Irreducible Graviton Floor from Reheating

James M. Cline; Yong Xu

arxiv: 2605.16201 · v1 · pith:MDKOPQ3Inew · submitted 2026-05-15 · ✦ hep-ph · astro-ph.CO· hep-th

Irreducible Graviton Floor from Reheating

James M. Cline , Yong Xu This is my paper

Pith reviewed 2026-05-20 16:22 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COhep-th

keywords gravitational wavesreheatingbremsstrahlungsoft graviton theoremstochastic backgroundinflaton decayhigh-frequency GW

0 comments

The pith

Inflaton decay during reheating produces an irreducible stochastic gravitational-wave background fixed by the soft-graviton theorem.

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

The paper demonstrates that bremsstrahlung emission of soft gravitons during inflaton decay inevitably generates a stochastic gravitational-wave background after cosmological redshifting. Weinberg's soft-graviton theorem fixes the infrared part of the spectrum to scale linearly with frequency, independent of the specific inflaton decay interaction. A reader would care because this establishes a minimum signal level from any perturbative reheating in conventional inflation, reaching up to order 10 to the minus 17 in energy density at frequencies above the GHz range. The amplitude is normalized by the hard decay rate and phase-space integrals, which are largest for two-body decays and decrease for higher n-body processes.

Core claim

Inflaton decay inevitably emits gravitons through bremsstrahlung during reheating. The soft part of this emission amplitude, fixed by Weinberg's soft-graviton theorem, becomes an irreducible stochastic gravitational-wave background after accounting for cosmological evolution. The theorem fixes the infrared branch of the spectrum, Ω_GW proportional to frequency, independently of the microscopic operator responsible for inflaton decay, while the normalization is controlled by the hard inflaton decay rate and by a phase-space factor. For inflaton n-body decays including the phase-space integrals, the maximum of the spectrum scales as 2/n relative to the n=2 case, and the signal can reach Ω_GW h

What carries the argument

Weinberg's soft-graviton theorem applied to the bremsstrahlung graviton emission amplitude in n-body inflaton decays, which fixes the infrared spectrum shape and makes it independent of the hard decay operator.

If this is right

The infrared spectrum of the GW background is always proportional to frequency, regardless of the underlying inflaton decay operator.
The peak amplitude decreases as 2/n for n-body inflaton decays compared with the two-body case.
This mechanism produces a stochastic graviton floor of order 10^{-17} in Ω_GW h^2 at frequencies above the GHz scale from any perturbative reheating.
A larger observed signal would require either non-perturbative processes beyond bremsstrahlung or inflationary scenarios beyond conventional single-field slow roll.

Where Pith is reading between the lines

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

High-frequency GW detectors could search for this floor to test whether reheating proceeded through standard perturbative channels.
Similar irreducible backgrounds might arise in other early-universe processes governed by soft theorems, linking quantum field theory symmetries to observable cosmology.
Non-observation at the predicted level could indicate additional suppression factors in the inflaton decay dynamics not included in the current normalization.

Load-bearing premise

The hard inflaton decay rate and phase-space factors can be treated as independent inputs that set the overall normalization without being constrained or altered by the same soft-graviton emission process itself.

What would settle it

A precision measurement or upper limit on the stochastic gravitational-wave energy density at or below 10^{-17} in Ω_GW h^2 for frequencies above 1 GHz would confirm or rule out the predicted irreducible floor from perturbative reheating.

Figures

Figures reproduced from arXiv: 2605.16201 by James M. Cline, Yong Xu.

