pith. sign in

arxiv: 2510.05967 · v2 · submitted 2025-10-07 · 🌌 astro-ph.CO · gr-qc· hep-ph

Stochastic Gravitational Waves from Modulated Reheating

Michele Benaco , Dimitrios Karamitros , Sami Nurmi , Kimmo Tuominen This is my paper

Pith reviewed 2026-05-18 08:56 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qchep-ph
keywords stochastic gravitational wavesmodulated reheatingspectator scalarcurvature perturbationsblue-tilted spectrumnon-Gaussian perturbationsBBODECIGO
0
0 comments X p. Extension

The pith

A spectator scalar modulating reheating can generate a stochastic gravitational wave background observable by BBO or DECIGO, but only with unexpectedly large couplings.

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

The paper examines how a spectator scalar field with Higgs-like couplings sources adiabatic curvature perturbations through the modulated reheating mechanism, where the inflaton decays via shift-symmetric dimension-five operators. The spectator, taken to be in the de Sitter vacuum, produces blue-tilted and strongly non-Gaussian perturbations that can dominate the spectrum on small scales. These perturbations induce a stochastic gravitational wave signal whose amplitude reaches levels potentially detectable by future observatories. The required coupling strengths, however, exceed those typical in low-energy particle physics models that remain perturbative when extrapolated to inflationary energies.

Core claim

We investigate scalar-induced stochastic gravitational waves from adiabatic curvature perturbations sourced by a spectator field via the modulated reheating mechanism. We consider a spectator scalar with Higgs-like couplings and inflaton decay via shift symmetric dimension-five operators. The spectator is assumed to be in the de Sitter vacuum and it sources blue-tilted, strongly non-Gaussian curvature perturbations which can dominate the spectrum on small scales k ≫ Mpc^{-1}. We find that the setup could generate a gravitational wave signal testable by surveys like BBO and DECIGO but only for large coupling values not expected in low-energy particle physics setups that can be perturbatively

What carries the argument

The modulated reheating mechanism in which a spectator scalar affects the inflaton decay rate through shift-symmetric dimension-five operators, generating blue-tilted non-Gaussian curvature perturbations from its de Sitter vacuum fluctuations.

If this is right

  • The induced gravitational wave background reaches amplitudes potentially accessible to BBO and DECIGO detectors.
  • The curvature perturbations are blue-tilted and strongly non-Gaussian, dominating for wavenumbers k much larger than inverse megaparsec.
  • Observable signals arise only when the coupling constants are larger than those expected from perturbative low-energy models.
  • The mechanism relies on scalar-induced effects rather than direct tensor modes from inflation.

Where Pith is reading between the lines

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

  • Detection of the predicted spectrum could indicate the presence of high-scale physics that generates the required large couplings without violating perturbativity.
  • Complementary small-scale measurements of non-Gaussianity in the curvature power spectrum would provide an independent test of the same spectator dynamics.
  • The setup illustrates how late-time reheating dynamics can imprint observable features on gravitational waves even when inflation itself produces negligible tensor modes.

Load-bearing premise

The spectator scalar remains in the de Sitter vacuum and its induced curvature perturbations dominate the spectrum on small scales.

What would settle it

A measurement by BBO or DECIGO of the stochastic gravitational wave spectrum that shows either an amplitude below the predicted level or a spectral shape inconsistent with the blue tilt from modulated reheating.

read the original abstract

We investigate scalar-induced stochastic gravitational waves from adiabatic curvature perturbations sourced by a spectator field via the modulated reheating mechanism. We consider a spectator scalar with Higgs-like couplings and inflaton decay via shift symmetric dimension-five operators. The spectator is assumed to be in the Sitter vacuum and it sources blue-tilted, strongly non-Gaussian curvature perturbations which can dominate the spectrum on small scales $k \gg \rm{Mpc}^{-1}$. We find that the setup could generate a gravitational wave signal testable by surveys like BBO and DECIGO but only for large coupling values not expected in low-energy particle physics setups that can be perturbatively extrapolated up to the inflationary scale.

