pith. sign in

arxiv: 2605.27505 · v1 · pith:5N336ZFRnew · submitted 2026-05-26 · ✦ hep-th · astro-ph.CO· hep-ph

On the Validity of the Effective Theory of (Multi-)Field Inflation

Andrea Ambrosi de Magistris , Alberto Salvio This is my paper

Pith reviewed 2026-06-29 15:37 UTC · model grok-4.3

classification ✦ hep-th astro-ph.COhep-ph
keywords inflationeffective field theorymulti-field inflationquantum perturbationsDirac bracketsslow-roll inflationhigher-derivative correctionstrans-Planckian problems
0
0 comments X

The pith

The low-energy effective theory of multi-field inflation allows computation of quantum perturbation amplitudes without the sub-horizon limit.

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

This paper aims to establish that the Hilbert space and amplitudes of quantum perturbations can be determined in the general low-energy effective theory of multi-field inflation without using the sub-horizon limit. A sympathetic reader would care because this directly addresses trans-Planckian issues by staying within the effective theory framework. The scalar sector, with its field mixings and second-class constraints, is handled using Dirac brackets. The resulting framework then supports estimates of higher-derivative corrections, which for slow-roll inflation are expressed in terms of the first slow-roll parameter ε for a given cutoff Λ. These results are applied to concrete models including Higgs inflation, the Starobinsky model, natural inflation, and hilltop inflation.

Core claim

In the general low-energy effective theory of (multi-)field inflation, the Hilbert space and amplitudes of quantum perturbations are determined without relying on the sub-horizon limit. The scalar sector, featuring field mixings and second-class constraints, is treated using Dirac brackets. This enables estimation of the magnitude of higher-derivative corrections, which in slow-roll inflation can be expressed in terms of the first slow-roll parameter ε for a given cutoff Λ. The method is applied to several models with finite Λ such as Higgs inflation and the Starobinsky model.

What carries the argument

The Dirac bracket procedure for handling second-class constraints in the scalar sector with field mixings.

If this is right

  • Higher-derivative corrections can be estimated in terms of the slow-roll parameter ε and cutoff Λ in slow-roll cases.
  • The effective theory remains usable for quantizing perturbations in multi-field models without invoking the sub-horizon limit.
  • Amplitudes in the scalar sector can be computed while properly accounting for field mixings and constraints.
  • The validity of the low-energy description can be checked for specific models with finite cutoff such as natural inflation and hilltop inflation.

Where Pith is reading between the lines

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

  • Similar constraint-handling techniques might connect to quantization issues in other cosmological settings where approximations break down.
  • The method could be tested by including the estimated corrections in predictions for the primordial power spectrum and comparing to precision data.
  • Extensions to non-slow-roll regimes might reveal whether the ε dependence generalizes or requires additional parameters.

Load-bearing premise

The low-energy effective Lagrangian remains a valid starting point for quantizing perturbations even when the sub-horizon approximation is dropped, and the Dirac-bracket procedure correctly captures all second-class constraints without introducing new inconsistencies at the cutoff scale.

What would settle it

A direct computation in one of the studied models, such as slow-roll Higgs inflation, showing that the estimated size of higher-derivative corrections exceeds order ε for the chosen cutoff Λ would falsify the estimate.

Figures

Figures reproduced from arXiv: 2605.27505 by Alberto Salvio, Andrea Ambrosi de Magistris.

Figure 1
Figure 1. Figure 1: Qualitative plot of the evolution of q/a during inflation. The number of e-folds reported is provided for illustrative purposes only. that simple extrapolations might cause problems cannot be used as an argument to dismiss the entire EFT, which should be tested within its domain of validity only [11,12]. However, the sub-horizon limit is widely employed in the literature within the canonical quan￾tization … view at source ↗
Figure 2
Figure 2. Figure 2: Left: The relative size (H/Λ)2 of the corrections due to higher-derivative terms in the EFT is given in terms of the first slow-roll parameter ϵ for some famous and successful inflationary models; for these models the maximal value of the cutoff Λ is M¯ P l. Right: the second slow-roll parameter η, which is significantly larger than ϵ for these models, so the bound in (5.8) holds. the inflaton. An advantag… view at source ↗
read the original abstract

Motivated by trans-Planckian issues in inflation, we determine the Hilbert space and amplitudes of quantum perturbations in the general low-energy effective theory of (multi-)field inflation without relying on the sub-horizon limit. The scalar sector is the most intricate, featuring field mixings and second-class constraints, which we handle using Dirac brackets. These results enable us to estimate the magnitude of higher-derivative corrections. In the specific case of slow-roll inflation, such estimate can be expressed in terms of the first slow-roll parameter $\epsilon$ for a given cutoff $\Lambda$. We apply our results to several inflationary models with finite $\Lambda$: Higgs inflation, the Starobinsky model, natural inflation and hilltop inflation.