**Figure 2.** Figure 2: FIG. 2. Comparison of the GW spectra from the three bench [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Graviton floor from bremsstrahlung during reheating. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

read the original abstract

Inflaton decay inevitably emits gravitons through bremsstrahlung during reheating. We show that the soft part of this emission amplitude, fixed by Weinberg's soft-graviton theorem, becomes an irreducible stochastic gravitational-wave (GW) background after accounting for cosmological evolution. The theorem fixes the infrared branch of the spectrum, $\Omega_{\rm GW}\propto f$, independently of the microscopic operator responsible for inflaton decay, while the normalization is controlled by the hard inflaton decay rate and by a phase-space factor. We carry this out for inflaton $n$-body decays, including the phase-space integrals, finding that the maximum of the spectrum scales as $2/n$ relative to the $n=2$ case. The signal can reach $\Omega_{\rm GW}h^2\sim \mathcal O(10^{-17})$ at frequencies above the GHz scale. This predicts a stochastic graviton floor from perturbative reheating: a larger signal would require either other processes beyond perturbative bremsstrahlung or inflationary scenarios beyond conventional single-field slow roll.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note private letter to a colleague

The paper uses Weinberg's soft theorem to fix an irreducible high-frequency GW floor from perturbative reheating at ~10^{-17}, with n-body scaling, but the flat-space to FRW step needs explicit justification.

read the letter

The main point is that soft graviton emission during inflaton decay produces a stochastic background whose infrared shape is fixed by the soft theorem, giving Omega_GW h^2 of order 10^{-17} above GHz after redshifting, and the amplitude falls as 2/n for n-body decays. This is the concrete lower bound they advertise. The calculation takes the known theorem, inserts the hard decay rate as normalization, and works out the phase-space integrals for different n. That part is straightforward and gives a definite prediction that does not depend on the microscopic inflaton coupling. The result is new in the sense that the specific floor amplitude and n-scaling for reheating had not been written down before. The paper does a clean job of separating the soft piece from the hard piece and showing how the spectrum behaves after expansion. The soft spots are modest but worth checking. The theorem is derived in flat space, while reheating occurs in an FRW background with H comparable to the decay rate and a coherent inflaton condensate. If the soft limit picks up corrections of order H over frequency or from the coherent state, the claimed independence of the infrared slope could shift. The paper treats the application as direct, so the reader has to accept that the corrections are negligible. The normalization is tied to the hard rate, which is an input rather than derived inside the work, but that is stated openly and does not make the shape claim circular. This is useful for people modeling high-frequency GW detectors or trying to connect reheating parameters to observables. A reader who wants a model-independent floor from standard perturbative reheating will get a clear number to compare against. The work is coherent enough and makes a falsifiable statement, so it deserves a serious referee even if the FRW applicability needs more explicit defense in the text.

Referee Report

1 major / 2 minor

Summary. The manuscript claims that inflaton decays during reheating inevitably emit gravitons via bremsstrahlung, with the soft part of the amplitude fixed by Weinberg's soft-graviton theorem. This produces an irreducible stochastic GW background whose infrared spectrum satisfies Ω_GW ∝ f independently of the microscopic decay operator, while the overall normalization is set by the hard inflaton decay rate together with phase-space factors. Explicit integrals are performed for n-body decays, yielding a maximum amplitude that scales as 2/n relative to the two-body case, with the signal reaching Ω_GW h² ∼ O(10^{-17}) at frequencies above the GHz scale. The result is presented as a model-independent floor for perturbative reheating in conventional single-field slow-roll inflation.

Significance. If the central derivation holds, the work supplies a concrete, theorem-protected lower bound on the stochastic GW background generated by standard reheating. The explicit evaluation of phase-space integrals for general n-body decays and the resulting 2/n scaling constitute a clear technical contribution. Such a floor would serve as a target for high-frequency GW detectors and could constrain the parameter space of inflationary models that rely on perturbative reheating.

major comments (1)

[Abstract and the paragraph deriving the soft amplitude] The applicability of Weinberg's flat-space soft-graviton theorem to the coherent, homogeneous inflaton condensate decaying in an expanding FRW background is load-bearing for the claimed spectral shape Ω_GW ∝ f and for the asserted independence from the microscopic operator. The manuscript should supply an explicit estimate (or reference to a controlled expansion) demonstrating that corrections of order H/ω or arising from the time-dependent metric and coherent-state nature remain sub-dominant in the soft limit throughout the relevant epoch.

