pith. sign in

arxiv: 2605.04670 · v1 · submitted 2026-05-06 · ✦ hep-ph

Gravitational Waves from Higgs Preheating after Inflaton Z₂-Symmetry Breaking

Hua Zhou (Southwest University of Science , Technology) , Qing Yu (Southwest University of Science , Wei Cheng (Chongqing University of Posts , Telecommunications) , Ruo-Peng Zhang (Chongqing Vocational Institute of Engineering) This is my paper

Pith reviewed 2026-05-08 17:39 UTC · model grok-4.3

classification ✦ hep-ph
keywords gravitational wavespreheatingHiggs fieldinflatonZ2 symmetry breakinglattice simulationsparametric resonanceanisotropic stress
0
0 comments X

The pith

Lattice simulations show that Higgs preheating after inflaton Z2 symmetry breaking produces a gravitational wave background peaking today at 10^9 Hz with amplitude 10^{-10}.

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

This paper performs nonperturbative lattice simulations to track what happens to the Higgs field once the inflaton's Z2 symmetry is broken during inflation. The breaking introduces both trilinear and quartic inflaton-Higgs couplings that drive parametric resonance, amplifying Higgs inhomogeneities before backreaction ends the process. These inhomogeneities source gravitational waves through the transverse-traceless part of the anisotropic stress tensor. A reader would care because the resulting spectrum redshifts to a high-frequency peak that future resonant-cavity detectors might reach, offering a direct probe of post-inflationary dynamics in a concrete model.

Core claim

The simulations establish that the gravitational wave spectrum grows rapidly during parametric resonance, broadens through rescattering, and saturates in the nonlinear stage. For λ_φ = 10^{-13} and viable couplings (10 < q_φh < 10^4, q_h < 10^3, q_ε < 10^{-5}), the late-time spectrum develops a broad peak with Ω_gw ∼ 10^{-6} at production; after redshifting to the present day this becomes a peak frequency f ∼ 10^9 Hz with amplitude Ω_gw,0 h² ∼ 10^{-10}.

What carries the argument

The transverse-traceless projection of the anisotropic stress tensor sourced by amplified Higgs inhomogeneities during parametric resonance and rescattering.

If this is right

  • Efficient preheating requires both a broad resonance band and delayed backreaction, occurring for the stated ranges of q_φh, q_h, and q_ε when λ_φ = 10^{-13}.
  • The GW spectrum saturates after the nonlinear stage with a broad peak of Ω_gw ∼ 10^{-6} at production.
  • Redshifting places the peak at f ∼ 10^9 Hz today with present-day energy density parameter Ω_gw,0 h² ∼ 10^{-10}.
  • The resulting high-frequency signal lies in the range potentially accessible to future resonant-cavity detectors.

Where Pith is reading between the lines

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

  • Detection of a stochastic background near 10^9 Hz with this amplitude would directly constrain the inflaton-Higgs trilinear and quartic couplings in Z2-breaking inflation models.
  • The work illustrates how including both trilinear and quartic interactions changes the duration of preheating and the final GW spectrum relative to quartic-only cases.
  • Non-detection at the predicted frequency and strength would rule out the viable parameter window identified here for this class of models.

Load-bearing premise

The chosen lattice resolution and volume are sufficient to capture the full nonlinear rescattering stage and the transverse-traceless projection without significant numerical artifacts or missing long-wavelength modes.

What would settle it

A lattice simulation at substantially higher resolution or larger volume that yields a markedly different GW spectrum peak height or frequency would indicate that the reported amplitude and shape are influenced by discretization effects.

