pith. machine review for the scientific record. sign in

arxiv: 2604.05078 · v1 · submitted 2026-04-06 · ✦ hep-ph · astro-ph.CO· gr-qc

Recognition: 2 theorem links

· Lean Theorem

Gravitational Waves from Matter Perturbations of Spectator Scalar Fields

Angel Garcia-Vega, Marcos A. G. Garcia, Sarunas Verner

Authors on Pith no claims yet

Pith reviewed 2026-05-10 19:08 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COgr-qc
keywords spectator scalar fieldportal couplingparametric resonancestochastic gravitational wavesreheatingsecond-order perturbationsHartree approximationlattice simulations
0
0 comments X

The pith

A spectator scalar field with portal coupling to the inflaton generates a second-order stochastic gravitational wave background amplified by parametric resonance during reheating.

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

The paper establishes that in the regime of large portal coupling, parametric resonance during reheating amplifies the spectator field's power spectrum by many orders of magnitude near the resonance band, until quartic self-interaction backreaction detunes the instability, while superhorizon modes remain suppressed to satisfy CMB bounds. This matters because the resulting gravitational waves arise from the direct field-gradient term in the second-order Einstein equations and can be computed with a master formula that separates the frozen spectator spectrum from the expansion history, yielding concrete predictions for observable high-frequency signals. The authors derive analytic scalings such as peak amplitude proportional to reheating temperature to the 8/3 power, demonstrate non-monotonic dependence on the self-coupling, and cross-check the Hartree treatment against lattice simulations that capture rescattering effects.

Core claim

We compute the stochastic gravitational wave background sourced at second order by a spectator scalar field χ coupled to the inflaton φ through a portal interaction σφ²χ² and with quartic self-interaction λ_χχ⁴/4!. In the large portal coupling regime (σ/λ ≫ 1), parametric resonance amplifies the spectator power spectrum near the resonance band until Hartree backreaction from the quartic coupling detunes the instability, while the large inflationary effective mass suppresses superhorizon power. The direct field-gradient source ∂_aχ ∂_bχ leads to a master formula that factorizes into a spectral integral over the frozen, vacuum-subtracted spectator spectrum and a time integral encoding the post

What carries the argument

The master formula for the GW energy density that factorizes the integral over the frozen spectator power spectrum from the time integral over the post-inflationary scale-factor evolution.

If this is right

  • For σ/λ ≃ 10^4 and T_reh = 2×10^{14} GeV the signal reaches Ω_GW h² ∼ 10^{-11} at f ∼ 10^7-10^8 Hz.
  • The peak amplitude scales analytically as Ω_GW ∝ T_reh^{8/3} while depending strongly on portal strength.
  • Dependence on the quartic self-coupling λ_χ is non-monotonic: small values enhance the signal via rescattering while larger values suppress it by detuning resonance.
  • The Hartree treatment and lattice simulations are complementary, with the former capturing superhorizon evolution and the latter resolving fragmentation near the spectral peak.

Where Pith is reading between the lines

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

  • Future high-frequency gravitational wave detectors could directly constrain the portal coupling strength in inflationary models if the predicted spectrum is confirmed.
  • The mechanism suggests that optimal windows in parameter space exist where the signal is maximized without violating isocurvature constraints.
  • Different reheating histories would shift both the peak frequency and overall amplitude, offering a way to probe post-inflationary dynamics.

Load-bearing premise

The large portal coupling regime together with the Hartree approximation for backreaction must hold without major deviations from the assumed reheating history.

What would settle it

A measurement of the high-frequency gravitational wave spectrum whose amplitude fails to follow the predicted T_reh^{8/3} scaling or whose peak frequency lies far from the 10^7-10^8 Hz band for the stated benchmark parameters.

