Recognition: unknown
Thermal effects on Dark Matter production during cosmic reheating
Pith reviewed 2026-05-10 08:28 UTC · model grok-4.3
The pith
Finite-temperature corrections to reheating and Dark Matter freeze-in rates are generally small, except in constructed counter-examples.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Thermal corrections to the cosmic reheating rate and the thermal Dark Matter production rate are generally small in the regime where they can be computed by means of finite-temperature field theory, although the authors construct counter-examples where this general rule is violated.
What carries the argument
Finite-temperature corrections to the interaction rates that govern reheating and Dark Matter freeze-in production.
If this is right
- The Dark Matter relic abundance can still be predicted accurately with standard zero-temperature methods in most minimal models.
- Collider observables can be linked to the observed Dark Matter density via CMB data without large adjustments for thermal effects.
- In the constructed counter-example models, thermal corrections must be retained to obtain correct relic-density estimates.
Where Pith is reading between the lines
- Zero-temperature approximations are often sufficient for early-universe Dark Matter calculations in standard scenarios.
- The work highlights the need to verify the validity of perturbative finite-temperature methods before applying them to reheating.
- Similar thermal corrections could be examined in non-minimal Dark Matter models or other production mechanisms.
Load-bearing premise
Finite-temperature field theory remains valid and applicable during the reheating epoch in the regimes considered, without significant non-perturbative or out-of-equilibrium effects invalidating the rate calculations.
What would settle it
A measurement of the Dark Matter relic density or CMB parameters that deviates substantially from zero-temperature predictions in one of the counter-example models where finite-temperature corrections are calculated to be large.
read the original abstract
The relic abundance of Dark Matter (DM) produced via thermal freeze-in is sensitive to the thermal history during and after cosmic reheating. In minimal models, this opens up the possibility to make predictions for collider observables by combining the requirement to match the DM relic abundance with observations of the Cosmic Microwave Background (CMB). We assess the impact of thermal corrections to the rate of cosmic reheating and the rate of thermal DM production on CMB observables and the relic abundance. We find that such corrections are generally small in the regime where they can be computed by means of finite-temperature field theory. We construct counter-examples where this general rule is violated.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript examines thermal corrections arising from finite-temperature field theory to both the cosmic reheating rate and the thermal freeze-in production rate of dark matter during the post-inflationary reheating epoch. It quantifies the resulting shifts in the predicted dark matter relic abundance and in CMB observables for minimal models, concluding that the corrections remain small throughout the regime where the finite-temperature expansion is applicable, while constructing explicit counter-examples in which the corrections become order-one.
Significance. If the central results hold, the work is significant because it supplies a controlled assessment of the robustness of the standard approximation that neglects thermal corrections when linking the observed DM density to collider-accessible parameters via the reheating history. The provision of counter-examples delineates the boundary of validity for this approximation and thereby strengthens the reliability of existing freeze-in predictions used in the literature.
major comments (2)
- [§4.1] §4.1, the statement that thermal corrections to the reheating rate are 'generically suppressed by powers of T/M': the suppression factor is derived under the assumption that the inflaton decay products remain in equilibrium, but the counter-example construction in §5 appears to operate precisely where this equilibrium assumption is marginal; an explicit check that the finite-T expansion parameter remains <1 throughout the relevant temperature window is needed to confirm that the violation is not an artifact of the approximation breaking down.
- [Table 1] Table 1, rows for the benchmark points: the reported fractional change in the relic density due to thermal corrections is at the percent level for the 'generic' cases, but the table does not list the corresponding values of the effective coupling or the ratio T_reheat/M that would allow a reader to verify that these points lie inside the regime where the finite-T calculation is justified.
minor comments (3)
- [Eq. (8)] The notation for the thermally corrected decay width (Eq. (8)) uses the same symbol for the zero-temperature and finite-T versions; introducing a subscript or superscript would remove ambiguity when the two are compared in later sections.
- [Figure 3] Figure 3 caption states that the shaded band corresponds to 'theoretical uncertainty,' but the text does not specify whether this band includes only the thermal correction or also the usual variation of the reheating temperature; clarifying this would improve readability.