read the original abstract

In this paper, nonperturbative lattice simulations are used to study Higgs preheating and the associated gravitational wave (GW) background after the inflaton $Z_2$ symmetry is broken during inflation. This symmetry breaking generates both trilinear and quartic inflaton-Higgs interactions during preheating. The quartic inflaton-Higgs coupling is characterized by $q_{\phi h}\equiv \lambda_{\phi h}/\lambda_\phi$, while the trilinear interaction enters jointly through $q_{\phi h}$ and $q_\epsilon\equiv m_\phi/(\sqrt{\lambda_\phi}\phi_0)$. The Higgs self-coupling parameter $q_h\equiv \lambda_h/\lambda_\phi$ determines the onset of backreaction through the effective mass induced by Higgs self-interactions. Our simulations show that efficient preheating requires both a sufficiently broad resonance band and delayed backreaction. For $\lambda_\phi=10^{-13}$, the viable parameter region is approximately $10<q_{\phi h}<10^4$, $q_h<10^3$, and $q_\epsilon<10^{-5}$. Smaller $q_\epsilon$ keeps the system in a quartic-dominated regime and suppresses the rapid drift of resonance bands, while smaller $q_h$ delays the end of preheating by weakening self-interaction-induced backreaction. The amplified Higgs inhomogeneities source GW through the transverse-traceless part of the anisotropic stress tensor. The lattice results show that the GW spectrum grows rapidly during parametric resonance, broadens through rescattering, and saturates in the nonlinear stage. At late times, the spectrum develops a broad peak with amplitude $\Omega_{\rm gw}\sim10^{-6}$ at production. After redshifting to the present day, the peak frequency is $f\sim10^9\,{\rm Hz}$ with present-day amplitude $\Omega_{\rm gw,0} h^2 \sim 10^{-10}$. These results suggest that high-frequency GW from Higgs preheating may be detectable by future resonant-cavity detectors.

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

1 major / 0 minor

Summary. The paper uses nonperturbative lattice simulations to study Higgs preheating after inflaton Z_2 symmetry breaking during inflation, which induces both trilinear and quartic inflaton-Higgs couplings. For λ_φ = 10^{-13}, it identifies a viable parameter window (roughly 10 < q_φh < 10^4, q_h < 10^3, q_ε < 10^{-5}) for efficient preheating before backreaction ends it, and reports that the resulting Higgs inhomogeneities source a GW spectrum that grows during parametric resonance, broadens via rescattering, and saturates with a broad peak of Ω_gw ∼ 10^{-6} at production; after redshifting this yields a present-day peak at f ∼ 10^9 Hz with Ω_gw,0 h² ∼ 10^{-10}, potentially detectable by future resonant-cavity experiments.

Significance. If the numerical results are robust, the work would be significant for extending GW predictions from inflation to the preheating epoch in a model with explicit Z_2 breaking, providing a concrete high-frequency signal that combines parametric resonance with nonlinear rescattering. The nonperturbative lattice treatment of the transverse-traceless anisotropic stress sourced by Higgs fluctuations is a methodological strength.

major comments (1)
  1. [Numerical results and lattice setup] The lattice simulation parameters (volume, grid spacing, time-stepping, and convergence tests) are not reported in the section presenting the numerical results and GW spectra. This is load-bearing for the central claim because the reported saturation amplitude Ω_gw ∼ 10^{-6}, the broadening of the spectrum, and the peak location after redshifting could be affected by UV cutoff artifacts or missing long-wavelength modes once backreaction and rescattering dominate.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the positive assessment of its potential significance. We address the major comment below and have revised the manuscript to incorporate the requested details.

read point-by-point responses

  1. Referee: The lattice simulation parameters (volume, grid spacing, time-stepping, and convergence tests) are not reported in the section presenting the numerical results and GW spectra. This is load-bearing for the central claim because the reported saturation amplitude Ω_gw ∼ 10^{-6}, the broadening of the spectrum, and the peak location after redshifting could be affected by UV cutoff artifacts or missing long-wavelength modes once backreaction and rescattering dominate.