minor comments (2)

[Normalization discussion] The normalization paragraph should state more precisely whether the hard inflaton decay rate is computed self-consistently within the same effective theory or is imported as an external parameter; this would clarify the degree of model independence.
[n-body decay calculation] The explicit phase-space integrals and the derivation of the 2/n scaling for the spectrum maximum should be displayed in a dedicated section or appendix rather than summarized, to facilitate direct verification.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and for recognizing the potential significance of our results. We address the major comment in detail below and will revise the manuscript accordingly to strengthen the justification for our approach.

read point-by-point responses

Referee: [Abstract and the paragraph deriving the soft amplitude] The applicability of Weinberg's flat-space soft-graviton theorem to the coherent, homogeneous inflaton condensate decaying in an expanding FRW background is load-bearing for the claimed spectral shape Ω_GW ∝ f and for the asserted independence from the microscopic operator. The manuscript should supply an explicit estimate (or reference to a controlled expansion) demonstrating that corrections of order H/ω or arising from the time-dependent metric and coherent-state nature remain sub-dominant in the soft limit throughout the relevant epoch.

Authors: We agree that a more rigorous justification of the flat-space soft-graviton theorem in the cosmological setting is necessary to support the model-independent infrared spectrum. In the revised manuscript, we will add a dedicated paragraph in the section deriving the soft amplitude, providing an explicit estimate of the corrections. The soft limit is defined with respect to the hard scale set by the inflaton mass m_φ (or the typical energy of the decay products), with ω ≪ m_φ. During reheating, the Hubble parameter satisfies H ≪ m_φ, as the inflaton energy density is dominated by the potential term with amplitude φ_0 ≪ M_Pl in standard slow-roll models. For the frequencies of interest in the stochastic background (corresponding to physical energies at production satisfying H < ω < m_φ), the ratio H/ω remains ≪ 1, ensuring that expansion effects are perturbative corrections to the flat-space result. The time-dependent metric can be treated in a controlled expansion around the local Minkowski frame over the timescale of the decay process, which is short compared to the Hubble time for the perturbative decay rates considered. Regarding the coherent-state nature of the inflaton condensate, the soft-graviton factor arises from the universal coupling of gravity to the energy-momentum tensor, which applies equally to the classical background or the underlying quantum state in the soft limit. This universality ensures independence from the specific microscopic decay operator, as the soft emission is determined by the external legs of the hard process. We will include this estimate and a reference to literature on soft theorems in curved spacetime where appropriate. revision: yes

Circularity Check

0 steps flagged

No circularity: spectrum shape fixed by external Weinberg theorem, normalization by independent hard decay rate

full rationale

The derivation applies the established Weinberg soft-graviton theorem to fix the infrared emission amplitude during inflaton decay, then evolves the resulting spectrum through standard cosmological redshifting and dilution to obtain Ω_GW ∝ f. Normalization is controlled by the hard inflaton decay rate (an external input) together with explicit phase-space integrals performed for n-body decays inside the paper. No equation reduces the final result to a self-definition, a fitted parameter renamed as prediction, or a load-bearing self-citation chain; the central claim remains independent of the paper's own outputs.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The claim rests on Weinberg's soft-graviton theorem as the source of the infrared spectrum and on the assumption that the hard decay rate is an independent input. No new particles or forces are postulated.

free parameters (2)

hard inflaton decay rate
Controls the overall normalization of the GW spectrum; treated as an external parameter set by the microscopic decay operator.
phase-space factor for n-body decays
Determines the 2/n scaling of the spectrum maximum relative to the two-body case.

axioms (1)

standard math Weinberg's soft-graviton theorem fixes the infrared emission amplitude independently of the microscopic operator.
Invoked to fix the Ω_GW ∝ f branch of the spectrum.

pith-pipeline@v0.9.0 · 5708 in / 1485 out tokens · 42808 ms · 2026-05-20T16:22:22.558799+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

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

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

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

the soft part of this emission amplitude, fixed by Weinberg’s soft-graviton theorem, becomes an irreducible stochastic gravitational-wave (GW) background... Ω_GW ∝ f, independently of the microscopic operator
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

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

J(n)_soft = 2/n ... phase-space average of the polarization-summed Weinberg soft factor

What do these tags mean?