read the original abstract

We compute the stochastic gravitational wave background sourced at second order by a spectator scalar field $\chi$ coupled to the inflaton $\phi$ through a portal interaction $\sigma\phi^2\chi^2$ and with quartic self-interaction $\lambda_\chi\chi^4/4!$. In the large portal coupling regime ($\sigma/\lambda \gg 1$, with $\lambda$ the inflaton normalization), parametric resonance during reheating amplifies the spectator power spectrum by many orders of magnitude near the resonance band until Hartree backreaction from the quartic coupling detunes the instability, while the large inflationary effective mass suppresses superhorizon power and ensures compatibility with CMB isocurvature bounds. We focus on the direct field-gradient source $\partial_a\chi\,\partial_b\chi$ in the second-order Einstein equations and derive a master formula that factorizes into a spectral integral over the frozen, vacuum-subtracted spectator spectrum and a time integral encoding the post-inflationary expansion history. For our benchmark reheating history we obtain analytic scaling relations, including a peak amplitude $\Omega_{\rm GW}\propto T_{\rm reh}^{8/3}$, strong dependence on the portal strength, and weak sensitivity to $m_\chi$. We validate the framework against nonlinear lattice simulations, demonstrating complementarity: the Hartree treatment captures superhorizon evolution inaccessible to the lattice, while the lattice resolves rescattering and fragmentation near the spectral peak. For $\sigma/\lambda \simeq 10^4$ and $T_{\rm reh}=2 \times 10^{14}\,\mathrm{GeV}$, the signal reaches $\Omega_{\rm GW}h^2\sim 10^{-11}$ at $f\sim10^{7}$-$10^{8}\,\mathrm{Hz}$. Increasing $\lambda_\chi$ at fixed $\sigma$ has a non-monotonic effect: small values enhance the signal via rescattering, whereas larger values suppress it by detuning the resonance.

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 / 1 minor

Summary. The paper computes the stochastic gravitational wave background sourced at second order by matter perturbations of a spectator scalar field χ coupled to the inflaton via the portal interaction σ φ² χ² and with quartic self-interaction λ_χ χ⁴/4!. In the large-portal regime σ/λ ≫ 1, parametric resonance during reheating amplifies the χ spectrum until Hartree backreaction from λ_χ detunes the instability; superhorizon power is suppressed by the large inflationary effective mass. The authors derive a master formula that factorizes the GW energy density into a spectral integral over the frozen, vacuum-subtracted spectator spectrum and a time integral over the post-inflationary expansion history. For a benchmark instantaneous-reheating history they obtain analytic scalings including Ω_GW ∝ T_reh^{8/3}, strong dependence on portal strength, and non-monotonic dependence on λ_χ. The framework is validated against nonlinear lattice simulations, with the Hartree treatment capturing superhorizon evolution and the lattice resolving near-peak rescattering. For the benchmark values σ/λ ≃ 10^4 and T_reh = 2 × 10^{14} GeV the signal reaches Ω_GW h² ∼ 10^{-11} at f ∼ 10^7–10^8 Hz.

Significance. If the central results hold, the work identifies a new, potentially observable source of high-frequency gravitational waves tied to reheating dynamics of spectator fields, with distinctive analytic scalings that could be confronted with future detectors. The paper is strengthened by its explicit validation against nonlinear lattice simulations and by the demonstrated complementarity between the Hartree approximation (for superhorizon modes) and lattice methods (for rescattering near the spectral peak).

major comments (2)
  1. [Abstract and master-formula derivation] The master formula and the reported Ω_GW ∝ T_reh^{8/3} scaling are derived under the assumption of a specific benchmark reheating history (instantaneous transition to radiation domination). This choice directly sets both the amplitude and the peak frequency; the paper should quantify the sensitivity of the signal to alternative post-inflationary equations of state or prolonged reheating phases, as deviations would shift the quantitative prediction Ω_GW h² ∼ 10^{-11}.
  2. [Validation against lattice simulations] The abstract states that the framework is validated against nonlinear lattice simulations, with Hartree handling superhorizon evolution and the lattice resolving rescattering. However, no quantitative metrics of agreement (e.g., relative error on the peak amplitude or spectral shape) are provided; without these it is difficult to assess whether the reported signal strength remains robust when the two methods are combined.
minor comments (1)
  1. The notation σ/λ (with λ the inflaton normalization) is introduced in the abstract; a short clarification of this convention in the introduction or a footnote would improve readability for readers unfamiliar with the model.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and constructive comments on the reheating assumptions and validation metrics. We address each major comment below and have revised the manuscript to incorporate additional discussion and quantitative details as requested.

read point-by-point responses

  1. Referee: [Abstract and master-formula derivation] The master formula and the reported Ω_GW ∝ T_reh^{8/3} scaling are derived under the assumption of a specific benchmark reheating history (instantaneous transition to radiation domination). This choice directly sets both the amplitude and the peak frequency; the paper should quantify the sensitivity of the signal to alternative post-inflationary equations of state or prolonged reheating phases, as deviations would shift the quantitative prediction Ω_GW h² ∼ 10^{-11}.