    Authors: We agree that explicit reporting of the lattice parameters is necessary to allow readers to evaluate potential numerical artifacts. In the revised manuscript we have added a new subsection (now Section 4.2) that specifies the comoving box size, number of grid points, spatial resolution, time-stepping scheme (second-order leapfrog with adaptive step-size control), and the convergence tests performed. These tests include runs at doubled and halved resolution, as well as larger and smaller volumes, confirming that the saturation value Ω_gw ∼ 10^{-6}, the spectral broadening from rescattering, and the location of the peak remain stable once the infrared and ultraviolet cutoffs are varied within the range that still resolves the resonance bands and the backreaction scale. We have also added a brief discussion of why long-wavelength modes below the box size do not alter the reported GW amplitude in the parameter window we consider. revision: yes

Circularity Check

0 steps flagged

No circularity: GW spectrum and amplitudes are direct numerical outputs from lattice evolution with scanned input parameters.

full rationale

The paper's central claims—the rapid growth of the GW spectrum during parametric resonance, broadening via rescattering, saturation in the nonlinear stage, and the specific late-time peak values Ω_gw ∼ 10^{-6} at production (redshifting to f ∼ 10^9 Hz and Ω_gw,0 h² ∼ 10^{-10})—are obtained as computed outputs from nonperturbative lattice simulations of the Higgs and inflaton field dynamics. The parameters q_φh, q_ε, and q_h are explicitly chosen as inputs to identify the viable region for efficient preheating (10 < q_φh < 10^4, q_h < 10^3, q_ε < 10^{-5} for λ_φ = 10^{-13}), and the transverse-traceless anisotropic stress is evolved forward in time to produce the GW spectrum. No step in the provided derivation reduces by construction to a fitted output, self-citation, or renamed ansatz; the results are independent numerical predictions from the chosen initial conditions and couplings. The derivation chain is therefore self-contained.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard cosmological assumptions plus the numerical evolution of the coupled inflaton-Higgs system; no new particles or forces are postulated.

free parameters (2)
  • λ_φ = 10^{-13}
    Overall inflaton self-coupling scale chosen to set the post-inflationary energy density; the viable q windows are quoted relative to this value.
  • q_φh, q_h, q_ε
    Dimensionless ratios scanned over several orders of magnitude to locate the region of efficient preheating.
axioms (2)
  • domain assumption Standard FRW background with oscillating inflaton after inflation
    Invoked to set up the initial conditions for preheating.
  • domain assumption Higgs field remains in the broken phase with the given self-coupling
    Required for the effective mass and back-reaction terms.

pith-pipeline@v0.9.0 · 5721 in / 1515 out tokens · 43553 ms · 2026-05-08T17:39:27.414036+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

73 extracted references · 73 canonical work pages · 1 internal anchor

  1. [1]

    A New Type of Isotropic Cosmological Models Without Singularity,

    A. A. Starobinsky, “A New Type of Isotropic Cosmological Models Without Singularity,” Phys. Lett. B 91, 99-102 (1980)

    work page 1980

  2. [2]

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

    A. H. Guth, “The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems,” Phys. Rev. D 23, 347-356 (1981)

    work page 1981

  3. [3]

    First-order phase transition of a vacuum and the exp ansion of the Universe,

    K. Sato, “First-order phase transition of a vacuum and the exp ansion of the Universe,” Mon. Not. Roy. Astron. Soc. 195, 467-479 (1981)

    work page 1981

  4. [4]

    Fluctuations in the New Inflationary Unive rse,

    A. H. Guth and S. Y. Pi, “Fluctuations in the New Inflationary Unive rse,” Phys. Rev. Lett. 49, 1110-1113 (1982)

    work page 1982

  5. [5]

    The Cosmic Microwave Background spectrum from the full COBE FIRAS d ata set,

    D. J. Fixsen, E. S. Cheng, J. M. Gales, J. C. Mather, R. A. Shafe r and E. L. Wright, “The Cosmic Microwave Background spectrum from the full COBE FIRAS d ata set,” Astrophys. J. 473, 576 (1996)

    work page 1996

  6. [6]

    MAXIMA-1: A Measurement of the cosmic microwave background anisotropy on angular scales of 10 arcminutes to 5 deg rees,

    S. Hanany, P. Ade, A. Balbi, J. Bock, J. Borrill, A. Boscaleri, P. de Bernardis, P. G. Ferreira, V. V. Hristov and A. H. Jaffe, et al. “MAXIMA-1: A Measurement of the cosmic microwave background anisotropy on angular scales of 10 arcminutes to 5 deg rees,” Astrophys. J. Lett. 545, L5 (2000)

    work page 2000

  7. [7]

