ying-li Zhang, and Zhongzhou Ren, “Enhancement of primordial curvature perturbations in R 3-corrected Starobinsky-Higgs infla- tion,” JCAP09, 011 (2025), arXiv:2504.12035 [astro- ph.CO]

work page arXiv 2025
[20]

How accidental was inflation?

Ignatios Antoniadis, John Ellis, Wenqi Ke, Dimitri V. Nanopoulos, and Keith A. Olive, “How accidental was inflation?” JCAP08, 090 (2025), arXiv:2504.12283 [hep- ph]

work page arXiv 2025
[21]

Reconciling Nonminimally Coupled Higgs Inflation with ACT DR6 Observations through Reheating

Lang Liu, Zhu Yi, and Yungui Gong, “Reconciling Higgs Inflation with ACT Observations through Reheating,” (2025), arXiv:2505.02407 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2025
[22]

Reheat- ing ACTs on Starobinsky and Higgs inflation,

D. S. Zharov, O. O. Sobol, and S. I. Vilchinskii, “Reheat- ing ACTs on Starobinsky and Higgs inflation,” (2025), arXiv:2505.01129 [astro-ph.CO]

work page arXiv 2025
[23]

Starobinsky like inflation and EGB Gravity in the light of ACT,

Yogesh, Abolhassan Mohammadi, Qiang Wu, and Tao Zhu, “Starobinsky like inflation and EGB Gravity in the light of ACT,” JCAP10, 010 (2025), arXiv:2505.05363 [astro-ph.CO]

work page arXiv 2025
[24]

Curvature corrections to Starobinsky inflation can explain the ACT results,

Andrea Addazi, Yermek Aldabergenov, and Sergei V. Ketov, “Curvature corrections to Starobinsky inflation can explain the ACT results,” Phys. Lett. B869, 139883 (2025), arXiv:2505.10305 [gr-qc]

work page arXiv 2025
[25]

Higgs-like inflation ACTivated mass,

Wen Yin, “Higgs-like inflation ACTivated mass,” JCAP 09, 062 (2025), arXiv:2505.03004 [hep-ph]

work page arXiv 2025
[26]

The curvaton ACTs again,

Christian T. Byrnes, Marina Cortˆ es, and An- drew R. Liddle, “The curvaton ACTs again,” (2025), arXiv:2505.09682 [astro-ph.CO]

work page arXiv 2025
[27]

Higgs pole inflation with loop corrections in light of ACT results

Jeonghak Han, Hyun Min Lee, and Jun-Ho Song, “Higgs pole inflation with loop corrections in light of ACT re- sults,” (2025), arXiv:2506.21189 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2025
[28]

Power Law Plateau Inflation and Primary Gravitational Waves in the light of ACT,

Abolhassan Mohammadi, Yogesh, and Anzhong Wang, “Power Law Plateau Inflation and Primary Gravitational Waves in the light of ACT,” (2025), arXiv:2507.06544 [astro-ph.CO]

work page arXiv 2025
[29]

ACT Implications for Hilltop Inflation,

Monika Lynker and Rolf Schimmrigk, “ACT Implications for Hilltop Inflation,” (2025), arXiv:2507.15076 [astro- ph.CO]

work page arXiv 2025
[30]

Chaotic Inflation RIDES Again,

Venus Keus and Stephen F. King, “Chaotic Inflation RIDES Again,” (2025), arXiv:2511.05799 [hep-ph]

work page arXiv 2025
[31]

Natural New Inflation in Broken Supergravity

K. I. Izawa and T. Yanagida, “Natural new inflation in broken supergravity,” Phys. Lett. B393, 331–336 (1997), arXiv:hep-ph/9608359

work page internal anchor Pith review Pith/arXiv arXiv 1997
[32]

New inflation, preinflation, and leptogenesis

Vedat Nefer Senoguz and Q. Shafi, “New inflation, pre- inflation, and leptogenesis,” Phys. Lett. B596, 8–15 (2004), arXiv:hep-ph/0403294

work page internal anchor Pith review Pith/arXiv arXiv 2004
[33]

Hilltop Inflation

Lotfi Boubekeur and David. H. Lyth, “Hilltop inflation,” JCAP07, 010 (2005), arXiv:hep-ph/0502047

work page internal anchor Pith review Pith/arXiv arXiv 2005
[34]

Modular invariant hill- top inflation,

Stephen F. King and Xin Wang, “Modular invariant hill- top inflation,” JCAP07, 073 (2024), arXiv:2405.08924 [hep-ph]

work page arXiv 2024
[35]