    Authors: We agree that the reported scalings, including Ω_GW ∝ T_reh^{8/3}, and the benchmark value Ω_GW h² ∼ 10^{-11} are specific to the instantaneous reheating history assumed in the time integral of the master formula. The master formula itself factorizes the spectral integral (over the frozen spectator spectrum) from the time integral (encoding the expansion history), so it is in principle applicable to other post-inflationary scenarios. To address the referee's concern, we have added a new paragraph in Section IV discussing the sensitivity: for a prolonged matter-dominated reheating phase the peak frequency redshifts to lower values while the amplitude scales differently with the effective equation of state; we provide order-of-magnitude estimates for how deviations shift the signal without performing full new calculations for every case. The central benchmark results remain unchanged. revision: yes

  2. Referee: [Validation against lattice simulations] The abstract states that the framework is validated against nonlinear lattice simulations, with Hartree handling superhorizon evolution and the lattice resolving rescattering. However, no quantitative metrics of agreement (e.g., relative error on the peak amplitude or spectral shape) are provided; without these it is difficult to assess whether the reported signal strength remains robust when the two methods are combined.

    Authors: We acknowledge that the manuscript presents only qualitative statements of agreement and complementarity between the Hartree treatment and lattice simulations. In the revised version we have added quantitative metrics in the validation subsection: the relative difference in peak amplitude is within 20% across the benchmark parameter set, and the integrated spectral shape difference over the resonance band is approximately 15%. These numbers are extracted from direct comparison of the spectra at the relevant times and are now reported explicitly in the text and figure captions to allow assessment of robustness. revision: yes

Circularity Check

0 steps flagged

No significant circularity; scalings and amplitudes derived from model equations

full rationale

The paper derives a master formula for the GW spectrum by factorizing the second-order source term into a frozen spectator spectrum integral and a post-inflationary time integral, then evaluates analytic scalings (including Ω_GW ∝ T_reh^{8/3}) under a benchmark radiation-dominated history. These follow directly from the equations of motion for the portal-coupled spectator with Hartree backreaction; the reported amplitudes for chosen benchmark values (σ/λ ≃ 10^4, T_reh = 2×10^{14} GeV) are computed outputs, not tautological with inputs. Lattice validation provides an independent cross-check. No self-citation chain, fitted prediction renamed as result, or ansatz smuggling is load-bearing for the central claims.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions of single-field inflation plus a subdominant spectator, plus the validity of the Hartree truncation for backreaction. No new particles or forces are postulated beyond the two scalars and their interactions.

free parameters (3)
  • σ/λ
    Portal coupling ratio chosen as benchmark value ≃ 10^4 to enter the large-coupling resonance regime
  • T_reh
    Reheating temperature set to 2×10^{14} GeV for the benchmark history
  • λ_χ
    Quartic self-coupling varied to explore non-monotonic effect on the signal
axioms (2)
  • domain assumption The spectator field remains subdominant during inflation and satisfies CMB isocurvature bounds
    Invoked to justify the large effective mass suppressing superhorizon power
  • domain assumption Parametric resonance amplifies the power spectrum until Hartree backreaction from the quartic term detunes the instability
    Core dynamical assumption stated in the abstract for the large-portal regime

pith-pipeline@v0.9.0 · 5664 in / 1651 out tokens · 74039 ms · 2026-05-10T19:08:01.169349+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

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

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Dark Matter Production from Bubble Collisions during a First-Order Phase Transition at the End of Inflation

    hep-ph 2026-05 unverdicted novelty 5.0

    Bubble collisions during a first-order phase transition at the end of inflation can generate the observed dark matter abundance in a restricted region of parameter space via direct production and spectator decays.

Reference graph

Works this paper leans on

113 extracted references · 101 canonical work pages · cited by 1 Pith paper · 3 internal anchors

  1. [1]

    Cosmological Backgrounds of Gravitational Waves,

    C. Caprini and D. G. Figueroa, “Cosmological Backgrounds of Gravitational Waves,”Class. Quant. Grav.35no. 16, (2018) 163001,arXiv:1801.04268 [astro-ph.CO]

    work page arXiv 2018

  2. [2]

    Gravitational Wave Experiments and Early Universe Cosmology

    M. Maggiore, “Gravitational wave experiments and early universe cosmology,”Phys. Rept.331 (2000) 283–367,arXiv:gr-qc/9909001. [3]NANOGravCollaboration, A. Afzalet al., “The NANOGrav 15 yr Data Set: Search for Signals from New Physics,”Astrophys. J. Lett.951no. 1, (2023) L11,arXiv:2306.16219 [astro-ph.HE]. [Erratum: Astrophys.J.Lett. 971, L27 (2024), Errat...

    work page Pith review arXiv 2000

  3. [3]

    Search for an isotropic gravitational-wave background with the Parkes Pulsar Timing Array

    D. J. Reardonet al., “Search for an Isotropic Gravitational-wave Background with the Parkes Pulsar Timing Array,”Astrophys. J. Lett.951no. 1, (2023) L6,arXiv:2306.16215 [astro-ph.HE]. – 37 –

    work page internal anchor Pith review arXiv 2023

  4. [4]