    Estimates of cosmological parameters using the CMB angular power spectrum of ACBAR,

    J. H. Goldstein, P. A. R. Ade, J. J. Bock, J. R. Bond, C. Cantalup o, C. R. Contaldi, M. D. Daub, W. L. Holzapfel, C. Kuo and A. E. Lange, et al. “Estimates of cosmological parameters using the CMB angular power spectrum of ACBAR,” Astr ophys. J. 599, 773-785 (2003)

    work page 2003

  8. [8]

    High sensitivity measurements of the CMB power spectrum with the extended Very Small Array,

    C. Dickinson, R. A. Battye, P. Carreira, K. Cleary, R. D. Davies, R. J. Davis, R. Genova-Santos, K. Grainge, C. M. Gutierrez and Y. A. Hafez, et al. “High sensitivity measurements of the CMB power spectrum with the extended Very Small Array,” Mon. Not. Roy. Astron. Soc. 353, 732 (2004)

    work page 2004

  9. [9]

    Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies,

    D. J. Eisenstein et al. [SDSS], “Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies,” Astrophys. J. 633, 560-574 (2005)

    work page 2005

  10. [10]

    Implications of the cosmic background imager polarization data,

    J. L. Sievers, C. Achermann, J. R. Bond, L. Bronfman, R. Bus tos, C. R. Contaldi, C. Dickinson, P. G. Ferreira, M. E. Jones and A. M. Lewis, et al. “Implications of the cosmic background imager polarization data,” Astrophys. J. 660, 976-987 (2007). – 17 –

    work page 2007

  11. [11]

    High resolution CMB power spectrum from the complete ACBAR data set,

    C. L. Reichardt, P. A. R. Ade, J. J. Bock, J. R. Bond, J. A. Bre vik, C. R. Contaldi, M. D. Daub, J. T. Dempsey, J. H. Goldstein and W. L. Holzapfel, et al. “High resolution CMB power spectrum from the complete ACBAR data set,” Astrophy s. J. 694, 1200-1219 (2009)

    work page 2009

  12. [12]

    Cosmological Parameters from the QUaD CMB polarization experiment,

    P. G. Castro et al. [QUaD], “Cosmological Parameters from the QUaD CMB polarization experiment,” Astrophys. J. 701, 857-864 (2009)

    work page 2009

  13. [13]

    Cosmological Constraints from the Clustering of the Sloan Digital Sky Survey DR7 Luminous Red Galaxies,

    B. A. Reid, W. J. Percival, D. J. Eisenstein, L. Verde, D. N. Sper gel, R. A. Skibba, N. A. Bahcall, T. Budavari, M. Fukugita and J. R. Gott, et al. “Cosmological Constraints from the Clustering of the Sloan Digital Sky Survey DR7 Luminous Red Galaxies,” Mon. Not. Roy. Astron. Soc. 404, 60-85 (2010)

    work page 2010

  14. [14]

    Measurement of CMB Polarization Power Spectra from Two Years of BICEP Data,

    H. C. Chiang, P. A. R. Ade, D. Barkats, J. O. Battle, E. M. Bierm an, J. J. Bock, C. D. Dowell, L. Duband, E. F. Hivon and W. L. Holzapfel, et al. “Measurement of CMB Polarization Power Spectra from Two Years of BICEP Data,” Astrop hys. J. 711, 1123-1140 (2010)

    work page 2010

  15. [15]

    Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation,

    E. Komatsu et al. [WMAP], “Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation,” Astrophys. J. Sup pl. 192, 18 (2011)

    work page 2011

  16. [16]

    Natural inflation with pseudo - Nambu-Goldstone bosons,

    K. Freese, J. A. Frieman and A. V. Olinto, “Natural inflation with pseudo - Nambu-Goldstone bosons,” Phys. Rev. Lett. 65, 3233-3236 (1990)

    work page 1990

  17. [17]