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

2 major / 2 minor

Summary. The manuscript investigates scalar-induced stochastic gravitational waves from adiabatic curvature perturbations sourced by a spectator scalar field via the modulated reheating mechanism. It considers a spectator with Higgs-like couplings and inflaton decay through shift-symmetric dimension-five operators. The spectator is assumed to sit in the de Sitter vacuum and thereby sources blue-tilted, strongly non-Gaussian curvature perturbations that can dominate the spectrum on small scales k ≫ Mpc^{-1}. The authors conclude that the setup can produce a GW background testable by BBO and DECIGO, but only for large coupling values not expected in perturbative low-energy particle-physics models that extrapolate to the inflationary scale.

Significance. If the central results hold, the work would supply a concrete, operator-level example of how modulated reheating with a spectator can source an observable stochastic GW background in future space-based interferometers. The explicit inclusion of Higgs-like couplings and shift-symmetric dimension-five decay operators is a positive feature that ties the calculation to a specific particle-physics setup and permits future falsification. The paper thereby adds a model-specific case to the broader literature on induced GW from non-standard reheating.

major comments (2)
  1. [Abstract] Abstract: The assertion that the spectator sources blue-tilted, strongly non-Gaussian curvature perturbations that 'can dominate the spectrum on small scales k ≫ Mpc^{-1}' is load-bearing for both the amplitude and the spectral shape of the predicted GW signal. The manuscript provides no quantitative demonstration that the modulated-reheating transfer function, once the shift-symmetric dimension-five operators and Higgs-like couplings are inserted, actually produces this dominance in the presence of possible inflaton back-reaction or non-vacuum initial conditions for the spectator.
  2. [Model setup and assumptions] Model setup and assumptions: The de Sitter vacuum assumption for the spectator scalar is central to the claimed perturbation spectrum and resulting GW reach. If the spectator instead acquires a non-vacuum initial state or experiences significant back-reaction, both the GW amplitude and the blue-tilted shape would change by orders of magnitude, directly affecting the testability claim for BBO and DECIGO.
minor comments (2)
  1. [Abstract] The statement that the required couplings are 'not expected in low-energy particle physics setups' would benefit from an explicit numerical range or comparison to typical values in the literature on Higgs-like spectators.
  2. Notation for the small-scale regime (k ≫ Mpc^{-1}) should be accompanied by a brief comparison to the CMB pivot scale to clarify the separation of scales.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments, which help clarify the scope and limitations of our results. We address each major comment below and indicate where revisions will be made to strengthen the presentation.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The assertion that the spectator sources blue-tilted, strongly non-Gaussian curvature perturbations that 'can dominate the spectrum on small scales k ≫ Mpc^{-1}' is load-bearing for both the amplitude and the spectral shape of the predicted GW signal. The manuscript provides no quantitative demonstration that the modulated-reheating transfer function, once the shift-symmetric dimension-five operators and Higgs-like couplings are inserted, actually produces this dominance in the presence of possible inflaton back-reaction or non-vacuum initial conditions for the spectator.

    Authors: We thank the referee for this observation. The modulated reheating transfer function employed in the manuscript follows the standard derivation in the literature for a spectator modulating the inflaton decay rate through the specified dimension-five operators. With Higgs-like couplings, the spectator fluctuations generate curvature perturbations whose spectrum is blue-tilted and can exceed the inflaton contribution on small scales when the spectator is light during inflation. We have performed order-of-magnitude estimates showing that, for the parameter values yielding observable GW signals, the spectator energy density remains subdominant and back-reaction on the inflaton is negligible. In the revised manuscript we will add an explicit subsection quantifying the regime of validity, including the condition for dominance over inflaton perturbations and the suppression of back-reaction effects. revision: yes

  2. Referee: [Model setup and assumptions] Model setup and assumptions: The de Sitter vacuum assumption for the spectator scalar is central to the claimed perturbation spectrum and resulting GW reach. If the spectator instead acquires a non-vacuum initial state or experiences significant back-reaction, both the GW amplitude and the blue-tilted shape would change by orders of magnitude, directly affecting the testability claim for BBO and DECIGO.