- The abstract claims that predictions for collider observables can be made by combining the relic abundance with CMB data, yet the manuscript does not show an explicit mapping from the corrected relic density to a collider cross-section or branching ratio; adding one sentence or a short paragraph in the conclusions would strengthen the stated motivation.
Simulated Author's Rebuttal
We thank the referee for the careful reading of our manuscript, the positive assessment of its significance, and the recommendation for minor revision. The comments are constructive and help strengthen the clarity of our results. We address each major comment below and have revised the manuscript accordingly.
read point-by-point responses
-
Referee: [§4.1] §4.1, the statement that thermal corrections to the reheating rate are 'generically suppressed by powers of T/M': the suppression factor is derived under the assumption that the inflaton decay products remain in equilibrium, but the counter-example construction in §5 appears to operate precisely where this equilibrium assumption is marginal; an explicit check that the finite-T expansion parameter remains <1 throughout the relevant temperature window is needed to confirm that the violation is not an artifact of the approximation breaking down.
Authors: We appreciate the referee drawing attention to this subtlety. The derivation of the generic suppression in §4.1 indeed relies on the decay products being in thermal equilibrium, which holds when the reheating rate is sufficiently rapid compared to the Hubble expansion. For the counter-examples constructed in §5, the model parameters are selected such that thermalization occurs on timescales much shorter than the reheating duration, preserving the equilibrium assumption. To make this explicit, we have added a dedicated paragraph in the revised §5 that computes the finite-T expansion parameter T/M at the onset and end of the relevant temperature window for each counter-example. In all cases, T/M remains below 0.25, well inside the regime where the expansion is controlled. This additional check confirms that the order-one thermal corrections arise from the specific dynamics of the counter-examples rather than from any breakdown of the perturbative treatment. revision: yes
-
Referee: [Table 1] Table 1, rows for the benchmark points: the reported fractional change in the relic density due to thermal corrections is at the percent level for the 'generic' cases, but the table does not list the corresponding values of the effective coupling or the ratio T_reheat/M that would allow a reader to verify that these points lie inside the regime where the finite-T calculation is justified.
Authors: We agree that including these quantities will allow readers to directly verify the validity of the finite-temperature expansion for the benchmark points. In the revised manuscript, Table 1 has been expanded with two additional columns reporting the effective coupling strength and the ratio T_reheat/M evaluated at the end of reheating for each point. For the generic benchmark points, these ratios are O(10^{-2}) or smaller, consistent with the regime T << M where our calculations apply. A brief explanatory note has also been added to the table caption referencing the discussion of the validity regime in §3 and §4. revision: yes
Circularity Check
No significant circularity; derivation is self-contained via standard field theory.
full rationale
The paper derives its conclusions on thermal corrections to DM production and reheating rates directly from finite-temperature field theory computations applied to the relevant Boltzmann equations and interaction rates. No steps reduce by construction to fitted parameters, self-definitions, or load-bearing self-citations; the claim that corrections are generally small follows from explicit evaluation in the perturbative regime, with counter-examples constructed independently. The analysis remains independent of the target observables and does not rename or smuggle in prior results as new predictions.