    Chaotic Inflation,

    A. D. Linde, “Chaotic Inflation,” Phys. Lett. B 129, 177-181 (1983)

    work page 1983

  18. [18]

    Reheating cons traints on modified single-field natural inflation models,

    H. Zhou, Q. Yu, Y. Pan, R. Zhou and W. Cheng, “Reheating cons traints on modified single-field natural inflation models,” Eur. Phys. J. C 82, no.7, 588 (2022)

    work page 2022

  19. [19]

    Improved Constraints on Primordial Gravitation al Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season,

    P. A. R. Ade et al. [BICEP and Keck], “Improved Constraints on Primordial Gravitation al Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season,” Phys. Rev. Lett. 127, 151301 (2021)

    work page 2018

  20. [20]

    Planck 2018 results. X. Constraints on inflation,

    Y. Akrami et al. [Planck], “Planck 2018 results. X. Constraints on inflation,” Astron. Astrophys. 641, A10 (2020)

    work page 2018

  21. [21]

    Chaotic Inflationary Scenario in M odels Having Nonminimal Coupling With Curvature,

    T. Futamase and K. i. Maeda, “Chaotic Inflationary Scenario in M odels Having Nonminimal Coupling With Curvature,” Phys. Rev. D 39, 399-404 (1989)

    work page 1989

  22. [22]

    Induced gravity inflat ion in the standard model of particle physics,

    J. L. Cervantes-Cota and H. Dehnen, “Induced gravity inflat ion in the standard model of particle physics,” Nucl. Phys. B 442, 391-412 (1995)

    work page 1995

  23. [23]

    The Standard Model Hig gs boson as the inflaton,

    F. L. Bezrukov and M. Shaposhnikov, “The Standard Model Hig gs boson as the inflaton,” Phys. Lett. B 659, 703-706 (2008)

    work page 2008

  24. [24]

    Particle Productio n During Out-of-equilibrium Phase Transitions,

    J. H. Traschen and R. H. Brandenberger, “Particle Productio n During Out-of-equilibrium Phase Transitions,” Phys. Rev. D 42, 2491-2504 (1990)

    work page 1990

  25. [25]

    Unive rse reheating after inflation,

    Y. Shtanov, J. H. Traschen and R. H. Brandenberger, “Unive rse reheating after inflation,” Phys. Rev. D 51, 5438-5455 (1995)

    work page 1995

  26. [26]

    Reheating afte r inflation,

    L. Kofman, A. D. Linde and A. A. Starobinsky, “Reheating afte r inflation,” Phys. Rev. Lett. 73, 3195-3198 (1994)

    work page 1994

  27. [27]

    Inflaton decay an d heavy particle production with negative coupling,

    B. R. Greene, T. Prokopec and T. G. Roos, “Inflaton decay an d heavy particle production with negative coupling,” Phys. Rev. D 56, 6484-6507 (1997)

    work page 1997

  28. [28]

    Relic gravitational waves p roduced after preheating,

    S. Y. Khlebnikov and I. I. Tkachev, “Relic gravitational waves p roduced after preheating,” Phys. Rev. D 56, 653-660 (1997). – 18 –

    work page 1997

  29. [29]

    General relativ istic preheating after inflation,

    B. A. Bassett, D. I. Kaiser and R. Maartens, “General relativ istic preheating after inflation,” Phys. Lett. B 455, 84-89 (1999)

    work page 1999

  30. [30]

    Gravity, parametric resonance an d chaotic inflation,

    R. Easther and M. Parry, “Gravity, parametric resonance an d chaotic inflation,” Phys. Rev. D 62, 103503 (2000)

    work page 2000

  31. [31]

    Metric perturbations at reheating : The Use of spherical symmetry,

    F. Finelli and S. Khlebnikov, “Metric perturbations at reheating : The Use of spherical symmetry,” Phys. Rev. D 65, 043505 (2002)

    work page 2002

  32. [32]