    Authors: The referee correctly notes the centrality of this assumption. Our calculation adopts the standard Bunch-Davies vacuum for a light spectator in de Sitter space, which is the usual starting point for such models and leads to the quoted blue-tilted, non-Gaussian spectrum. We agree that deviations from this initial state or strong back-reaction could alter the results substantially. The manuscript focuses on the regime where the spectator remains light and its fluctuations are generated during inflation without significant back-reaction for the couplings that produce detectable GW signals. In the revision we will expand the discussion of the assumption's validity range, add estimates of the back-reaction threshold, and explicitly state that the BBO/DECIGO reach applies only within this regime. revision: partial

Circularity Check

0 steps flagged

Derivation is self-contained forward computation from model assumptions

full rationale

The paper assumes a spectator scalar in the de Sitter vacuum with Higgs-like couplings and shift-symmetric decay operators, derives the resulting blue-tilted non-Gaussian curvature perturbations that dominate on small scales, and computes the induced stochastic GW spectrum as a prediction for BBO/DECIGO. No quoted equation or self-citation reduces the GW amplitude or shape to a fitted input or tautological redefinition of the target observable. The central result remains a model-dependent forecast rather than an input renamed as output.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard inflationary cosmology plus two model-specific assumptions about the spectator vacuum and the form of the decay operators; the large coupling values needed for detection are acknowledged as outside typical perturbative regimes.

free parameters (1)
  • spectator-inflaton coupling strength
    Large values are required to produce a detectable GW signal; these values lie outside the perturbative regime expected for low-energy extrapolations.
axioms (2)
  • domain assumption Spectator scalar remains in the de Sitter vacuum during inflation
    This vacuum state supplies the quantum fluctuations that source the curvature perturbations via modulated reheating.
  • domain assumption Inflaton decay proceeds through shift-symmetric dimension-five operators
    This operator choice defines the modulated reheating mechanism under study.

pith-pipeline@v0.9.0 · 5646 in / 1522 out tokens · 62623 ms · 2026-05-18T08:56:19.231925+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

106 extracted references · 106 canonical work pages · 70 internal anchors

  1. [1]

    D. H. Lyth and D. Wands,Generating the curvature perturbation without an inflaton,Phys. Lett. B524(2002) 5 [hep-ph/0110002]. – 20 –

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  2. [2]

    Effects of Cosmological Moduli Fields on Cosmic Microwave Background

    T. Moroi and T. Takahashi,Effects of cosmological moduli fields on cosmic microwave background,Phys. Lett. B522(2001) 215 [hep-ph/0110096]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  3. [3]

    Adiabatic CMB perturbations in pre-big bang string cosmology

    K. Enqvist and M. S. Sloth,Adiabatic CMB perturbations in pre - big bang string cosmology, Nucl. Phys. B626(2002) 395 [hep-ph/0109214]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  4. [4]

    A. D. Linde and V. F. Mukhanov,Nongaussian isocurvature perturbations from inflation, Phys. Rev. D56(1997) R535 [astro-ph/9610219]

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  5. [5]

    Mollerach,Isocurvature Baryon Perturbations and Inflation,Phys

    S. Mollerach,Isocurvature Baryon Perturbations and Inflation,Phys. Rev. D42(1990) 313

    work page 1990

  6. [6]

    Probing String Theory with Modulated Cosmological Fluctuations

    L. Kofman,Probing string theory with modulated cosmological fluctuations, (2003) [astro-ph/0303614]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  7. [7]

    A new mechanism for generating density perturbations from inflation

    G. Dvali, A. Gruzinov and M. Zaldarriaga,A new mechanism for generating density perturbations from inflation,Phys. Rev. D69(2004) 023505 [astro-ph/0303591]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  8. [8]

    Matter Creation via Vacuum Fluctuations in the Early Universe and Observed Ultra-High Energy Cosmic Ray Events

    V. Kuzmin and I. Tkachev,Matter creation via vacuum fluctuations in the early universe and observed ultrahigh-energy cosmic ray events,Phys. Rev. D59(1999) 123006 [hep-ph/9809547]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  9. [9]

    P. J. E. Peebles and A. Vilenkin,Noninteracting dark matter,Phys. Rev. D60(1999) 103506 [astro-ph/9904396]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  10. [10]

    D. J. E. Marsh,Axion Cosmology,Phys. Rept.643(2016) 1 [1510.07633]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  11. [11]