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

Reference graph

Works this paper leans on

39 extracted references · 39 canonical work pages · 9 internal anchors

[1]

A. A. Starobinsky, Phys. Lett. B91, 99 (1980)

work page 1980
[2]

A. H. Guth, Phys. Rev. D23, 347 (1981)

work page 1981
[3]

A. D. Linde, Phys. Lett. B108, 389 (1982)

work page 1982
[4]

Albrecht and P

A. Albrecht and P. J. Steinhardt, Phys. Rev. Lett.48, 1220 (1982). 200 400 600 800 1000 ﬁnal-state multiplicity n 10−3 10−2 10−1 J (n) soft Soft factor up to Inﬂaton1000-body decay Scaling: 2 /n Monte Carlo FIG. S5. Same as Fig. 1 in the main text but for larger multiplicityn∈[10 2,10 3]

work page 1982
[5]

Reheating in Inflationary Cosmology: Theory and Applications

R. Allahverdi, R. Brandenberger, F.-Y. Cyr-Racine, and A. Mazumdar, Ann. Rev. Nucl. Part. Sci.60, 27 (2010), arXiv:1001.2600 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2010
[6]

M. A. Amin, M. P. Hertzberg, D. I. Kaiser, and J. Karouby, Int. J. Mod. Phys. D24, 1530003 (2014), arXiv:1410.3808 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[7]

Nakayama and Y

K. Nakayama and Y. Tang, Phys. Lett. B788, 341 (2019), [Erratum: Phys.Lett.B 839, 137787 (2023)], arXiv:1810.04975 [hep-ph]

work page arXiv 2019
[8]

Barman, N

B. Barman, N. Bernal, Y. Xu, and ´O. Zapata, JCAP 05, 019 (2023), arXiv:2301.11345 [hep-ph]

work page arXiv 2023
[9]

Barman, N

B. Barman, N. Bernal, Y. Xu, and ´O. Zapata, Phys. Rev. D108, 083524 (2023), arXiv:2305.16388 [hep-ph]

work page arXiv 2023
[10]

Kanemura and K

S. Kanemura and K. Kaneta, Phys. Lett. B855, 138807 (2024), arXiv:2310.12023 [hep-ph]

work page arXiv 2024
[11]

Bernal, S

N. Bernal, S. Cl´ ery, Y. Mambrini, and Y. Xu, JCAP01, 065 (2024), arXiv:2311.12694 [hep-ph]

work page arXiv 2024
[12]

Tokareva, Phys

A. Tokareva, Phys. Lett. B853, 138695 (2024), arXiv:2312.16691 [hep-ph]

work page arXiv 2024
[13]

Xu, JHEP10, 174 (2024), arXiv:2407.03256 [hep-ph]

Y. Xu, JHEP10, 174 (2024), arXiv:2407.03256 [hep-ph]

work page arXiv 2024
[14]

Bernal, Q.-f

N. Bernal, Q.-f. Wu, X.-J. Xu, and Y. Xu, JHEP08, 125 (2025), arXiv:2503.10756 [hep-ph]

work page arXiv 2025
[15]

X.-J. Xu, Y. Xu, Q. Yin, and J. Zhu, JHEP10, 141 (2025), arXiv:2505.08868 [hep-ph]

work page arXiv 2025
[16]

Weinberg, Phys

S. Weinberg, Phys. Rev.140, B516 (1965)

work page 1965
[17]

Reheating after Inflation

L. Kofman, A. D. Linde, and A. A. Starobinsky, Phys. Rev. Lett.73, 3195 (1994), arXiv:hep-th/9405187

work page internal anchor Pith review Pith/arXiv arXiv 1994
[18]