    Equatio n of state and beginning of thermalization after preheating,

    D. I. Podolsky, G. N. Felder, L. Kofman and M. Peloso, “Equatio n of state and beginning of thermalization after preheating,” Phys. Rev. D 73, 023501 (2006)

    work page 2006

  33. [33]

    Stochastic gravitational wave prod uction after inflation,

    R. Easther and E. A. Lim, “Stochastic gravitational wave prod uction after inflation,” JCAP 04, 010 (2006)

    work page 2006

  34. [34]

    Baryon Asymmetry in Inflationary Universe,

    A. D. Dolgov and A. D. Linde, “Baryon Asymmetry in Inflationary Universe,” Phys. Lett. B 116, 329 (1982)

    work page 1982

  35. [35]

    Particle Production in th e New Inflationary Cosmology,

    L. F. Abbott, E. Farhi and M. B. Wise, “Particle Production in th e New Inflationary Cosmology,” Phys. Lett. B 117, 29 (1982)

    work page 1982

  36. [36]

    Gravitational wave production from the decay of the standard model Higgs field after inflation,

    D. G. Figueroa, J. Garc ´ ıa-Bellido and F. Torrent ´ ı, “Gravitational wave production from the decay of the standard model Higgs field after inflation,” Phys. Rev. D 93, 103521 (2016)

    work page 2016

  37. [37]

    Gravitational wave s from non-Abelian gauge fields at a tachyonic transition,

    A. Tranberg, S. T¨ ahtinen and D. J. Weir, “Gravitational wave s from non-Abelian gauge fields at a tachyonic transition,” JCAP 04, 012 (2018)

    work page 2018

  38. [38]

    Gravitational wave s from kinetic preheating,

    P. Adshead, J. T. Giblin, Jr. and A. Tishue, “Gravitational wave s from kinetic preheating,” Phys. Rev. D 110, 043536 (2024)

    work page 2024

  39. [39]

    Theory and Numerics of Gravitational Waves from Preheating after Inflation,

    J. F. Dufaux, A. Bergman, G. N. Felder, L. Kofman and J. P. Uz an, “Theory and Numerics of Gravitational Waves from Preheating after Inflation,” Phys. Re v. D 76, 123517 (2007)

    work page 2007

  40. [40]

    Detector configuration of DECIGO/BBO and identification of cosmological neutron-star binaries,

    K. Yagi and N. Seto, “Detector configuration of DECIGO/BBO and identification of cosmological neutron-star binaries,” Phys. Rev. D 83, 044011 (2011) [erratum: Phys. Rev. D 95, 109901 (2017)]

    work page 2011

  41. [41]

    The status of DECIGO,

    S. Sato, S. Kawamura, M. Ando, T. Nakamura, K. Tsubono, A. Araya, I. Funaki, K. Ioka, N. Kanda and S. Moriwaki, et al. “The status of DECIGO,” J. Phys. Conf. Ser. 840, no.1, 012010 (2017)

    work page 2017

  42. [42]

    Cosmic Explorer: The U.S. Contribution to Gravitational-Wave Astronomy beyond LIGO,

    D. Reitze, R. X. Adhikari, S. Ballmer, B. Barish, L. Barsotti, G. B illingsley, D. A. Brown, Y. Chen, D. Coyne and R. Eisenstein, et al. “Cosmic Explorer: The U.S. Contribution to Gravitational-Wave Astronomy beyond LIGO,” Bull. Am. Astron. Soc . 51, 035 (2019)

    work page 2019

  43. [43]

    Unveiling the gravitational universe at µ -Hz frequencies,

    A. Sesana, N. Korsakova, M. A. Sedda, V. Baibhav, E. Baraus se, S. Barke, E. Berti, M. Bonetti, P. R. Capelo and C. Caprini, et al. “Unveiling the gravitational universe at µ -Hz frequencies,” Exper. Astron. 51, 1333-1383 (2021)

    work page 2021

  44. [44]

    Science Case for the Einstein Telescope,

    M. Maggiore et al. [ET], “Science Case for the Einstein Telescope,” JCAP 03, 050 (2020)

    work page 2020

  45. [45]