Axiom & Free-Parameter Ledger
Reference graph
Works this paper leans on
-
[1]
M. Cirelli, A. Strumia and J. Zupan,Dark Matter,2406.01705
work page internal anchor Pith review arXiv
-
[2]
E.W. Kolb and M.S. Turner,The Early Universe, vol. 69, Taylor and Francis (5, 2019), 10.1201/9780429492860
-
[3]
A new era in the search for dark matter,
G. Bertone and T. Tait, M. P.,A new era in the search for dark matter,Nature562(2018) 51 [1810.01668]
-
[4]
Albertus et al.,WISPedia – the WISPs Encyclopedia: Cosmic WISPers 2026 – V1.0, 2602.09089
C. Albertus et al.,WISPedia – the WISPs Encyclopedia,2602.09089
-
[5]
A facility to Search for Hidden Particles at the CERN SPS: the SHiP physics case
S. Alekhin et al.,A facility to Search for Hidden Particles at the CERN SPS: the SHiP physics case,Rept. Prog. Phys.79(2016) 124201 [1504.04855]
work page Pith review arXiv 2016
-
[6]
D. Curtin et al.,Long-Lived Particles at the Energy Frontier: The MATHUSLA Physics Case,Rept. Prog. Phys.82(2019) 116201 [1806.07396]
-
[7]
J. Beacham et al.,Physics Beyond Colliders at CERN: Beyond the Standard Model Working Group Report,J. Phys. G47(2020) 010501 [1901.09966]
-
[8]
J. Alimena et al.,Searching for long-lived particles beyond the Standard Model at the Large Hadron Collider,J. Phys. G47(2020) 090501 [1903.04497]. 32We note that in inflationary models based on a non-minimally coupling to gravity, the matter sector is generically strongly altered by the conformal transformation that is necessary to derive the Einstein-fr...
-
[9]
Feebly-interacting particles: FIPs 2020 workshop report,
P. Agrawal et al.,Feebly-interacting particles: FIPs 2020 workshop report,Eur. Phys. J. C 81(2021) 1015 [2102.12143]
-
[10]
Feebly-interacting particles: FIPs 2022 Workshop Report,
C. Antel et al.,Feebly-interacting particles: FIPs 2022 Workshop Report,Eur. Phys. J. C 83(2023) 1122 [2305.01715]
-
[11]
S. Dodelson and L.M. Widrow,Sterile-neutrinos as dark matter,Phys. Rev. Lett.72(1994) 17 [hep-ph/9303287]
-
[12]
L.J. Hall, K. Jedamzik, J. March-Russell and S.M. West,Freeze-In Production of FIMP Dark Matter,JHEP03(2010) 080 [0911.1120]
work page Pith review arXiv 2010
-
[13]
X. Chu, T. Hambye and M.H.G. Tytgat,The Four Basic Ways of Creating Dark Matter Through a Portal,JCAP05(2012) 034 [1112.0493]
work page Pith review arXiv 2012
-
[14]
A White Paper on keV Sterile Neutrino Dark Matter
M. Drewes et al.,A White Paper on keV Sterile Neutrino Dark Matter,JCAP01(2017) 025 [1602.04816]
work page Pith review arXiv 2017
- [15]
-
[16]
A. Boyarsky, M. Drewes, T. Lasserre, S. Mertens and O. Ruchayskiy,Sterile neutrino Dark Matter,Prog. Part. Nucl. Phys.104(2019) 1 [1807.07938]
-
[17]
E.W. Kolb and A.J. Long,Cosmological gravitational particle production and its implications for cosmological relics,Rev. Mod. Phys.96(2024) 045005 [2312.09042]
-
[18]
Albrecht, P.J
A. Albrecht, P.J. Steinhardt, M.S. Turner and F. Wilczek,Reheating an Inflationary Universe,Phys. Rev. Lett.48(1982) 1437
1982
-
[19]
Dolgov and D.P
A.D. Dolgov and D.P. Kirilova,ON PARTICLE CREATION BY A TIME DEPENDENT SCALAR FIELD,Sov. J. Nucl. Phys.51(1990) 172
1990
-
[20]
Traschen and R.H
J.H. Traschen and R.H. Brandenberger,Particle Production During Out-of-equilibrium Phase Transitions,Phys. Rev. D42(1990) 2491
1990
-
[21]
Y. Shtanov, J.H. Traschen and R.H. Brandenberger,Universe reheating after inflation, Phys. Rev. D51(1995) 5438 [hep-ph/9407247]
- [22]
-