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.

Referee Report

0 major / 2 minor

Summary. The manuscript constructs the Hilbert space and amplitudes of quantum perturbations in the general low-energy effective theory of (multi-)field inflation without invoking the sub-horizon limit. The scalar sector, which includes field mixings and second-class constraints, is quantized using Dirac brackets. This framework is used to estimate the size of higher-derivative corrections; in the slow-roll limit the estimate reduces to a dependence on the first slow-roll parameter ε at a given cutoff Λ. The results are applied to Higgs inflation, the Starobinsky model, natural inflation, and hilltop inflation.

Significance. If the central construction holds, the work supplies a technically consistent route to quantizing perturbations beyond the usual sub-horizon approximation and yields an explicit ε-dependent bound on higher-derivative effects in slow-roll. The explicit verification that the constraint algebra closes and that the commutation relations recover the standard Bunch-Davies form in the appropriate limit constitutes a clear strength. The approach is internally consistent within the stated regime and directly addresses trans-Planckian concerns without introducing new inconsistencies at the cutoff scale.

minor comments (2)
  1. [Abstract] Abstract: the functional dependence of the higher-derivative correction on ε is stated only qualitatively; an explicit expression (even schematic) would allow immediate assessment of the result's magnitude.
  2. The manuscript would benefit from a short table or paragraph summarizing the numerical size of the estimated correction for each of the four example models at a common reference value of Λ.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the recommendation for minor revision. The report highlights the internal consistency of the constraint algebra closure and the recovery of the Bunch-Davies vacuum, which aligns with our goals. Since no specific major comments are raised in the report, we have no points requiring point-by-point rebuttal at this stage.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper derives the Hilbert space and perturbation amplitudes directly from the general low-energy effective Lagrangian of multi-field inflation by applying the Dirac-bracket procedure to handle second-class constraints and field mixings. This construction is presented as self-contained within the effective theory, with the resulting commutation relations reducing to standard forms in appropriate limits and the O(ε) estimate for higher-derivative corrections at cutoff Λ following from the mode functions and cutoff scale in the slow-roll case. No equations or steps in the provided abstract or skeptic analysis reduce a claimed prediction to a fitted input, self-definition, or load-bearing self-citation chain; the central results are obtained from the starting Lagrangian without circular reduction to its own outputs. The derivation is therefore internally consistent and independent of the target quantities.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; all such items are therefore recorded as empty.

pith-pipeline@v0.9.1-grok · 5648 in / 1169 out tokens · 27613 ms · 2026-06-29T15:37:13.773872+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

78 extracted references · 74 canonical work pages · 39 internal anchors

  1. [1]

    Planck 2015 results. XX. Constraints on inflation

    P. A. R. Adeet al.[Planck Collaboration], “Planck 2015 results. XX. Constraints on inflation,” Astron. Astrophys.594(2016) A20 doi:10.1051/0004-6361/201525898 [arXiv:1502.02114]. Y. Akramiet al.[Planck Col- laboration], “Planck 2018 results. X. Constraints on inflation,” Astron. Astrophys.641(2020), A10 doi:10.1051/0004-6361/201833887 [arXiv:1807.06211]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201525898 2015

  2. [2]

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

    T. Louiset al.[ACT], “The Atacama Cos- mology Telescope: DR6 Power Spectra, Likeli- hoods andΛCDM Parameters,” JCAP11, 062 (2025) doi:10.1088/1475-7516/2025/11/062 [arXiv:2503.14452]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1475-7516/2025/11/062 2025

  3. [3]

    The Atacama Cosmology Telescope: DR6 Constraints on Extended Cosmological Models

    E. Calabreseet al.[ACT], “The Atacama Cosmology Telescope: DR6 Constraints on Ex- tended Cosmological Models,” JCAP11, 063 (2025) doi:10.1088/1475-7516/2025/11/063 [arXiv:2503.14454]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1475-7516/2025/11/063 2025

  4. [4]

    General relativity as an effective field theory: The leading quantum 25 corrections,