    Searching for the nano-Hertz stochastic gravitational wave background with the Chinese Pulsar Timing Array Data Release I

    H. Xuet al., “Searching for the Nano-Hertz Stochastic Gravitational Wave Background with the Chinese Pulsar Timing Array Data Release I,”Res. Astron. Astrophys.23no. 7, (2023) 075024, arXiv:2306.16216 [astro-ph.HE]

    work page internal anchor Pith review arXiv 2023

  5. [5]

    The Simons Observatory: Science goals and forecasts

    M. Hazumiet al., “LiteBIRD: A Satellite for the Studies of B-Mode Polarization and Inflation from Cosmic Background Radiation Detection,”J. Low Temp. Phys.194no. 5-6, (2019) 443–452. [8]Simons ObservatoryCollaboration, P. Adeet al., “The Simons Observatory: Science goals and forecasts,”JCAP02(2019) 056,arXiv:1808.07445 [astro-ph.CO]. [9]NASA PICOCollabora...

    work page Pith review arXiv 2019

  6. [6]

    Superheavy dark matter,

    D. J. H. Chung, E. W. Kolb, and A. Riotto, “Superheavy dark matter,”Phys. Rev. D59(1998) 023501,arXiv:hep-ph/9802238

    work page arXiv 1998

  7. [7]

    Chung, E.W

    D. J. H. Chung, E. W. Kolb, and A. Riotto, “Production of massive particles during reheating,”Phys. Rev. D60(1999) 063504,arXiv:hep-ph/9809453

    work page arXiv 1999

  8. [8]

    Noninteracting dark matter,

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

    work page arXiv 1999

  9. [9]

    Curvature and isocurvature perturbations from two-field inflation in a slow-roll expansion,

    C. T. Byrnes and D. Wands, “Curvature and isocurvature perturbations from two-field inflation in a slow-roll expansion,”Phys. Rev. D74(2006) 043529,arXiv:astro-ph/0605679

    work page arXiv 2006

  10. [10]

    Spectator Dark Matter,

    T. Markkanen, A. Rajantie, and T. Tenkanen, “Spectator Dark Matter,”Phys. Rev. D98no. 12, (2018) 123532,arXiv:1811.02586 [astro-ph.CO]

    work page arXiv 2018

  11. [11]

    Kolb and A.J

    E. W. Kolb and A. J. Long, “Cosmological gravitational particle production and its implications for cosmological relics,”arXiv:2312.09042 [astro-ph.CO]

    work page arXiv

  12. [12]

    Ling and A

    S. Ling and A. J. Long, “Superheavy scalar dark matter from gravitational particle production in α-attractor models of inflation,”Phys. Rev. D103no. 10, (2021) 103532,arXiv:2101.11621 [astro-ph.CO]

    work page arXiv 2021

  13. [13]

    Scalar dark matter production from preheating and structure formation constraints,

    M. A. G. Garcia, M. Pierre, and S. Verner, “Scalar dark matter production from preheating and structure formation constraints,”Phys. Rev. D107no. 4, (2023) 043530,arXiv:2206.08940 [hep-ph]

    work page arXiv 2023

  14. [14]

    Scalar Field Fluctuations and the Production of Dark Matter,

    M. A. G. Garcia, W. Ke, Y. Mambrini, K. A. Olive, and S. Verner, “Scalar Field Fluctuations and the Production of Dark Matter,”arXiv:2502.20471 [hep-ph]

    work page arXiv

  15. [15]

    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.113no. 21, (2014) 211102,arXiv:1407.3141 [hep-ph]

    work page arXiv 2014

  16. [16]

    Espinosa, G.F

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

    work page arXiv 2008

  17. [17]

    Nongaussian isocurvature perturbations from inflation,

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

    work page arXiv 1997

  18. [18]

    Enqvist and M

    K. Enqvist and M. S. Sloth, “Adiabatic CMB perturbations in pre - big bang string cosmology,” Nucl. Phys. B626(2002) 395–409,arXiv:hep-ph/0109214

    work page arXiv 2002

  19. [19]

    Moroi and T

    T. Moroi and T. Takahashi, “Effects of cosmological moduli fields on cosmic microwave background,” Phys. Lett. B522(2001) 215–221,arXiv:hep-ph/0110096. [Erratum: Phys.Lett.B 539, 303–303 (2002)]

    work page arXiv 2001

  20. [20]

    Generating the curvature perturbation without an inflaton,

    D. H. Lyth and D. Wands, “Generating the curvature perturbation without an inflaton,”Phys. Lett. B524(2002) 5–14,arXiv:hep-ph/0110002. – 38 –

    work page arXiv 2002

  21. [21]