WIMPflation

D. Hooper, G. Krnjaic, A. J. Long, and S. D. Mcdermott, Phys. Rev. Lett.122, 091802 (2019), arXiv:1807.03308 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[19]

J. F. Dufaux, G. N. Felder, L. Kofman, M. Peloso, and D. Podolsky, JCAP07, 006 (2006), arXiv:hep- ph/0602144

work page arXiv 2006
[20]

J. Fan, K. D. Lozanov, and Q. Lu, JHEP05, 069 (2021), arXiv:2101.11008 [hep-ph]

work page arXiv 2021
[21]

Navaset al.(Particle Data Group), Phys

S. Navaset al.(Particle Data Group), Phys. Rev. D110, 030001 (2024)

work page 2024
[22]

Planck 2018 results. VI. Cosmological parameters

N. Aghanimet al.(Planck), Astron. Astrophys.641, A6 15 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2020
[23]

P. A. R. Adeet al.(BICEP, Keck), Phys. Rev. Lett.127, 151301 (2021), arXiv:2110.00483 [astro-ph.CO]

work page arXiv 2021
[24]

Universality Class in Conformal Inflation

R. Kallosh and A. Linde, JCAP07, 002 (2013), arXiv:1306.5220 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2013
[25]

H. M. Hodges, G. R. Blumenthal, L. A. Kofman, and J. R. Primack, Nucl. Phys. B335, 197 (1990)

work page 1990
[26]

Drees and Y

M. Drees and Y. Xu, JCAP12, 005 (2022), arXiv:2209.07545 [astro-ph.CO]

work page arXiv 2022
[27]

A. D. Linde, Phys. Rev. D49, 748 (1994), arXiv:astro- ph/9307002

work page arXiv 1994
[28]

Aggarwalet al., Challenges and opportunities of 15 gravitational-wave searches above 10 kHz, Living Rev

N. Aggarwalet al., Living Rev. Rel.28, 10 (2025), arXiv:2501.11723 [gr-qc]

work page arXiv 2025
[29]

Maggiore, Phys

M. Maggiore, Phys. Rept.331, 283 (2000), arXiv:gr- qc/9909001

work page arXiv 2000
[30]

Y. Ema, R. Jinno, and K. Nakayama, JCAP09, 015 (2020), arXiv:2006.09972 [astro-ph.CO]

work page arXiv 2020
[31]

Gravitational wave background from Standard Model physics: Qualitative features

J. Ghiglieri and M. Laine, JCAP07, 022 (2015), arXiv:1504.02569 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[32]

Ghiglieri, G

J. Ghiglieri, G. Jackson, M. Laine, and Y. Zhu, JHEP 07, 092 (2020), arXiv:2004.11392 [hep-ph]

work page arXiv 2020
[33]

Ringwald, J

A. Ringwald, J. Sch¨ utte-Engel, and C. Tamarit, JCAP 03, 054 (2021), arXiv:2011.04731 [hep-ph]

work page arXiv 2021
[34]

Bernal and Y

N. Bernal and Y. Xu, JHEP01, 137 (2025), arXiv:2410.21385 [hep-ph]

work page arXiv 2025
[35]

Xu, Phys

Y. Xu, Phys. Lett. B865, 139483 (2025), arXiv:2412.21137 [hep-ph]

work page arXiv 2025
[36]

We recall Einstein’s belief that gravitational waves would never be observable at all

work page
[37]

S. Y. Choi, J. S. Shim, and H. S. Song, Phys. Rev. D 51, 2751 (1995), arXiv:hep-th/9411092

work page internal anchor Pith review Pith/arXiv arXiv 1995
[38]

Simulating graviton production at hadron colliders

P. de Aquino, K. Hagiwara, Q. Li, and F. Maltoni, JHEP 06, 132 (2011), arXiv:1101.5499 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2011
[39]

Kleiss, W

R. Kleiss, W. J. Stirling, and S. D. Ellis, Comput. Phys. Commun.40, 359 (1986)

work page 1986

[1] [1]