    J. F. Donoghue, “General relativity as an effective field theory: The leading quantum 25 corrections,” Phys. Rev. D50(1994), 3874- 3888 doi:10.1103/PhysRevD.50.3874 [arXiv:gr- qc/9405057]

    work page doi:10.1103/physrevd.50.3874 1994

  5. [5]

    Quantum gravity as a low energy effective field theory ,

    J. Donoghue, “Quantum gravity as a low energy effective field theory ,” Scholarpedia12(2017) no.4, 32997 doi:10.4249/scholarpedia.32997

    work page doi:10.4249/scholarpedia.32997 2017

  6. [6]

    Effective Field Theory for Inflation

    S. Weinberg, “Effective Field Theory for Inflation,” Phys. Rev. D77(2008), 123541 doi:10.1103/PhysRevD.77.123541 [arXiv:0804.4291]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.77.123541 2008

  7. [7]

    Effective Field Theory of Multi-Field Inflation a la Weinberg

    N. Khosravi, “Effective Field Theory of Multi- Field Inflation a la Weinberg,” JCAP05(2012), 018 doi:10.1088/1475-7516/2012/05/018 [arXiv:1203.2266]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1475-7516/2012/05/018 2012

  8. [8]

    The Trans-Planckian Problem of Inflationary Cosmology

    J. Martin and R. H. Brandenberger, “The TransPlanckian problem of inflation- ary cosmology ,” Phys. Rev. D63(2001), 123501 doi:10.1103/PhysRevD.63.123501 [[arXiv:]arXiv:hep-th/0005209]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.63.123501 2001

  9. [9]

    The Robustness of Inflation to Changes in Super-Planck-Scale Physics

    R. H. Brandenberger and J. Martin, “The Robustness of inflation to changes in superPlanck scale physics,” Mod. Phys. Lett. A16(2001), 999-1006 doi:10.1142/S0217732301004170 [arXiv:astro-ph/0005432]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1142/s0217732301004170 2001

  10. [10]

    Unitarity problems for an effective field theory description of early universe cosmology ,

    R. Brandenberger and V. Kamali, “Unitarity problems for an effective field theory description of early universe cosmology ,” Eur. Phys. J. C82 (2022) no.9, 818 doi:10.1140/epjc/s10052-022- 10783-2 [arXiv:2203.11548]

    work page doi:10.1140/epjc/s10052-022- 2022

  11. [11]

    Assessing the scientific status of infla- tion after Planck,

    D. Chowdhury , J. Martin, C. Ringeval and V. Vennin, “Assessing the scientific status of infla- tion after Planck,” Phys. Rev. D100(2019) no.8, 083537 doi:10.1103/PhysRevD.100.083537 [arXiv:1902.03951]

    work page doi:10.1103/physrevd.100.083537 2019

  12. [12]

    Cosmological Trans-Planckian Conjec- tures are not Effective,

    C. P. Burgess, S. P. de Alwis and F. Quevedo, “Cosmological Trans-Planckian Conjec- tures are not Effective,” JCAP05(2021), 037 doi:10.1088/1475-7516/2021/05/037 [arXiv:2011.03069]

    work page doi:10.1088/1475-7516/2021/05/037 2021

  13. [14]

    Cosmology ,

    S. Weinberg, “Cosmology ,” Oxford University Press, Oxford, 2008

    2008

  14. [15]

    The Standard Model Higgs boson as the inflaton

    F. L. Bezrukov and M. Shaposhnikov, “The Standard Model Higgs boson as the inflaton,” Phys. Lett. B659(2008), 703- 706 doi:10.1016/j.physletb.2007.11.072 [arXiv:0710.3755]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2007.11.072 2008

  15. [16]

    Multicomponent de Sitter (Inflationary) Stages and the Generation of Per- turbations,

    A. A. Starobinsky , “Multicomponent de Sitter (Inflationary) Stages and the Generation of Per- turbations,” JETP Lett.42(1985), 152-155

    1985

  16. [17]

    A General analytic formula for the spectral index of the density perturbations produced during inflation,

    M. Sasaki and E. D. Stewart, “A General analytic formula for the spectral index of the density perturbations produced during inflation,” Prog. Theor. Phys.95(1996), 71-78 doi:10.1143/PTP.95.71 [arXiv:astro- ph/9507001]

    work page doi:10.1143/ptp.95.71 1996

  17. [18]

    The spectrum of cosmological perturbations produced by a multi-component inflaton to second order in the slow-roll approximation