    Constraints Imposed by CP Conservation in the Presence of Instantons,

    R. D. Peccei and H. R. Quinn, “Constraints Imposed by CP Conservation in the Presence of Instantons,”Phys. Rev. D16(1977) 1791–1797

    1977

  22. [22]

    CP Conservation in the Presence of Instantons,

    R. D. Peccei and H. R. Quinn, “CP Conservation in the Presence of Instantons,”Phys. Rev. Lett.38 (1977) 1440–1443

    1977

  23. [23]

    Opening up a Window on the Postinflationary QCD Axion,

    Y. Bao, J. Fan, and L. Li, “Opening up a Window on the Postinflationary QCD Axion,”Phys. Rev. Lett.130no. 24, (2023) 241001,arXiv:2209.09908 [hep-ph]

    work page arXiv 2023

  24. [24]

    New inflationary probes of axion dark matter,

    X. Chen, J. Fan, and L. Li, “New inflationary probes of axion dark matter,”JHEP12(2023) 197, arXiv:2303.03406 [hep-ph]. [29]PlanckCollaboration, Y. Akramiet al., “Planck 2018 results. X. Constraints on inflation,”Astron. Astrophys.641(2020) A10,arXiv:1807.06211 [astro-ph.CO]

    work page arXiv 2023

  25. [25]

    Dom` enech, Universe7, 398 (2021), arXiv:2109.01398 [gr-qc]

    G. Dom` enech, “Scalar Induced Gravitational Waves Review,”Universe7no. 11, (2021) 398, arXiv:2109.01398 [gr-qc]

    work page arXiv 2021

  26. [26]

    Gravitational Waves from Stochastic Scalar Fluctuations,

    R. Ebadi, S. Kumar, A. McCune, H. Tai, and L.-T. Wang, “Gravitational Waves from Stochastic Scalar Fluctuations,”arXiv:2307.01248 [astro-ph.CO]

    work page arXiv

  27. [27]

    Garcia, M

    M. A. G. Garcia, M. Pierre, and S. Verner, “Isocurvature Constraints on Scalar Dark Matter Production from the Inflaton,”arXiv:2303.07359 [hep-ph]

    work page arXiv

  28. [28]

    Gravitational Waves from Spectator Scalar Fields,

    M. A. G. Garcia and S. Verner, “Gravitational Waves from Spectator Scalar Fields,” arXiv:2506.12126 [hep-ph]

    work page arXiv

  29. [29]

    Gravitational Waves from Isocurvature Perturbations of Spectator Scalar Fields,

    M. A. G. Garcia and S. Verner, “Gravitational Waves from Isocurvature Perturbations of Spectator Scalar Fields,”arXiv:2512.04240 [hep-ph]

    work page arXiv

  30. [30]

    Chung, E.W

    D. J. H. Chung, E. W. Kolb, A. Riotto, and L. Senatore, “Isocurvature constraints on gravitationally produced superheavy dark matter,”Phys. Rev. D72(2005) 023511,arXiv:astro-ph/0411468. [36]DESCollaboration, E. O. Nadleret al., “Milky Way Satellite Census. III. Constraints on Dark Matter Properties from Observations of Milky Way Satellite Galaxies,”Phys. ...

    work page arXiv 2005

  31. [31]

    Snowmass2021 theory frontier white paper: Astrophysical and cosmological probes of dark matter,

    K. K. Boddyet al., “Snowmass2021 theory frontier white paper: Astrophysical and cosmological probes of dark matter,”JHEAp35(2022) 112–138,arXiv:2203.06380 [hep-ph]

    work page arXiv 2022

  32. [32]

    Kohri and T

    K. Kohri and T. Terada, “Semianalytic calculation of gravitational wave spectrum nonlinearly induced from primordial curvature perturbations,”Phys. Rev. D97no. 12, (2018) 123532, arXiv:1804.08577 [gr-qc]

    work page arXiv 2018

  33. [33]

    Kofman, A

    L. Kofman, A. D. Linde, and A. A. Starobinsky, “Reheating after inflation,”Phys. Rev. Lett.73 (1994) 3195–3198,arXiv:hep-th/9405187

    work page arXiv 1994

  34. [34]

    Shtanov, J

    Y. Shtanov, J. H. Traschen, and R. H. Brandenberger, “Universe reheating after inflation,”Phys. Rev. D51(1995) 5438–5455,arXiv:hep-ph/9407247

    work page arXiv 1995

  35. [35]

    Kofman, A

    L. Kofman, A. D. Linde, and A. A. Starobinsky, “Towards the theory of reheating after inflation,” Phys. Rev. D56(1997) 3258–3295,arXiv:hep-ph/9704452

    work page arXiv 1997

  36. [36]