    Standard Model with a real singlet scalar and inflation

    K. Enqvist, S. Nurmi, T. Tenkanen and K. Tuominen,Standard Model with a real singlet scalar and inflation,JCAP08(2014) 035 [1407.0659]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  12. [12]

    Inflationary Imprints on Dark Matter

    S. Nurmi, T. Tenkanen and K. Tuominen,Inflationary Imprints on Dark Matter,JCAP11 (2015) 001 [1506.04048]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  13. [13]

    Isocurvature Constraints on Portal Couplings

    K. Kainulainenet al.,Isocurvature Constraints on Portal Couplings,JCAP06(2016) 022 [1601.07733]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  14. [14]

    Spectator Dark Matter

    T. Markkanen, A. Rajantie and T. Tenkanen,Spectator Dark Matter,Phys. Rev. D98(12) (2018) 123532 [1811.02586]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  15. [15]

    Dark matter from gravitational particle production at reheating

    T. Markkanen and S. Nurmi,Dark matter from gravitational particle production at reheating, JCAP02(2017) 008 [1512.07288]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  16. [16]

    Y. Ema, K. Nakayama and Y. Tang,Production of Purely Gravitational Dark Matter,JHEP 09(2018) 135 [1804.07471]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  17. [17]

    Scale-invariant scalar field dark matter through the Higgs portal

    C. Cosme, J. G. Rosa and O. Bertolami,Scale-invariant scalar field dark matter through the Higgs portal,JHEP05(2018) 129 [1802.09434]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  18. [18]

    Lightish but clumpy: scalar dark matter from inflationary fluctuations

    G. Alonso-Álvarez and J. Jaeckel,Lightish but clumpy: scalar dark matter from inflationary fluctuations,JCAP10(2018) 022 [1807.09785]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  19. [19]

    Alonso-Álvarez, T

    G. Alonso-Álvarez, T. Hugle and J. Jaeckel,Misalignment & Co.: (Pseudo-)scalar and vector dark matter with curvature couplings,JCAP02(2020) 014 [1905.09836]

    work page arXiv 2020

  20. [20]

    D. G. Figueroa and C. T. Byrnes,The Standard Model Higgs as the origin of the hot Big Bang,Phys. Lett. B767(2017) 272 [1604.03905]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  21. [21]

    Non-minimal gravitational reheating during kination

    K. Dimopoulos and T. Markkanen,Non-minimal gravitational reheating during kination, JCAP06(2018) 021 [1803.07399]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  22. [22]

    Reheating through the Higgs amplified by spinodal instabilities and gravitational creation of gravitons

    T. Nakama and J. Yokoyama,Reheating through the Higgs amplified by spinodal instabilities and gravitational creation of gravitons,PTEP2019(3)(2019) 033E02 [1803.07111]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  23. [23]

    Ricci Reheating

    T. Opferkuch, P. Schwaller and B. A. Stefanek,Ricci Reheating,JCAP07(2019) 016 [1905.06823]. – 21 –

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  24. [24]

    M. Dine, L. Randall and S. D. Thomas,Baryogenesis from flat directions of the supersymmetric standard model,Nucl. Phys. B458(1996) 291 [hep-ph/9507453]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  25. [25]

    Affleck and M

    I. Affleck and M. Dine,A New Mechanism for Baryogenesis,Nucl. Phys. B249(1985) 361

    work page 1985

  26. [26]

    J. R. Espinosa, G. F. Giudice and A. Riotto,Cosmological implications of the Higgs mass measurement,JCAP05(2008) 002 [0710.2484]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  27. [27]

    On Stability of the Electroweak Vacuum and the Higgs Portal

    O. Lebedev,On Stability of the Electroweak Vacuum and the Higgs Portal,Eur. Phys. J. C 72(2012) 2058 [1203.0156]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  28. [28]

    Metastable Electroweak Vacuum: Implications for Inflation

    O. Lebedev and A. Westphal,Metastable Electroweak Vacuum: Implications for Inflation, Phys. Lett. B719(2013) 415 [1210.6987]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  29. [29]

    Electroweak Vacuum (In)Stability in an Inflationary Universe

    A. Kobakhidze and A. Spencer-Smith,Electroweak Vacuum (In)Stability in an Inflationary Universe,Phys. Lett. B722(2013) 130 [1301.2846]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  30. [30]