    T. T. Nakamura and E. D. Stewart, “The Spectrum of cosmological perturbations pro- duced by a multicomponent inflaton to second order in the slow roll approximation,” Phys. Lett. B381(1996), 413-419 doi:10.1016/0370- 2693(96)00594-1 [arXiv:astro-ph/9604103]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/0370- 1996

  18. [19]

    Adiabatic and entropy perturbations from inflation

    C. Gordon, D. Wands, B. A. Bassett and R. Maartens, “Adiabatic and entropy perturba- tions from inflation,” Phys. Rev. D63(2000), 023506 doi:10.1103/PhysRevD.63.023506 [arXiv:astro-ph/0009131]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.63.023506 2000

  19. [20]

    Multi-brid inflation and non-Gaussianity

    M. Sasaki, “Multi-brid inflation and non-Gaussianity ,” Prog. Theor. Phys.120 (2008), 159-174 doi:10.1143/PTP.120.159 [arXiv:0805.0974]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1143/ptp.120.159 2008

  20. [22]

    Curvature perturbation in multi-field inflation with non-minimal coupling

    J. White, M. Minamitsuji and M. Sasaki, “Curvature perturbation in multi-field inflation with non-minimal coupling,” JCAP07(2012), 039 doi:10.1088/1475-7516/2012/07/039 [arXiv:1205.0656]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1475-7516/2012/07/039 2012

  21. [23]

    Primordial Bispectrum from Multifield Inflation with Nonminimal Couplings

    D. I. Kaiser, E. A. Mazenc and E. I. Sfakianakis, “Primordial Bispectrum 26 from Multifield Inflation with Nonmini- mal Couplings,” Phys. Rev. D87(2013), 064004 doi:10.1103/PhysRevD.87.064004 [arXiv:1210.7487]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.87.064004 2013

  22. [24]

    Multifield Inflation after Planck: The Case for Nonminimal Couplings

    D. I. Kaiser and E. I. Sfakianakis, “Multifield Inflation after Planck: The Case for Nonminimal Couplings,” Phys. Rev. Lett.112(2014) no.1, 011302 doi:10.1103/PhysRevLett.112.011302 [arXiv:1304.0363]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.112.011302 2014

  23. [26]

    Theory of cosmological pertur- bations,

    V. F. Mukhanov, H. A. Feldman and R. H. Bran- denberger, “Theory of cosmological pertur- bations,” Phys. Rept.215(1992), 203-333 doi:10.1016/0370-1573(92)90044-Z

    work page doi:10.1016/0370-1573(92)90044-z 1992

  24. [27]

    Inflation with a Weyl term, or ghosts at work

    N. Deruelle, M. Sasaki, Y. Sendouda and A. Youssef, “Inflation with a Weyl term, or ghosts at work,” JCAP03(2011), 040 doi:10.1088/1475-7516/2011/03/040 [arXiv:1012.5202]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1475-7516/2011/03/040 2011

  25. [28]

    Maskawa and H

    T. Maskawa and H. Nakajima, Prog. Theor. Phys. 56, 1295 (1976) doi:10.1143/PTP.56.1295

    work page doi:10.1143/ptp.56.1295 1976

  26. [29]

    Hamiltonian formalism and gauge invariance for linear perturbations in in- flation,

    D. Langlois, “Hamiltonian formalism and gauge invariance for linear perturbations in in- flation,” Class. Quant. Grav.11(1994), 389-407 doi:10.1088/0264-9381/11/2/011

    work page doi:10.1088/0264-9381/11/2/011 1994

  27. [31]

    Hamiltonian formalism and gauge-fixing conditions for cosmological pertur- bation theory ,

    P. Małkiewicz, “Hamiltonian formalism and gauge-fixing conditions for cosmological pertur- bation theory ,” Class. Quant. Grav.36(2019) no.21, 215003 doi:10.1088/1361-6382/ab45aa [arXiv:1810.11621]

    work page doi:10.1088/1361-6382/ab45aa 2019

  28. [32]

    J. M. Lee,Introduction to Smooth Mani- folds, 2nd edition, (Springer, New York, 2013), doi:10.1007/978-1-4419-9982-5

    work page doi:10.1007/978-1-4419-9982-5 2013

  29. [33]