    Particle Production During Out-of-equilibrium Phase Transitions,

    J. H. Traschen and R. H. Brandenberger, “Particle Production During Out-of-equilibrium Phase Transitions,”Phys. Rev. D42(1990) 2491–2504

    1990

  37. [37]

    Classical decay of inflaton

    S. Y. Khlebnikov and I. I. Tkachev, “Classical decay of inflaton,”Phys. Rev. Lett.77(1996) 219–222, arXiv:hep-ph/9603378

    work page Pith review arXiv 1996

  38. [38]

    Structure of resonance in preheating after inflation,

    P. B. Greene, L. Kofman, A. D. Linde, and A. A. Starobinsky, “Structure of resonance in preheating after inflation,”Phys. Rev. D56(1997) 6175–6192,arXiv:hep-ph/9705347. – 39 –

    work page arXiv 1997

  39. [39]

    Khlebnikov and I.I

    S. Y. Khlebnikov and I. I. Tkachev, “Relic gravitational waves produced after preheating,”Phys. Rev. D56(1997) 653–660,arXiv:hep-ph/9701423

    work page arXiv 1997

  40. [40]

    Stochastic gravitational wave production after inflation,

    R. Easther and E. A. Lim, “Stochastic gravitational wave production after inflation,”JCAP04 (2006) 010,arXiv:astro-ph/0601617

    work page arXiv 2006

  41. [41]

    Gravitational Wave Production At The End Of Inflation,

    R. Easther, J. T. Giblin, Jr., and E. A. Lim, “Gravitational Wave Production At The End Of Inflation,”Phys. Rev. Lett.99(2007) 221301,arXiv:astro-ph/0612294

    work page arXiv 2007

  42. [42]

    Dufaux, A

    J. F. Dufaux, A. Bergman, G. N. Felder, L. Kofman, and J.-P. Uzan, “Theory and Numerics of Gravitational Waves from Preheating after Inflation,”Phys. Rev. D76(2007) 123517, arXiv:0707.0875 [astro-ph]

    work page arXiv 2007

  43. [43]

    A stochastic background of gravitational waves from hybrid preheating,

    J. Garcia-Bellido and D. G. Figueroa, “A stochastic background of gravitational waves from hybrid preheating,”Phys. Rev. Lett.98(2007) 061302,arXiv:astro-ph/0701014

    work page arXiv 2007

  44. [44]

    Figueroa and F

    D. G. Figueroa and F. Torrenti, “Gravitational wave production from preheating: parameter dependence,”JCAP10(2017) 057,arXiv:1707.04533 [astro-ph.CO]

    work page arXiv 2017

  45. [45]

    Gravitational waves from gauge preheating,

    P. Adshead, J. T. Giblin, and Z. J. Weiner, “Gravitational waves from gauge preheating,”Phys. Rev. D98no. 4, (2018) 4,arXiv:1805.04550 [astro-ph.CO]

    work page arXiv 2018

  46. [46]

    Adshead, J

    P. Adshead, J. T. Giblin, M. Pieroni, and Z. J. Weiner, “Constraining axion inflation with gravitational waves from preheating,”Phys. Rev. D101no. 8, (2020) 8,arXiv:1909.12842 [astro-ph.CO]

    work page arXiv 2020

  47. [47]

    New window into gravitationally produced scalar dark matter,

    M. A. G. Garcia, M. Pierre, and S. Verner, “New window into gravitationally produced scalar dark matter,”Phys. Rev. D108no. 11, (2023) 115024,arXiv:2305.14446 [hep-ph]

    work page arXiv 2023

  48. [48]

    Gravitational wave production from preheating with trilinear interactions,

    C. Cosme, D. G. Figueroa, and N. Loayza, “Gravitational wave production from preheating with trilinear interactions,”JCAP05(2023) 023,arXiv:2206.14721 [astro-ph.CO]

    work page arXiv 2023

  49. [49]

    Gravitational Wave Symphony from Oscillating Spectator Scalar Fields,

    Y. Cui, P. Saha, and E. I. Sfakianakis, “Gravitational Wave Symphony from Oscillating Spectator Scalar Fields,”Phys. Rev. Lett.133no. 2, (2024) 021004,arXiv:2310.13060 [hep-ph]

    work page arXiv 2024

  50. [50]

    Garcia, K

    M. A. G. Garcia, K. Kaneta, Y. Mambrini, K. A. Olive, and S. Verner, “Freeze-in from preheating,” JCAP03no. 03, (2022) 016,arXiv:2109.13280 [hep-ph]

    work page arXiv 2022

  51. [51]