A. A. Starobinsky, Phys. Lett. B91, 99 (1980)

work page 1980

[2] [2]

A. H. Guth, Phys. Rev. D23, 347 (1981)

work page 1981

[3] [3]

A. D. Linde, Phys. Lett. B108, 389 (1982)

work page 1982

[4] [4]

Albrecht and P

A. Albrecht and P. J. Steinhardt, Phys. Rev. Lett.48, 1220 (1982). 200 400 600 800 1000 ﬁnal-state multiplicity n 10−3 10−2 10−1 J (n) soft Soft factor up to Inﬂaton1000-body decay Scaling: 2 /n Monte Carlo FIG. S5. Same as Fig. 1 in the main text but for larger multiplicityn∈[10 2,10 3]

work page 1982

[5] [5]

Reheating in Inflationary Cosmology: Theory and Applications

R. Allahverdi, R. Brandenberger, F.-Y. Cyr-Racine, and A. Mazumdar, Ann. Rev. Nucl. Part. Sci.60, 27 (2010), arXiv:1001.2600 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2010

[6] [6]

M. A. Amin, M. P. Hertzberg, D. I. Kaiser, and J. Karouby, Int. J. Mod. Phys. D24, 1530003 (2014), arXiv:1410.3808 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2014

[7] [7]

Nakayama and Y

K. Nakayama and Y. Tang, Phys. Lett. B788, 341 (2019), [Erratum: Phys.Lett.B 839, 137787 (2023)], arXiv:1810.04975 [hep-ph]

work page arXiv 2019

[8] [8]

Barman, N

B. Barman, N. Bernal, Y. Xu, and ´O. Zapata, JCAP 05, 019 (2023), arXiv:2301.11345 [hep-ph]

work page arXiv 2023

[9] [9]

Barman, N

B. Barman, N. Bernal, Y. Xu, and ´O. Zapata, Phys. Rev. D108, 083524 (2023), arXiv:2305.16388 [hep-ph]

work page arXiv 2023

[10] [10]

Kanemura and K

S. Kanemura and K. Kaneta, Phys. Lett. B855, 138807 (2024), arXiv:2310.12023 [hep-ph]

work page arXiv 2024

[11] [11]

Bernal, S

N. Bernal, S. Cl´ ery, Y. Mambrini, and Y. Xu, JCAP01, 065 (2024), arXiv:2311.12694 [hep-ph]

work page arXiv 2024

[12] [12]

Tokareva, Phys

A. Tokareva, Phys. Lett. B853, 138695 (2024), arXiv:2312.16691 [hep-ph]

work page arXiv 2024

[13] [13]

Xu, JHEP10, 174 (2024), arXiv:2407.03256 [hep-ph]

Y. Xu, JHEP10, 174 (2024), arXiv:2407.03256 [hep-ph]

work page arXiv 2024

[14] [14]

Bernal, Q.-f

N. Bernal, Q.-f. Wu, X.-J. Xu, and Y. Xu, JHEP08, 125 (2025), arXiv:2503.10756 [hep-ph]

work page arXiv 2025

[15] [15]

X.-J. Xu, Y. Xu, Q. Yin, and J. Zhu, JHEP10, 141 (2025), arXiv:2505.08868 [hep-ph]

work page arXiv 2025

[16] [16]

Weinberg, Phys

S. Weinberg, Phys. Rev.140, B516 (1965)

work page 1965

[17] [17]

Reheating after Inflation

L. Kofman, A. D. Linde, and A. A. Starobinsky, Phys. Rev. Lett.73, 3195 (1994), arXiv:hep-th/9405187

work page internal anchor Pith review Pith/arXiv arXiv 1994

[18] [18]

WIMPflation

D. Hooper, G. Krnjaic, A. J. Long, and S. D. Mcdermott, Phys. Rev. Lett.122, 091802 (2019), arXiv:1807.03308 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2019