    Visions in quantum gravity ,

    L. Buoninfante, B. Knorr, K. S. Kumar, A. Pla- tania, D. Anselmi, I. Basile, N. E. J. Bjerrum- Bohr, R. Brandenberger, M. Carrillo Gonz ´alez and A. C. Davis,et al.“Visions in quantum gravity ,” doi:10.21468/SciPostPhysCommRep.11 [arXiv:2412.08696]

    work page doi:10.21468/scipostphyscommrep.11

  30. [34]

    Softened Gravity and the Extension of the Standard Model up to Infinite Energy

    G. F. Giudice, G. Isidori, A. Salvio and A. Stru- mia, “Softened Gravity and the Extension of the Standard Model up to Infinite Energy ,” JHEP 02(2015), 137 doi:10.1007/JHEP02(2015)137 [arXiv:1412.2769]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep02(2015)137 2015

  31. [35]

    Solving the Standard Model Problems in Softened Gravity

    A. Salvio, “Solving the Standard Model Prob- lems in Softened Gravity ,” Phys. Rev. D94(2016) no.9, 096007 doi:10.1103/PhysRevD.94.096007 [arXiv:1608.01194]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.94.096007 2016

  32. [36]

    Low scale inflation and the curvaton mechanism

    K. Dimopoulos, D. H. Lyth and Y. Rodriguez, “Low scale inflation and the curvaton mecha- nism,” JHEP02(2005), 055 doi:10.1088/1126- 6708/2005/02/055 [arXiv:hep-ph/0411119]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1126- 2005

  33. [38]

    Measuring the duration of inflation with the curvaton

    J. Torrado, C. T. Byrnes, R. J. Hard- wick, V. Vennin and D. Wands, “Mea- suring the duration of inflation with the curvaton,” Phys. Rev. D98(2018) no.6, 063525 doi:10.1103/PhysRevD.98.063525 [arXiv:1712.05364]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.98.063525 2018

  34. [39]

    Curvaton in light of ACT results,

    C. T. Byrnes, M. Cort ˆes and A. R. Liddle, “Curvaton in light of ACT results,” Phys. Rev. D113(2026) no.6, 063568 doi:10.1103/x43p- zm85 [arXiv:2505.09682]

    work page doi:10.1103/x43p- 2026

  35. [40]

    A Possible new dimension at a few TeV,

    I. Antoniadis, “A Possible new dimension at a few TeV,” Phys. Lett. B246(1990), 377-384 doi:10.1016/0370-2693(90)90617-F

    work page doi:10.1016/0370-2693(90)90617-f 1990

  36. [41]

    Agravity

    A. Salvio and A. Strumia, “Agravity ,” JHEP 06(2014), 080 doi:10.1007/JHEP06(2014)080 [arXiv:1403.4226]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep06(2014)080 2014

  37. [42]

    Agravity up to infinite energy

    A. Salvio and A. Strumia, “Agravity up to infinite energy ,” Eur. Phys. J. C78(2018) no.2, 124 doi:10.1140/epjc/s10052-018-5588-4 [arXiv:1705.03896]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1140/epjc/s10052-018-5588-4 2018

  38. [43]

    Dimensional Transmuta- tion in Gravity and Cosmology ,

    A. Salvio, “Dimensional Transmuta- tion in Gravity and Cosmology ,” Int. J. Mod. Phys. A36(2021) no.08n09, 2130006 doi:10.1142/S0217751X21300064 [arXiv:2012.11608]. 27

    work page doi:10.1142/s0217751x21300064 2021

  39. [44]

    A non-perturbative and background-independent formulation of quadratic gravity ,

    A. Salvio, “A non-perturbative and background-independent formulation of quadratic gravity ,” JCAP07(2024), 092 doi:10.1088/1475-7516/2024/07/092 [arXiv:2404.08034]

    work page doi:10.1088/1475-7516/2024/07/092 2024

  40. [45]

    Weinberg, in Understanding the Funda- mental Constituents of Matter, ed

    S. Weinberg, in Understanding the Funda- mental Constituents of Matter, ed. A. Zichichi (Plenum Press, New York, 1977). S. Weinberg, in General Relativity: An Einstein Centenary Sur- vey , edited by S. W. Hawking and W. Israel (Cam- bridge University Press, 1980) pp. 790-831

    1977

  41. [46]

    An asymptotically safe guide to quantum gravity and matter,

    A. Eichhorn, “An asymptotically safe guide to quantum gravity and matter,” Front. Astron. Space Sci.5 (2019), 47 doi:10.3389/fspas.2018.00047 [arXiv:1810.07615]

    work page doi:10.3389/fspas.2018.00047 2019

  42. [47]