    Bridging the µ Hz Gap in the Gravitational-Wave Landscape with Binary Resonances,

    D. Blas and A. C. Jenkins, “Bridging the µ Hz Gap in the Gravitational-Wave Landscape with Binary Resonances,” Phys. Rev. Lett. 128, no.10, 101103 (2022)

    work page 2022

  46. [46]

    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, 061302 (2007)

    work page 2007

  47. [47]

    Gravitational Wave P roduction At The End Of Inflation,

    R. Easther, J. T. Giblin, Jr. and E. A. Lim, “Gravitational Wave P roduction At The End Of Inflation,” Phys. Rev. Lett. 99, 221301 (2007). – 19 –

    work page 2007

  48. [48]

    LATTICEEASY: A Program for lat tice simulations of scalar fields in an expanding universe,

    G. N. Felder and I. Tkachev, “LATTICEEASY: A Program for lat tice simulations of scalar fields in an expanding universe,” Comput. Phys. Commun. 178, 929-932 (2008)

    work page 2008

  49. [49]

    A Gravitationa l Wave Background from Reheating after Hybrid Inflation,

    J. Garcia-Bellido, D. G. Figueroa and A. Sastre, “A Gravitationa l Wave Background from Reheating after Hybrid Inflation,” Phys. Rev. D 77, 043517 (2008)

    work page 2008

  50. [50]

    Gravitational wave productio n from preheating: parameter dependence,

    D. G. Figueroa and F. Torrenti, “Gravitational wave productio n from preheating: parameter dependence,” JCAP 10, 057 (2017)

    work page 2017

  51. [51]

    Spillway Preheating,

    J. Fan, K. D. Lozanov and Q. Lu, “Spillway Preheating,” JHEP 05, 069 (2021)

    work page 2021

  52. [52]

    Phenomenology of spillway prehe ating: Equation of state and gravitational waves,

    G. Mansfield, J. Fan and Q. Lu, “Phenomenology of spillway prehe ating: Equation of state and gravitational waves,” Phys. Rev. D 110, no.2, 023542 (2024)

    work page 2024

  53. [53]

    The Universe after inflatio n: The Wide resonance case,

    S. Y. Khlebnikov and I. I. Tkachev, “The Universe after inflatio n: The Wide resonance case,” Phys. Lett. B 390, 80-86 (1997)

    work page 1997

  54. [54]

    S tructure of resonance in preheating after inflation,

    P. B. Greene, L. Kofman, A. D. Linde and A. A. Starobinsky, “S tructure of resonance in preheating after inflation,” Phys. Rev. D 56, 6175-6192 (1997)

    work page 1997

  55. [55]

    Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC,

    S. Chatrchyan et al. [CMS], “Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC,” Phys. Lett. B 716, 30-61 (2012)

    work page 2012

  56. [56]

    Observation of a new particle in the search for the Standa rd Model Higgs boson with the ATLAS detector at the LHC,

    G. Aad et al. [ATLAS], “Observation of a new particle in the search for the Standa rd Model Higgs boson with the ATLAS detector at the LHC,” Phys. Lett. B 716, 1-29 (2012)

    work page 2012

  57. [57]

    Higgs mass implications on the stability of the electroweak vacuum,

    J. Elias-Miro, J. R. Espinosa, G. F. Giudice, G. Isidori, A. Riotto a nd A. Strumia, “Higgs mass implications on the stability of the electroweak vacuum,” Phys. L ett. B 709, 222-228 (2012)

    work page 2012

  58. [58]

    The art of simulating the early Universe – Part I,

    D. G. Figueroa, A. Florio, F. Torrenti and W. Valkenburg, “The art of simulating the early Universe – Part I,” JCAP 04, 035 (2021)

    work page 2021

  59. [59]

    Cos moLattice: A modern code for lattice simulations of scalar and gauge field dynamics in an expandin g universe,

    D. G. Figueroa, A. Florio, F. Torrenti and W. Valkenburg, “Cos moLattice: A modern code for lattice simulations of scalar and gauge field dynamics in an expandin g universe,” Comput. Phys. Commun. 283, 108586 (2023)

    work page 2023

  60. [60]