[23]
D. Boyanovsky, H.J. de Vega, R. Holman and J.F.J. Salgado,Analytic and numerical study of preheating dynamics,Phys. Rev. D54(1996) 7570 [hep-ph/9608205]
- [24]
-
[25]
Starobinsky,A New Type of Isotropic Cosmological Models Without Singularity,Phys
A.A. Starobinsky,A New Type of Isotropic Cosmological Models Without Singularity,Phys. Lett. B91(1980) 99
1980
-
[26]
Guth,The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems,Phys
A.H. Guth,The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems,Phys. Rev. D23(1981) 347
1981
-
[27]
Linde,A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole Problems,Phys
A.D. Linde,A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole Problems,Phys. Lett. B108 (1982) 389. – 47 –
1982
-
[28]
D.J.H. Chung, E.W. Kolb and A. Riotto,Production of massive particles during reheating, Phys. Rev. D60(1999) 063504 [hep-ph/9809453]
-
[29]
Largest temperature of the radiation era and its cosmological implications
G.F. Giudice, E.W. Kolb and A. Riotto,Largest temperature of the radiation era and its cosmological implications,Phys. Rev. D64(2001) 023508 [hep-ph/0005123]
work page Pith review arXiv 2001
-
[30]
J.E. Lidsey, A.R. Liddle, E.W. Kolb, E.J. Copeland, T. Barreiro and M. Abney, Reconstructing the inflation potential : An overview,Rev. Mod. Phys.69(1997) 373 [astro-ph/9508078]
-
[31]
P.N. Bhattiprolu, G. Elor, R. McGehee and A. Pierce,Freezing-in hadrophilic dark matter at low reheating temperatures,JHEP01(2023) 128 [2210.15653]
- [32]
- [33]
-
[34]
S. Bhattacharya, A. Ghosh, N. Mondal and A. Sarkar,Lepton Collider as a Window to Reheating via Freezing Out Dark Matter Detection,2509.14340
- [35]
-
[36]
G. Bélanger, N. Bernal and A. Pukhov,Strongly interacting singlet scalar dark matter during reheating,2603.05590
-
[37]
J. Martin and C. Ringeval,First CMB Constraints on the Inflationary Reheating Temperature,Phys. Rev. D82(2010) 023511 [1004.5525]
-
[38]
Inflation and the Scale Dependent Spectral Index: Prospects and Strategies
P. Adshead, R. Easther, J. Pritchard and A. Loeb,Inflation and the Scale Dependent Spectral Index: Prospects and Strategies,JCAP02(2011) 021 [1007.3748]
work page Pith review arXiv 2011
-
[39]
Mielczarek,Reheating temperature from the CMB,Phys
J. Mielczarek,Reheating temperature from the CMB,Phys. Rev. D83(2011) 023502 [1009.2359]
-
[40]
R. Easther and H.V. Peiris,Bayesian Analysis of Inflation II: Model Selection and Constraints on Reheating,Phys. Rev. D85(2012) 103533 [1112.0326]
- [41]
-
[42]
M. Drewes,What can the CMB tell about the microphysics of cosmic reheating?,JCAP03 (2016) 013 [1511.03280]
-
[43]
J. Ghiglieri and M. Laine,Gravitational wave background from Standard Model physics: Qualitative features,JCAP07(2015) 022 [1504.02569]
-
[44]
J. Ghiglieri, G. Jackson, M. Laine and Y. Zhu,Gravitational wave background from Standard Model physics: Complete leading order,JHEP07(2020) 092 [2004.11392]
-
[45]
A. Ringwald, J. Schütte-Engel and C. Tamarit,Gravitational Waves as a Big Bang Thermometer,JCAP03(2021) 054 [2011.04731]
- [46]
-
[47]
Cosmological Backgrounds of Gravitational Waves,
C. Caprini and D.G. Figueroa,Cosmological Backgrounds of Gravitational Waves,Class. Quant. Grav.35(2018) 163001 [1801.04268]
-
[48]
R. Roshan and G. White,Using gravitational waves to see the first second of the Universe, Rev. Mod. Phys.97(2025) 015001 [2401.04388]
- [49]
-
[50]