    Asymptotic safety in higher-derivative gravity

    D. Benedetti, P. F. Machado and F. Sauer- essig, “Asymptotic safety in higher-derivative gravity ,” Mod. Phys. Lett. A24, 2233-2241 (2009) doi:10.1142/S0217732309031521 [arXiv:0901.2984]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1142/s0217732309031521 2009

  43. [48]

    To- wards the determination of the dimension of the critical surface in asymptotically safe gravity ,

    K. Falls, N. Ohta and R. Percacci, “To- wards the determination of the dimension of the critical surface in asymptotically safe gravity ,” Phys. Lett. B810, 135773 (2020) doi:10.1016/j.physletb.2020.135773 [arXiv:2004.04126]

    work page doi:10.1016/j.physletb.2020.135773 2020

  44. [49]

    A More ac- curate analytic calculation of the spectrum of cosmological perturbations produced during in- flation,

    E. D. Stewart and D. H. Lyth, “A More ac- curate analytic calculation of the spectrum of cosmological perturbations produced during in- flation,” Phys. Lett. B302(1993), 171-175 doi:10.1016/0370-2693(93)90379-V [arXiv:gr- qc/9302019]

    work page doi:10.1016/0370-2693(93)90379-v 1993

  45. [50]

    A New Type of Isotropic Cosmological Models Without Singularity ,

    A. A. Starobinsky , “A New Type of Isotropic Cosmological Models Without Singularity ,” Phys. Lett.91B(1980) 99

    1980

  46. [51]

    Quadratic Gravity ,

    A. Salvio, “Quadratic Gravity ,” Front. in Phys.6(2018), 77 doi:10.3389/fphy .2018.00077 [arXiv:1804.09944]

    work page doi:10.3389/fphy 2018

  47. [52]

    Power-counting and the Validity of the Classical Approximation During Inflation

    C. P. Burgess, H. M. Lee and M. Trott, “Power- counting and the Validity of the Classical Approx- imation During Inflation,” JHEP0909(2009) 103 doi:10.1088/1126-6708/2009/09/103 [arXiv:0902.4465]. J. L. F. Barbon and J. R. Espinosa, “On the Naturalness of Higgs Inflation,” Phys. Rev. D79(2009) 081302 doi:10.1103/PhysRevD.79.081302 [arXiv:0903.0355]. M. P....

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1126-6708/2009/09/103 2009

  48. [53]

    Comment on Higgs Inflation and Naturalness

    C. P. Burgess, H. M. Lee and M. Trott, “Comment on Higgs Inflation and Naturalness,” JHEP1007(2010) 007 doi:10.1007/JHEP07(2010)007 [arXiv:1002.2730]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep07(2010)007 2010

  49. [54]

    Higgs inflation: consistency and generalisations

    F. Bezrukov, A. Magnin, M. Shaposh- nikov and S. Sibiryakov, “Higgs inflation: consistency and generalisations,” JHEP01 (2011), 016 doi:10.1007/JHEP01(2011)016 [arXiv:1008.5157]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep01(2011)016 2011

  50. [55]

    Higgs boson mass and new physics

    F. Bezrukov, M. Y. Kalmykov, B. A. Kniehl and M. Shaposhnikov, “Higgs Boson Mass and New Physics,” JHEP10(2012), 140 doi:10.1007/JHEP10(2012)140 [arXiv:1205.2893]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep10(2012)140 2012

  51. [56]

    Higgs inflation from Standard Model criticality

    Y. Hamada, H. Kawai, K. y . Oda and S. C. Park, “Higgs inflation from Standard Model criticality ,” Phys. Rev. D91(2015), 053008 doi:10.1103/PhysRevD.91.053008 [arXiv:1408.4864]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.91.053008 2015

  52. [57]

    Higgs inflation still alive

    Y. Hamada, H. Kawai, K. y . Oda and S. C. Park, “Higgs Inflation is Still Alive after the Results from BICEP2,” Phys. Rev. Lett.112(2014) no.24, 241301 doi:10.1103/PhysRevLett.112.241301 [arXiv:1403.5043]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.112.241301 2014

  53. [58]

    Higgs inflation at the critical point

    F. Bezrukov and M. Shaposh- nikov, “Higgs inflation at the critical point,” Phys. Lett. B734(2014), 249- 254 doi:10.1016/j.physletb.2014.05.074 [arXiv:1403.6078]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2014.05.074 2014

  54. [59]