    Electroweak Vacuum Stability in light of BICEP2

    M. Fairbairn and R. Hogan,Electroweak Vacuum Stability in light of BICEP2,Phys. Rev. Lett.112(2014) 201801 [1403.6786]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  31. [31]

    Higgs Dynamics during Inflation

    K. Enqvist, T. Meriniemi and S. Nurmi,Higgs Dynamics during Inflation,JCAP07(2014) 025 [1404.3699]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  32. [32]

    A. Hook, J. Kearney, B. Shakya and K. M. Zurek,Probable or Improbable Universe? Correlating Electroweak Vacuum Instability with the Scale of Inflation,JHEP01(2015) 061 [1404.5953]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  33. [33]

    Spacetime curvature and the Higgs stability during inflation

    M. Herranen, T. Markkanen, S. Nurmi and A. Rajantie,Spacetime curvature and the Higgs stability during inflation,Phys. Rev. Lett.113(21)(2014) 211102 [1407.3141]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  34. [34]

    Inflationary cosmology and the standard model Higgs with a small Hubble induced mass

    K. Kamada,Inflationary cosmology and the standard model Higgs with a small Hubble induced mass,Phys. Lett. B742(2015) 126 [1409.5078]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  35. [35]

    J. R. Espinosaet al.,The cosmological Higgstory of the vacuum instability,JHEP09(2015) 174 [1505.04825]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  36. [36]

    Spacetime curvature and Higgs stability after inflation

    M. Herranen, T. Markkanen, S. Nurmi and A. Rajantie,Spacetime curvature and Higgs stability after inflation,Phys. Rev. Lett.115(2015) 241301 [1506.04065]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  37. [37]

    D. G. Figueroa, A. Rajantie and F. Torrenti,Higgs field-curvature coupling and postinflationary vacuum instability,Phys. Rev. D98(2)(2018) 023532 [1709.00398]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  38. [38]

    P. A. Klimai and E. V. Bugaev,Primordial black hole formation from non-Gaussian curvature perturbations, in17th International Seminar on High Energy Physics, vol. 2, (Moscow, Russia), pp. 163–174, INR, 10, 2012,1210.3262

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  39. [39]

    Primordial black holes in non-Gaussian regimes

    S. Young and C. T. Byrnes,Primordial black holes in non-Gaussian regimes,JCAP08(2013) 052 [1307.4995]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  40. [40]

    Primordial black hole formation from an axion-like curvaton model

    M. Kawasaki, N. Kitajima and T. T. Yanagida,Primordial black hole formation from an axionlike curvaton model,Phys. Rev. D87(6)(2013) 063519 [1207.2550]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  41. [41]

    B. Carr, F. Kuhnel and M. Sandstad,Primordial Black Holes as Dark Matter,Phys. Rev. D 94(8)(2016) 083504 [1607.06077]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  42. [42]

    B. Carr, T. Tenkanen and V. Vaskonen,Primordial black holes from inflaton and spectator field perturbations in a matter-dominated era,Phys. Rev. D96(6)(2017) 063507 [1706.03746]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  43. [43]

    J. R. Espinosa, D. Racco and A. Riotto,Cosmological Signature of the Standard Model Higgs Vacuum Instability: Primordial Black Holes as Dark Matter,Phys. Rev. Lett.120(12)(2018) 121301 [1710.11196]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  44. [44]

    D. N. Maesoet al.,Primordial black holes from spectator field bubbles,JCAP02(02)(2022) 017 [2112.01505]. – 22 –

    work page arXiv 2022

  45. [45]

    Passaglia and M

    S. Passaglia and M. Sasaki,Primordial black holes from CDM isocurvature perturbations, Phys. Rev. D105(10)(2022) 103530 [2109.12824]

    work page arXiv 2022

  46. [46]

    Stamou and S

    I. Stamou and S. Clesse,Primordial black holes without fine-tuning from a light stochastic spectator field,Phys. Rev. D109(4)(2024) 043522 [2310.04174]

    work page arXiv 2024

  47. [47]

    A. D. Gow, T. Miranda and S. Nurmi,Primordial black holes from a curvaton scenario with strongly non-Gaussian perturbations,JCAP11(2023) 006 [2307.03078]

    work page arXiv 2023

  48. [48]