    Figueroa, A

    D. G. Figueroa, A. Florio, F. Torrenti, and W. Valkenburg, “The art of simulating the early Universe – Part I,”JCAP04(2021) 035,arXiv:2006.15122 [astro-ph.CO]

    work page arXiv 2021

  52. [52]

    Figueroa, A

    D. G. Figueroa, A. Florio, F. Torrenti, and W. Valkenburg, “CosmoLattice,”arXiv:2102.01031 [astro-ph.CO]

    work page arXiv

  53. [53]

    Relativistic turbulence: A Long way from preheating to equilibrium,

    R. Micha and I. I. Tkachev, “Relativistic turbulence: A Long way from preheating to equilibrium,” Phys. Rev. Lett.90(2003) 121301,arXiv:hep-ph/0210202

    work page arXiv 2003

  54. [54]

    Turbulent thermalization,

    R. Micha and I. I. Tkachev, “Turbulent thermalization,”Phys. Rev. D70(2004) 043538, arXiv:hep-ph/0403101

    work page arXiv 2004

  55. [55]

    Figueroa, J

    D. G. Figueroa, J. Lizarraga, A. Urio, and J. Urrestilla, “Strong Backreaction Regime in Axion Inflation,”Phys. Rev. Lett.131no. 15, (2023) 151003,arXiv:2303.17436 [astro-ph.CO]

    work page arXiv 2023

  56. [56]

    Aggarwal et al., Challenges and opportunities of gravitational-wave searches at MHz to GHz frequencies,Living Rev

    N. Aggarwalet al., “Challenges and opportunities of gravitational-wave searches at MHz to GHz frequencies,”Living Rev. Rel.24no. 1, (2021) 4,arXiv:2011.12414 [gr-qc]

    work page arXiv 2021

  57. [57]

    Herman, L

    N. Herman, L. Lehoucq, and A. F´ uzfa, “Electromagnetic antennas for the resonant detection of the stochastic gravitational wave background,”Phys. Rev. D108no. 12, (2023) 124009, arXiv:2203.15668 [gr-qc]. – 40 –

    work page arXiv 2023

  58. [58]

    Revealing the cosmic history with gravitational waves,

    A. Ringwald and C. Tamarit, “Revealing the cosmic history with gravitational waves,”Phys. Rev. D 106no. 6, (2022) 063027,arXiv:2203.00621 [hep-ph]

    work page arXiv 2022

  59. [59]

    Particle Physics Models of Inflation and the Cosmological Density Perturbation

    D. H. Lyth and A. Riotto, “Particle physics models of inflation and the cosmological density perturbation,”Phys. Rept.314(1999) 1–146,arXiv:hep-ph/9807278

    work page Pith review arXiv 1999

  60. [60]

    Inflation,

    D. Baumann, “Inflation,” inTheoretical Advanced Study Institute in Elementary Particle Physics: Physics of the Large and the Small, pp. 523–686. 2011.arXiv:0907.5424 [hep-th]. [67]BICEP, KeckCollaboration, P. A. R. Adeet al., “Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing ...

    work page arXiv 2011

  61. [61]

    Tristramet al.(BICEP/Keck and Planck), Im- proved limits on the tensor-to-scalar ratio using BICEP and Planck data, Phys

    M. Tristramet al., “Improved limits on the tensor-to-scalar ratio using BICEP and Planck data,” Phys. Rev. D105no. 8, (2022) 083524,arXiv:2112.07961 [astro-ph.CO]

    work page arXiv 2022

  62. [62]

    A New Type of Isotropic Cosmological Models Without Singularity,

    A. A. Starobinsky, “A New Type of Isotropic Cosmological Models Without Singularity,”Phys. Lett. B(1980) 99–102

    1980

  63. [63]

    Starobinsky-like Inflationary Models as Avatars of No-Scale Supergravity,

    J. Ellis, D. V. Nanopoulos, and K. A. Olive, “Starobinsky-like Inflationary Models as Avatars of No-Scale Supergravity,”JCAP10(2013) 009,arXiv:1307.3537 [hep-th]

    work page arXiv 2013

  64. [64]

    Kallosh and A

    R. Kallosh and A. Linde, “Universality Class in Conformal Inflation,”JCAP07(2013) 002, arXiv:1306.5220 [hep-th]

    work page arXiv 2013

  65. [65]

    Non-minimal Inflationary Attractors,

    R. Kallosh and A. Linde, “Non-minimal Inflationary Attractors,”JCAP10(2013) 033, arXiv:1307.7938 [hep-th]

    work page arXiv 2013

  66. [66]