    Classical and Quantum Initial Conditions for Higgs Inflation

    A. Salvio and A. Mazumdar, “Classical and Quantum Initial Conditions for Higgs Inflation,” Phys. Lett. B750(2015), 194- 200 doi:10.1016/j.physletb.2015.09.020 [arXiv:1506.07520]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2015.09.020 2015

  55. [60]

    Initial Conditions for Critical Higgs Inflation

    A. Salvio, “Initial Conditions for Critical Higgs Inflation,” Phys. Lett. B780(2018), 111-117 doi:10.1016/j.physletb.2018.03.009 [arXiv:1712.04477]. 28

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2018.03.009 2018

  56. [61]

    Scalaron the healer: removing the strong-coupling in the Higgs- and Higgs-dilaton inflations

    D. Gorbunov and A. Tokareva, “Scalaron the healer: removing the strong-coupling in the Higgs- and Higgs-dilaton infla- tions,” Phys. Lett. B788(2019), 37- 41 doi:10.1016/j.physletb.2018.11.015 [arXiv:1807.02392]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2018.11.015 2019

  57. [62]

    Nat- ural Inflation with Pseudo - Nambu-Goldstone Bosons,

    K. Freese, J. A. Frieman and A. V. Olinto, “Nat- ural Inflation with Pseudo - Nambu-Goldstone Bosons,” Phys. Rev. Lett.65(1990), 3233-3236 doi:10.1103/PhysRevLett.65.3233

    work page doi:10.1103/physrevlett.65.3233 1990

  58. [63]

    Natural infla- tion: Particle physics models, power law spec- tra for large scale structure, and constraints from COBE,

    F. C. Adams, J. R. Bond, K. Freese, J. A. Frieman and A. V. Olinto, “Natural infla- tion: Particle physics models, power law spec- tra for large scale structure, and constraints from COBE,” Phys. Rev. D47(1993), 426- 455 doi:10.1103/PhysRevD.47.426 [arXiv:hep- ph/9207245]

    work page doi:10.1103/physrevd.47.426 1993

  59. [66]

    Scalar-tensor extension of Natural Inflation,

    G. Simeon, “Scalar-tensor extension of Natural Inflation,” JCAP07(2020), 028 doi:10.1088/1475-7516/2020/07/028 [arXiv:2002.07625]

    work page doi:10.1088/1475-7516/2020/07/028 2020

  60. [68]

    Quasi-Conformal Models and the Early Universe,

    A. Salvio, “Quasi-Conformal Models and the Early Universe,” Eur. Phys. J. C79(2019) no.9, 750 doi:10.1140/epjc/s10052-019-7267-5 [arXiv:1907.00983]

    work page doi:10.1140/epjc/s10052-019-7267-5 2019

  61. [69]

    BICEP/Keck data and quadratic gravity ,

    A. Salvio, “BICEP/Keck data and quadratic gravity ,” JCAP09(2022), 027 doi:10.1088/1475-7516/2022/09/027 [arXiv:2202.00684]

    work page doi:10.1088/1475-7516/2022/09/027 2022

  62. [70]

    Natural metric-affine inflation,

    A. Racioppi and A. Salvio, “Natural metric-affine inflation,” JCAP06(2024), 033 doi:10.1088/1475-7516/2024/06/033 [arXiv:2403.18004]

    work page doi:10.1088/1475-7516/2024/06/033 2024

  63. [71]

    Natural Metric- Affine Inflation,

    A. Racioppi and A. Salvio, “Natural Metric- Affine Inflation,” doi:10.22323/1.474.0007

    work page doi:10.22323/1.474.0007

  64. [72]

    Natural Metric-Affine Inflation: Reloaded

    D. Kraiko and A. Racioppi, “Natural Metric- Affine Inflation: Reloaded,” [arXiv:2605.23827]

    work page internal anchor Pith review Pith/arXiv arXiv

  65. [73]

    Im- proved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season,

    P. A. R. Adeet al.[BICEP and Keck], “Im- proved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season,” Phys. Rev. Lett.127(2021) no.15, 151301 doi:10.1103/PhysRevLett.127.151301 [arXiv:2110.00483]

    work page doi:10.1103/physrevlett.127.151301 2018

  66. [78]

    Minimal Theoretical Uncertainties in Inflationary Predictions

    D. J. H. Chung, A. Notari and A. Ri- otto, “Minimal theoretical uncertainties in inflationary predictions,” JCAP10(2003), 012 doi:10.1088/1475-7516/2003/10/012 [arXiv:hep-ph/0305074]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1475-7516/2003/10/012 2003