    C. Chen, A. Ghoshal, G. Tasinato and E. Tomberg,Stochastic axionlike curvaton: Non-Gaussianity and primordial black holes without a large power spectrum,Phys. Rev. D 111(6)(2025) 063539 [2409.12950]

    work page arXiv 2025

  49. [49]

    Kuroda, A

    T. Kuroda, A. Naruko, V. Vennin and M. Yamaguchi,Primordial black holes from a curvaton: the role of bimodal distributions,JCAP07(2025) 052 [2504.09548]

    work page arXiv 2025

  50. [50]

    Gravitational waves at interferometer scales and primordial black holes in axion inflation

    J. Garcia-Bellido, M. Peloso and C. Unal,Gravitational waves at interferometer scales and primordial black holes in axion inflation,JCAP12(2016) 031 [1610.03763]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  51. [51]

    Primordial black hole forma- tion in nonminimal curvaton scenarios,

    S. Pi and M. Sasaki,Primordial black hole formation in nonminimal curvaton scenarios, Phys. Rev. D108(10)(2023) L101301 [2112.12680]

    work page arXiv 2023

  52. [52]

    The Maximal Amount of Gravitational Waves in the Curvaton Scenario

    N. Bartolo, S. Matarrese, A. Riotto and A. Vaihkonen,The Maximal Amount of Gravitational Waves in the Curvaton Scenario,Phys. Rev. D76(2007) 061302 [0705.4240]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  53. [53]

    Gravitational waves from dark matter isocurvature,

    G. Domènech, S. Passaglia and S. Renaux-Petel,Gravitational waves from dark matter isocurvature,JCAP03(03)(2022) 023 [2112.10163]

    work page arXiv 2022

  54. [54]

    Cosmological gravitational waves from isocurvature fluctuations,

    G. Domènech,Cosmological gravitational waves from isocurvature fluctuations,AAPPS Bull. 34(1)(2024) 4 [2311.02065]

    work page arXiv 2024

  55. [55]

    Y. Cui, P. Saha and E. I. Sfakianakis,Gravitational Wave Symphony from Oscillating Spectator Scalar Fields,Phys. Rev. Lett.133(2)(2024) 021004 [2310.13060]

    work page arXiv 2024

  56. [56]

    Kumar, H

    S. Kumar, H. Tai and L.-T. Wang,Towards a complete treatment of scalar-induced gravitational waves with early matter domination,JCAP07(2025) 089 [2410.17291]

    work page arXiv 2025

  57. [57]

    Ebadi, S

    R. Ebadiet al.,Gravitational waves from stochastic scalar fluctuations,Phys. Rev. D109(8) (2024) 083519 [2307.01248]

    work page arXiv 2024

  58. [58]

    Inomata, M

    K. Inomata, M. Kawasaki, K. Mukaida and T. T. Yanagida,Axion curvaton model for the gravitational waves observed by pulsar timing arrays,Phys. Rev. D109(4)(2024) 043508 [2309.11398]

    work page arXiv 2024

  59. [59]

    M. A. G. Garcia and S. Verner,Gravitational Waves from Spectator Scalar Fields, (2025) [2506.12126]. [60]Planckcollaboration,Planck 2018 results. VI. Cosmological parameters,Astron. Astrophys. 641(2020) A6 [1807.06209]. [61]Planckcollaboration,Planck 2018 results. IX. Constraints on primordial non-Gaussianity, Astron. Astrophys.641(2020) A9 [1905.05697]

    work page arXiv 2025

  60. [60]

    A. A. Starobinsky,Spectrum of relict gravitational radiation and the early state of the universe,JETP Lett.30(1979) 682

    work page 1979

  61. [61]

    Comments on the Starobinsky Model of Inflation and its Descendants

    A. Kehagias, A. Moradinezhad Dizgah and A. Riotto,Remarks on the Starobinsky model of inflation and its descendants,Phys. Rev. D89(4)(2014) 043527 [1312.1155]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  62. [62]

    A. A. Starobinsky,STOCHASTIC DE SITTER (INFLATIONARY) STAGE IN THE EARLY UNIVERSE,Lect. Notes Phys.246(1986) 107

    work page 1986

  63. [63]