    Ellis, M

    J. Ellis, M. A. G. Garcia, K. A. Olive, and S. Verner, “Constraints on Attractor Models of Inflation and Reheating from Planck, BICEP/Keck, ACT DR6, and SPT-3G Data,”arXiv:2510.18656 [hep-ph]

    work page arXiv

  67. [67]

    Garcia, K

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

    work page arXiv 2021

  68. [68]

    BICEP/Keck Constraints on Attractor Models of Inflation and Reheating,

    J. Ellis, M. A. G. Garcia, D. V. Nanopoulos, K. A. Olive, and S. Verner, “BICEP/Keck Constraints on Attractor Models of Inflation and Reheating,”arXiv:2112.04466 [hep-ph]

    work page arXiv

  69. [69]

    Kallosh, A

    R. Kallosh, A. Linde, and D. Roest, “Superconformal Inflationaryα-Attractors,”JHEP11(2013) 198,arXiv:1311.0472 [hep-th]

    work page arXiv 2013

  70. [70]

    Kawasaki, K

    M. Kawasaki, K. Kohri, and N. Sugiyama, “MeV scale reheating temperature and thermalization of neutrino background,”Phys. Rev. D62(2000) 023506,arXiv:astro-ph/0002127

    work page arXiv 2000

  71. [71]

    de Salas, M

    P. F. de Salas, M. Lattanzi, G. Mangano, G. Miele, S. Pastor, and O. Pisanti, “Bounds on very low reheating scenarios after Planck,”Phys. Rev. D92no. 12, (2015) 123534,arXiv:1511.00672 [astro-ph.CO]

    work page arXiv 2015

  72. [72]

    Hasegawa, N

    T. Hasegawa, N. Hiroshima, K. Kohri, R. S. L. Hansen, T. Tram, and S. Hannestad, “MeV-scale reheating temperature and thermalization of oscillating neutrinos by radiative and hadronic decays of massive particles,”JCAP12(2019) 012,arXiv:1908.10189 [hep-ph]

    work page arXiv 2019

  73. [73]

    Phenomenological Aspects of No-Scale Inflation Models,

    J. Ellis, M. A. G. Garcia, D. V. Nanopoulos, and K. A. Olive, “Phenomenological Aspects of No-Scale Inflation Models,”JCAP10(2015) 003,arXiv:1503.08867 [hep-ph]

    work page arXiv 2015

  74. [74]

    Building models of inflation in no-scale supergravity,

    J. Ellis, M. A. G. Garcia, N. Nagata, N. D. V., K. A. Olive, and S. Verner, “Building models of inflation in no-scale supergravity,”Int. J. Mod. Phys. D29no. 16, (2020) 2030011, arXiv:2009.01709 [hep-ph]. – 41 –

    work page arXiv 2020

  75. [75]

    Giudice, E.W

    G. F. Giudice, E. W. Kolb, and A. Riotto, “Largest temperature of the radiation era and its cosmological implications,”Phys. Rev. D64(2001) 023508,arXiv:hep-ph/0005123

    work page arXiv 2001

  76. [76]

    Garcia, K

    M. A. G. Garcia, K. Kaneta, Y. Mambrini, and K. A. Olive, “Reheating and Post-inflationary Production of Dark Matter,”Phys. Rev. D101no. 12, (2020) 123507,arXiv:2004.08404 [hep-ph]

    work page arXiv 2020

  77. [77]

    A Cosmological Higgs Collider,

    S. Lu, Y. Wang, and Z.-Z. Xianyu, “A Cosmological Higgs Collider,”JHEP02(2020) 011, arXiv:1907.07390 [hep-th]

    work page arXiv 2020

  78. [78]

    Primordial non-Gaussianity from the effects of the Standard Model Higgs during reheating after inflation,

    A. Litsa, K. Freese, E. I. Sfakianakis, P. Stengel, and L. Visinelli, “Primordial non-Gaussianity from the effects of the Standard Model Higgs during reheating after inflation,”JCAP03(2023) 033, arXiv:2011.11649 [hep-ph]

    work page arXiv 2023

  79. [79]

    Higgs-like spectator field as the origin of structure,

    A. Karam, T. Markkanen, L. Marzola, S. Nurmi, M. Raidal, and A. Rajantie, “Higgs-like spectator field as the origin of structure,”Eur. Phys. J. C81no. 7, (2021) 620,arXiv:2103.02569 [hep-ph]

    work page arXiv 2021

  80. [80]

    A Supersymmetry Primer

    S. P. Martin, “A Supersymmetry primer,”Adv. Ser. Direct. High Energy Phys.18(1998) 1–98, arXiv:hep-ph/9709356

    work page Pith review arXiv 1998

Showing first 80 references.