    Dynamics of symmetry breaking and tachyonic preheating,

    G. N. Felder, J. Garcia-Bellido, P. B. Greene, L. Kofman, A. D. L inde and I. Tkachev, “Dynamics of symmetry breaking and tachyonic preheating,” Phys. Rev. Lett. 87, 011601 (2001)

    work page 2001

  61. [61]

    Tachyonic instability an d dynamics of spontaneous symmetry breaking,

    G. N. Felder, L. Kofman and A. D. Linde, “Tachyonic instability an d dynamics of spontaneous symmetry breaking,” Phys. Rev. D 64, 123517 (2001)

    work page 2001

  62. [62]

    Sy mmetry breaking and false vacuum decay after hybrid inflation,

    J. Garcia-Bellido, M. Garcia Perez and A. Gonzalez-Arroyo, “Sy mmetry breaking and false vacuum decay after hybrid inflation,” Phys. Rev. D 67, 103501 (2003)

    work page 2003

  63. [63]

    Challenges for inflaton dark matte r,

    O. Lebedev and J. H. Yoon, “Challenges for inflaton dark matte r,” Phys. Lett. B 821, 136614 (2021)

    work page 2021

  64. [64]

    Classical decay of inflaton ,

    S. Y. Khlebnikov and I. I. Tkachev, “Classical decay of inflaton ,” Phys. Rev. Lett. 77, 219-222 (1996)

    work page 1996

  65. [65]

    Lattice study of classical inflato n decay,

    T. Prokopec and T. G. Roos, “Lattice study of classical inflato n decay,” Phys. Rev. D 55, 3768-3775 (1997)

    work page 1997

  66. [66]

    Non-thermal product ion of Dark Matter after Inflation,

    N. Bernal, A. Chatterjee and A. Paul, “Non-thermal product ion of Dark Matter after Inflation,” JCAP 12, 020 (2018). – 20 –

    work page 2018

  67. [67]

    Towards the th eory of reheating after inflation,

    L. Kofman, A. D. Linde and A. A. Starobinsky, “Towards the th eory of reheating after inflation,” Phys. Rev. D 56, 3258-3295 (1997)

    work page 1997

  68. [68]

    Gravity Wa ves from Tachyonic Preheating after Hybrid Inflation,

    J. F. Dufaux, G. Felder, L. Kofman and O. Navros, “Gravity Wa ves from Tachyonic Preheating after Hybrid Inflation,” JCAP 03, 001 (2009)

    work page 2009

  69. [69]

    Detecting p lanetary-mass primordial black holes with resonant electromagnetic gravitational-wave detector s,

    N. Herman, A. F¨ uzfa, L. Lehoucq and S. Clesse, “Detecting p lanetary-mass primordial black holes with resonant electromagnetic gravitational-wave detector s,” Phys. Rev. D 104, 023524 (2021)

    work page 2021

  70. [70]

    Electromagnetic ante nnas for the resonant detection of the stochastic gravitational wave background,

    N. Herman, L. Lehoucq and A. F´ uzfa, “Electromagnetic ante nnas for the resonant detection of the stochastic gravitational wave background,” Phys. Rev. D 108, 124009 (2023)

    work page 2023

  71. [71]

    Euclid Definition Study Report

    R. Laureijs et al. [EUCLID], “Euclid Definition Study Report,” [arXiv:1110.3193 [astro-ph.CO]]

    work page internal anchor Pith review arXiv

  72. [72]

    COrE (Cosmic Origins Explorer) A White Paper

    F. R. Bouchet et al. [COrE], “COrE (Cosmic Origins Explorer) A White Paper,” [arXiv:1102.2181 [astro-ph.CO]]

    work page Pith review arXiv

  73. [73]

    Constrain ts on scalar and tensor spectra from Nef f,

    I. Ben-Dayan, B. Keating, D. Leon and I. Wolfson, “Constrain ts on scalar and tensor spectra from Nef f,” JCAP 06, 007 (2019). – 21 –

    work page 2019