    A. A. Starobinsky and J. Yokoyama,Equilibrium state of a selfinteracting scalar field in the De Sitter background,Phys. Rev. D50(1994) 6357 [astro-ph/9407016]. – 23 –

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  64. [64]

    A. A. Starobinsky,Multicomponent de Sitter (Inflationary) Stages and the Generation of Perturbations,JETP Lett.42(1985) 152

    work page 1985

  65. [65]

    D. S. Salopek and J. R. Bond,Nonlinear evolution of long wavelength metric fluctuations in inflationary models,Phys. Rev. D42(1990) 3936

    work page 1990

  66. [66]

    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 [astro-ph/9507001]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  67. [67]

    A new approach to the evolution of cosmological perturbations on large scales

    D. Wands, K. A. Malik, D. H. Lyth and A. R. Liddle,A New approach to the evolution of cosmological perturbations on large scales,Phys. Rev. D62(2000) 043527 [astro-ph/0003278]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  68. [68]

    D. H. Lyth, K. A. Malik and M. Sasaki,A General proof of the conservation of the curvature perturbation,JCAP05(2005) 004 [astro-ph/0411220]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  69. [69]

    Spectator field dynamics in de Sitter and curvaton initial conditions

    K. Enqvist, R. N. Lerner, O. Taanila and A. Tranberg,Spectator field dynamics in de Sitter and curvaton initial conditions,JCAP10(2012) 052 [1205.5446]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  70. [70]

    R. J. Hardwicket al.,The stochastic spectator,JCAP10(2017) 018 [1701.06473]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  71. [71]

    A. D. Linde and V. Mukhanov,The curvaton web,JCAP04(2006) 009 [astro-ph/0511736]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  72. [72]

    Detecting a small perturbation through its non-Gaussianity

    L. Boubekeur and D. H. Lyth,Detecting a small perturbation through its non-Gaussianity, Phys. Rev. D73(2006) 021301 [astro-ph/0504046]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  73. [73]

    Markkanen, A

    T. Markkanen, A. Rajantie, S. Stopyra and T. Tenkanen,Scalar correlation functions in de Sitter space from the stochastic spectral expansion,Journal of Cosmology and Astroparticle Physics2019(08)(2019) 001 [1904.11917]

    work page arXiv 2019

  74. [74]

    Markkanen and A

    T. Markkanen and A. Rajantie,Scalar correlation functions for a double-well potential in de Sitter space,Journal of Cosmology and Astroparticle Physics2020(03)(2020) 049 [2001.04494]

    work page arXiv 2020

  75. [75]

    S. Lu, Y. Wang and Z.-Z. Xianyu,A Cosmological Higgs Collider,JHEP02(2020) 011 [1907.07390]

    work page arXiv 2020

  76. [76]

    Universe Reheating after Inflation

    Y. Shtanov, J. H. Traschen and R. H. Brandenberger,Universe reheating after inflation,Phys. Rev. D51(1995) 5438 [hep-ph/9407247]

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  77. [77]

    Primordial Curvature Fluctuation and Its Non-Gaussianity in Models with Modulated Reheating

    K. Ichikawa, T. Suyama, T. Takahashi and M. Yamaguchi,Primordial Curvature Fluctuation and Its Non-Gaussianity in Models with Modulated Reheating,Phys. Rev. D78(2008) 063545 [0807.3988]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  78. [78]

    M. A. G. Garcia, K. Kaneta, Y. Mambrini and K. A. Olive,Inflaton Oscillations and Post-Inflationary Reheating,JCAP04(2021) 012 [2012.10756]

    work page arXiv 2021

  79. [79]

    M. A. G. Garciaet al.,The role of vectors in reheating,JCAP06(2024) 014 [2311.14794]

    work page arXiv 2024

  80. [80]

    Do metric fluctuations affect the Higgs dynamics during inflation?

    T. Markkanen, S. Nurmi and A. Rajantie,Do metric fluctuations affect the Higgs dynamics during inflation?,JCAP12(2017) 026 [1707.00866]. [83]ACTcollaboration,The Atacama Cosmology Telescope: DR6 Power Spectra, Likelihoods and ΛCDM Parameters, (2025) [2503.14452]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

Showing first 80 references.