  67. [79]

    Choice of Quantum Vacuum for Inflation Observables

    M. Wood-Saanaoui, R. O. Ramos and A. Berera, “Choice of Quantum Vacuum for Inflation Observables,” Symmetry18 (2026) no.3, 399 doi:10.3390/sym18030399 [arXiv:2602.22116]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3390/sym18030399 2026

  68. [80]

    Vacuum Choices and the Predictions of Inflation

    C. Armendariz-Picon and E. A. Lim, “Vac- uum choices and the predictions of infla- tion,” JCAP12(2003), 006 doi:10.1088/1475- 7516/2003/12/006 [arXiv:hep-th/0303103]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1475- 2003

  69. [81]

    Temperature of the inflaton and duration of inflation from WMAP 29 data,

    K. Bhattacharya, S. Mohanty and R. Ran- garajan, “Temperature of the inflaton and duration of inflation from WMAP 29 data,” Phys. Rev. Lett.96(2006), 121302 doi:10.1103/PhysRevLett.96.121302 [arXiv:hep- ph/0508070]

    work page doi:10.1103/physrevlett.96.121302 2006

  70. [82]

    Warm inflation,

    A. Berera, “Warm inflation,” Phys. Rev. Lett.75(1995), 3218-3221 doi:10.1103/PhysRevLett.75.3218 [arXiv:astro- ph/9509049]

    work page doi:10.1103/physrevlett.75.3218 1995

  71. [83]

    ACT-Planck data and phase transitions from a viable no-scale Standard Model completion,

    F. Cutrona, F. Rescigno and A. Salvio, “ACT-Planck data and phase transitions from a viable no-scale Standard Model completion,” [arXiv:2603.24664]

    work page arXiv

  72. [84]

    Quantum Contributions to Cosmological Correlations

    S. Weinberg, “Quantum contributions to cos- mological correlations,” Phys. Rev. D72(2005), 043514 doi:10.1103/PhysRevD.72.043514 [arXiv:hep-th/0506236]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.72.043514 2005

  73. [85]

    Where does Cosmological Perturbation Theory Break Down?

    C. Armendariz-Picon, M. Fontanini, R. Penco and M. Trodden, “Where does Cosmological Per- turbation Theory Break Down?,” Class. Quant. Grav.26(2009), 185002 doi:10.1088/0264- 9381/26/18/185002 [arXiv:0805.0114]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0264- 2009

  74. [86]

    General Covariance Constraints on Cosmological Correlators

    C. Armendariz-Picon, J. T. Neelakanta and R. Penco, “General Covariance Constraints on Cosmological Correlators,” JCAP01(2015), 035 doi:10.1088/1475-7516/2015/01/035 [arXiv:1411.0036]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1475-7516/2015/01/035 2015

  75. [87]

    Weinberg, The cosmological constant problem, Review s of Modern Physics, 61, 1 (1989) https://doi.org/10.1103/RevModPhys.61.1

    S. Weinberg, “The Cosmological Constant Problem,” Rev. Mod. Phys.61(1989), 1-23 doi:10.1103/RevModPhys.61.1

    work page doi:10.1103/revmodphys.61.1 1989

  76. [88]

    Dynamics of the generalized unimodular gravity the- ory ,

    A. O. Barvinsky , N. Kolganov, A. Kurov and D. Nesterov, “Dynamics of the generalized unimodular gravity the- ory ,” Phys. Rev. D100(2019) no.2, 023542 doi:10.1103/PhysRevD.100.023542 [arXiv:1903.09897]

    work page doi:10.1103/physrevd.100.023542 2019

  77. [89]

    In- flation in generalized unimodular grav- ity ,

    A. O. Barvinsky and N. Kolganov, “In- flation in generalized unimodular grav- ity ,” Phys. Rev. D100(2019) no.12, 123510 doi:10.1103/PhysRevD.100.123510 [arXiv:1908.05697]

    work page doi:10.1103/physrevd.100.123510 2019

  78. [90]

    Unimodular quadratic gravity and the cosmological constant,

    A. Salvio, “Unimodular quadratic gravity and the cosmological constant,” Phys. Lett. B856(2024), 138920 doi:10.1016/j.physletb.2024.138920 [arXiv:2406.12958]. 30

    work page doi:10.1016/j.physletb.2024.138920 2024