[19] [19]

J. F. Dufaux, G. N. Felder, L. Kofman, M. Peloso, and D. Podolsky, JCAP07, 006 (2006), arXiv:hep- ph/0602144

work page arXiv 2006

[20] [20]

J. Fan, K. D. Lozanov, and Q. Lu, JHEP05, 069 (2021), arXiv:2101.11008 [hep-ph]

work page arXiv 2021

[21] [21]

Navaset al.(Particle Data Group), Phys

S. Navaset al.(Particle Data Group), Phys. Rev. D110, 030001 (2024)

work page 2024

[22] [22]

Planck 2018 results. VI. Cosmological parameters

N. Aghanimet al.(Planck), Astron. Astrophys.641, A6 15 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2020

[23] [23]

P. A. R. Adeet al.(BICEP, Keck), Phys. Rev. Lett.127, 151301 (2021), arXiv:2110.00483 [astro-ph.CO]

work page arXiv 2021

[24] [24]

Universality Class in Conformal Inflation

R. Kallosh and A. Linde, JCAP07, 002 (2013), arXiv:1306.5220 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2013

[25] [25]

H. M. Hodges, G. R. Blumenthal, L. A. Kofman, and J. R. Primack, Nucl. Phys. B335, 197 (1990)

work page 1990

[26] [26]

Drees and Y

M. Drees and Y. Xu, JCAP12, 005 (2022), arXiv:2209.07545 [astro-ph.CO]

work page arXiv 2022

[27] [27]

A. D. Linde, Phys. Rev. D49, 748 (1994), arXiv:astro- ph/9307002

work page arXiv 1994

[28] [28]

Aggarwalet al., Challenges and opportunities of 15 gravitational-wave searches above 10 kHz, Living Rev

N. Aggarwalet al., Living Rev. Rel.28, 10 (2025), arXiv:2501.11723 [gr-qc]

work page arXiv 2025

[29] [29]

Maggiore, Phys

M. Maggiore, Phys. Rept.331, 283 (2000), arXiv:gr- qc/9909001

work page arXiv 2000

[30] [30]

Y. Ema, R. Jinno, and K. Nakayama, JCAP09, 015 (2020), arXiv:2006.09972 [astro-ph.CO]

work page arXiv 2020

[31] [31]

Gravitational wave background from Standard Model physics: Qualitative features

J. Ghiglieri and M. Laine, JCAP07, 022 (2015), arXiv:1504.02569 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2015

[32] [32]

Ghiglieri, G

J. Ghiglieri, G. Jackson, M. Laine, and Y. Zhu, JHEP 07, 092 (2020), arXiv:2004.11392 [hep-ph]

work page arXiv 2020

[33] [33]

Ringwald, J

A. Ringwald, J. Sch¨ utte-Engel, and C. Tamarit, JCAP 03, 054 (2021), arXiv:2011.04731 [hep-ph]

work page arXiv 2021

[34] [34]

Bernal and Y

N. Bernal and Y. Xu, JHEP01, 137 (2025), arXiv:2410.21385 [hep-ph]

work page arXiv 2025

[35] [35]

Xu, Phys

Y. Xu, Phys. Lett. B865, 139483 (2025), arXiv:2412.21137 [hep-ph]

work page arXiv 2025

[36] [36]

We recall Einstein’s belief that gravitational waves would never be observable at all

work page

[37] [37]

S. Y. Choi, J. S. Shim, and H. S. Song, Phys. Rev. D 51, 2751 (1995), arXiv:hep-th/9411092

work page internal anchor Pith review Pith/arXiv arXiv 1995

[38] [38]

Simulating graviton production at hadron colliders

P. de Aquino, K. Hagiwara, Q. Li, and F. Maltoni, JHEP 06, 132 (2011), arXiv:1101.5499 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2011

[39] [39]

Kleiss, W

R. Kleiss, W. J. Stirling, and S. D. Ellis, Comput. Phys. Commun.40, 359 (1986)

work page 1986