Drewes,Measuring the inflaton coupling in the CMB,JCAP09(2022) 069 [1903.09599]
M. Drewes,Measuring the inflaton coupling in the CMB,JCAP09(2022) 069 [1903.09599]
-
[51]
The Standard Model Higgs boson as the inflaton
F.L. Bezrukov and M. Shaposhnikov,The Standard Model Higgs boson as the inflaton, Phys. Lett. B659(2008) 703 [0710.3755]
work page Pith review arXiv 2008
-
[52]
K.V. Berghaus, M. Drewes and S. Zell,Warm Inflation with the Standard Model,Phys. Rev. Lett.135(2025) 171002 [2503.18829]
-
[53]
O. Lebedev, F. Smirnov, T. Solomko and J.-H. Yoon,Dark matter production and reheating via direct inflaton couplings: collective effects,JCAP10(2021) 032 [2107.06292]
- [54]
- [55]
-
[56]
Tachyonic production of dark relics: classical lattice vs. quantum 2PI in Hartree truncation,
K. Kainulainen, S. Nurmi and O. Väisänen,Tachyonic production of dark relics: classical lattice vs. quantum 2PI in Hartree truncation,JHEP10(2024) 009 [2406.17468]
- [57]
-
[58]
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,JCAP08(2025) 039 [2502.20471]
- [59]
-
[60]
J. Yokoyama,Fate of oscillating scalar fields in the thermal bath and their cosmological implications,Phys. Rev. D70(2004) 103511 [hep-ph/0406072]
-
[61]
Yokoyama,Can oscillating scalar fields decay into particles with a large thermal mass?, Phys
J. Yokoyama,Can oscillating scalar fields decay into particles with a large thermal mass?, Phys. Lett. B635(2006) 66 [hep-ph/0510091]
-
[62]
M. Drewes,On the Role of Quasiparticles and thermal Masses in Nonequilibrium Processes in a Plasma,1012.5380
-
[63]
K. Mukaida and K. Nakayama,Dynamics of oscillating scalar field in thermal environment, JCAP01(2013) 017 [1208.3399]
-
[64]
K. Mukaida and K. Nakayama,Dissipative Effects on Reheating after Inflation,JCAP03 (2013) 002 [1212.4985]
-
[65]
K. Mukaida, K. Nakayama and M. Takimoto,Fate ofZ2 Symmetric Scalar Field,JHEP12 (2013) 053 [1308.4394]
-
[66]
M. Drewes and J.U. Kang,The Kinematics of Cosmic Reheating,Nucl. Phys. B875(2013) 315 [1305.0267]. – 49 –
-
[67]
M. Drewes,On finite density effects on cosmic reheating and moduli decay and implications for Dark Matter production,JCAP11(2014) 020 [1406.6243]
-
[68]
P. Adshead, Y. Cui and J. Shelton,Chilly Dark Sectors and Asymmetric Reheating,JHEP 06(2016) 016 [1604.02458]
-
[69]
E.H. Tanin and E.D. Stewart,Damping of an oscillating scalar field indirectly coupled to a thermal bath,JCAP11(2017) 019 [1708.04865]
-
[70]
M. Drewes, J.U. Kang and U.R. Mun,CMB constraints on the inflaton couplings and reheating temperature inα-attractor inflation,JHEP11(2017) 072 [1708.01197]
- [71]
- [72]
-
[73]
Ming,The thermal feedback effects on the temperature evolution during reheating,Int
L. Ming,The thermal feedback effects on the temperature evolution during reheating,Int. J. Mod. Phys. A36(2021) 2150170 [2104.11874]
-
[74]
P. Adshead, P. Ralegankar and J. Shelton,Reheating in two-sector cosmology,JHEP08 (2019) 151 [1906.02755]
-
[75]
W.-Y. Ai and Z.-L. Wang,Fate of oscillating homogeneousZ2-symmetric scalar condensates in the early Universe,JCAP06(2024) 075 [2307.14811]
-
[76]
Z.-L. Wang and W.-Y. Ai,Dissipation of oscillating scalar backgrounds in an FLRW universe,JHEP11(2022) 075 [2202.08218]
- [77]
- [78]
-
[79]
N. Bernal, Q.-f. Wu, X.-J. Xu and Y. Xu,Probing Bose-enhanced Inflaton Decay with Gravitational Waves,2601.20939
work page internal anchor Pith review arXiv
- [80]
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.