Modu- lar invariant slow roll inflation,

Gui-Jun Ding, Si-Yi Jiang, and Wenbin Zhao, “Modu- lar invariant slow roll inflation,” JCAP10, 016 (2024), arXiv:2405.06497 [hep-ph]

work page arXiv 2024
[36]

Hilltop inflation with preinflation from coupling to matter fields

Stefan Antusch, David Nolde, and Stefano Orani, “Hill- top inflation with preinflation from coupling to matter fields,” JCAP05, 034 (2014), arXiv:1402.5328 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[37]

Non- gaussian isocurvature perturbations from inflation,

Andrei D. Linde and Viatcheslav F. Mukhanov, “Non- gaussian isocurvature perturbations from inflation,” Phys. Rev. D56, R535–R539 (1997), arXiv:astro- ph/9610219

work page arXiv 1997
[38]

Generating the curvature perturbation without an inflaton

David H. Lyth and David Wands, “Generating the cur- vature perturbation without an inflaton,” Phys. Lett. B 524, 5–14 (2002), arXiv:hep-ph/0110002

work page internal anchor Pith review Pith/arXiv arXiv 2002
[39]

Effects of cos- mological moduli fields on cosmic microwave back- ground,

Takeo Moroi and Tomo Takahashi, “Effects of cos- mological moduli fields on cosmic microwave back- ground,” Phys. Lett. B522, 215–221 (2001), [Erra- tum: Phys.Lett.B 539, 303–303 (2002)], arXiv:hep- ph/0110096

work page arXiv 2001
[40]

Cosmic Density Perturbations from Late-Decaying Scalar Condensations

Takeo Moroi and Tomo Takahashi, “Cosmic density perturbations from late decaying scalar condensations,” Phys. Rev. D66, 063501 (2002), arXiv:hep-ph/0206026

work page internal anchor Pith review Pith/arXiv arXiv 2002
[41]

The Primordial density perturbation in the curvaton scenario,

David H. Lyth, Carlo Ungarelli, and David Wands, “The Primordial density perturbation in the curvaton scenario,” Phys. Rev. D67, 023503 (2003), arXiv:astro- ph/0208055

work page arXiv 2003
[42]

Equilibrium State of a Massless Self-Interacting Scalar Field in the De Sitter Background

Alexei A. Starobinsky and Junichi Yokoyama, “Equilib- rium state of a selfinteracting scalar field in the De Sit- ter background,” Phys. Rev. D50, 6357–6368 (1994), arXiv:astro-ph/9407016

work page internal anchor Pith review Pith/arXiv arXiv 1994
[43]

Spectator field dynamics in de Sitter and curvaton initial conditions

Kari Enqvist, Rose N. Lerner, Olli Taanila, and An- ders Tranberg, “Spectator field dynamics in de Sitter and curvaton initial conditions,” JCAP10, 052 (2012), arXiv:1205.5446 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[44]

The stochastic spectator

Robert J. Hardwick, Vincent Vennin, Christian T. Byrnes, Jes´ us Torrado, and David Wands, “The stochas- tic spectator,” JCAP10, 018 (2017), arXiv:1701.06473 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[45]

Eternally Existing Selfreproducing Chaotic Inflationary Universe,

Andrei D. Linde, “Eternally Existing Selfreproducing Chaotic Inflationary Universe,” Phys. Lett. B175, 395– 400 (1986)

work page 1986
[46]

Conditions for (No) Eternal Inflation,

Tom Rudelius, “Conditions for (No) Eternal Inflation,” JCAP08, 009 (2019), arXiv:1905.05198 [hep-th]

work page arXiv 2019
[47]

Vacuum stability, wormholes, cosmic rays and the cosmological bounds on m(t) and m(H),

John R. Ellis, Andrei D. Linde, and Marc Sher, “Vacuum stability, wormholes, cosmic rays and the cosmological bounds on m(t) and m(H),” Phys. Lett. B252, 203–211 (1990)

work page 1990
[48]

Hard art of the universe creation (stochastic approach to tunneling and baby universe for- mation),

Andrei D. Linde, “Hard art of the universe creation (stochastic approach to tunneling and baby universe for- mation),” Nucl. Phys. B372, 421–442 (1992), arXiv:hep- th/9110037

work page arXiv 1992
[49]

Cosmological implications of the Higgs mass measurement

J. R. Espinosa, G. F. Giudice, and A. Riotto, “Cos- mological implications of the Higgs mass measurement,” JCAP05, 002 (2008), arXiv:0710.2484 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2008
[50]

Stochastic inflation with an extremely large number ofe-folds,

Naoya Kitajima, Yuichiro Tada, and Fuminobu Taka- hashi, “Stochastic inflation with an extremely large number ofe-folds,” Phys. Lett. B800, 135097 (2020), arXiv:1908.08694 [hep-ph]

work page arXiv 2020
[51]

Primordial black holes from stochastic tunnelling,

Chiara Animali and Vincent Vennin, “Primordial black holes from stochastic tunnelling,” JCAP02, 043 (2023), arXiv:2210.03812 [astro-ph.CO]

work page arXiv 2023
[52]

Improved Con- straints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season,

P. A. R. Adeet al.(BICEP, Keck), “Improved Con- straints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season,” Phys. Rev. Lett.127, 151301 (2021), arXiv:2110.00483 [astro-ph.CO]. 15

work page arXiv 2018
[53]

A General Analytic Formula for the Spectral Index of the Density Perturbations produced during Inflation

Misao Sasaki and Ewan D. Stewart, “A General analytic formula for the spectral index of the density perturba- tions produced during inflation,” Prog. Theor. Phys.95, 71–78 (1996), arXiv:astro-ph/9507001

work page internal anchor Pith review Pith/arXiv arXiv 1996
[54]

The inflationary prediction for primordial non-gaussianity

David H. Lyth and Yeinzon Rodriguez, “The Inflationary prediction for primordial non-Gaussianity,” Phys. Rev. Lett.95, 121302 (2005), arXiv:astro-ph/0504045

work page internal anchor Pith review Pith/arXiv arXiv 2005
[55]

Acoustic Signatures in the Primary Microwave Background Bispectrum

Eiichiro Komatsu and David N. Spergel, “Acoustic signa- tures in the primary microwave background bispectrum,” Phys. Rev. D63, 063002 (2001), arXiv:astro-ph/0005036

work page internal anchor Pith review Pith/arXiv arXiv 2001
[56]

Non-Gaussianity from Inflation: Theory and Observations

N. Bartolo, E. Komatsu, Sabino Matarrese, and A. Riotto, “Non-Gaussianity from inflation: Theory and observations,” Phys. Rept.402, 103–266 (2004), arXiv:astro-ph/0406398

work page internal anchor Pith review Pith/arXiv arXiv 2004
[57]

Primordial Non-Gaussianities from Inflation Models

Xingang Chen, “Primordial Non-Gaussianities from In- flation Models,” Adv. Astron.2010, 638979 (2010), arXiv:1002.1416 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2010
[58]

Probing Cosmic Infla- tion with the LiteBIRD Cosmic Microwave Background Polarization Survey,

E. Allyset al.(LiteBIRD), “Probing Cosmic Infla- tion with the LiteBIRD Cosmic Microwave Background Polarization Survey,” PTEP2023, 042F01 (2023), arXiv:2202.02773 [astro-ph.IM]

work page arXiv 2023
[59]

Snowmass2021 Cosmic Fron- tier: Cosmic Microwave Background Measurements White Paper,

Clarence L. Changet al., “Snowmass2021 Cosmic Fron- tier: Cosmic Microwave Background Measurements White Paper,” (2022), arXiv:2203.07638 [astro-ph.CO]

work page arXiv 2022
[60]

The Atacama Cosmology Telescope: DR6 Constraints on Extended Cosmological Models

Erminia Calabreseet al.(Atacama Cosmology Tele- scope), “The Atacama Cosmology Telescope: DR6 con- straints on extended cosmological models,” JCAP11, 063 (2025), arXiv:2503.14454 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2025
[61]

STOCHASTIC DE SITTER (INFLATIONARY) STAGE IN THE EARLY UNI- VERSE,

Alexei A. Starobinsky, “STOCHASTIC DE SITTER (INFLATIONARY) STAGE IN THE EARLY UNI- VERSE,” Lect. Notes Phys.246, 107–126 (1986)

work page 1986
[62]

A general proof of the conservation of the curvature perturbation

David H. Lyth, Karim A. Malik, and Misao Sasaki, “A General proof of the conservation of the curvature pertur- bation,” JCAP05, 004 (2005), arXiv:astro-ph/0411220

work page internal anchor Pith review Pith/arXiv arXiv 2005