{"id":"36e7535d-1cd4-4d0d-9df4-68a6855e68fc","arxiv_id":"2412.04550","paper_version":2,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":5,"one_line_summary":"In the minimal freeze-in dark photon model, low-temperature reheating pushes the required portal coupling to larger values, and the exact curve depends on the equation of state during reheating, widening the reach of direct detection experiments.","lead":"This paper calculates how strongly dark matter must interact with ordinary matter if the early universe reheated slowly after inflation, in a simple freeze-in model with a dark photon. It finds that lower reheating temperatures require a stronger coupling, which makes the model much easier for upcoming direct detection experiments to test.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"No significant objection identified: the reheating-parameterization assumption is acknowledged and bracketed; the low-Trh increase in κ is robust to the quoted band of durations.","rationale":"After reading the manuscript in good faith, I do not find a load-bearing flaw in the central argument. The strongest claim is a comparative statement: low Trh requires larger κ, and the enlarged κ region is more accessible to direct detection. This holds across the scenarios the paper actually computes: instantaneous reheating (Fig. 2), matter-dominated reheating with entropy injection (Fig. 3), and kination (Fig. 4). The reheating parameterization in Eqs. (2.9) and (2.13) is the main modeling assumption, but the paper treats it as a controlled parameter scan and brackets the duration uncertainty; the qualitative conclusion survives on both edges of the band. The quantum-statistics correction (Appendix A) is a ~10% effect and does not affect the central message. The absence of the modified code is a reproducibility limitation, but not evidence of an error. I therefore see no reason to change the reader's ACCEPT verdict. The proposed concrete test is the natural verification step: independent numerical reproduction of a benchmark using the public code, plus an analytic scaling check, would close the residual reproducibility gap.","tokens_in":17897,"tokens_out":19772,"duration_ms":209217,"concrete_test":"Independently recompute the relic-abundance condition for one benchmark (e.g., Trh = 0.1 GeV, mχ = 1 GeV, ω = 0, α = 3/8, maximal Tmax from Eq. 2.14) using the public FREEZEIN code [70] with the background of Eqs. (2.9)-(2.13); compare the resulting κ to the lower edge of the Fig. 3 band. As a cross-check, derive the asymptotic scaling of κ with mχ/Trh for Trh << mχ from Eq. (3.2) in the matter-dominated reheating phase and verify that the plotted lower-edge curve follows the same power law.","verdict_should_be":"UNCHANGED","load_bearing_attack":"No significant objection identified. The paper's central claim does not rest on any single unguarded assumption: the reheating history is parameterized by (ω, α) and explicitly bracketed between instantaneous reheating and the maximal-duration case saturating the BICEP/Keck bound (Eqs. 2.9, 2.13, 2.14). For the matter-dominated case (ω=0, α=3/8), the gray bands in Fig. 3 show that the required coupling κ varies by at most the band thickness, and even the lower edge (maximal duration) lies above the high-Trh curve in the low-Trh regime, so the qualitative claim that low-Trh increases κ and boosts direct-detection sensitivity is robust. The quantitative reach of next-generation experiments is conditional on the assumed power-law thermal-bath evolution, but this is a stated modeling choice rather than an internal inconsistency. The main residual risk is numerical: the modified FREEZEIN code is not shipped, so the plotted κ(mχ) curves have not been independently reproduced.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies the minimal freeze-in dark matter model, a Dirac fermion coupled to a very light dark photon through kinetic mixing, and asks how a non-instantaneous reheating phase changes the portal coupling κ required to reproduce the observed relic abundance Ωh²≈0.12. The reheating epoch is parameterized by the inflaton equation of state ω and the scaling exponent α of the SM bath temperature with scale factor (Eqs. 2.9 and 2.13), with the maximal possible duration bracketed by the BICEP/Keck bound on H_I (Eq. 2.14). The Boltzmann equation (3.2) is solved numerically with the FREEZEIN code, modified to include full quantum statistics for all initial states as described in Appendix A. The authors present results for instantaneous reheating, for a matter-dominated reheating phase (ω=0, α=3/8) with bands bracketing the duration, and for a kination-like phase (ω=α=1). The central finding is that for reheating temperatures Trh at or below the DM mass mχ, the required κ increases sharply, bringing the model into the reach of current and next-generation direct detection experiments.","tokens_in":17992,"tokens_out":13757,"duration_ms":140932,"significance":"If correct, the paper establishes that the reach of direct detection for freeze-in dark matter depends sensitively on the reheating history, and it provides a concrete, physically motivated framework for quantifying this dependence. The analysis has several notable strengths: the collision-term derivation in Appendix A is detailed and standard; the results are checked against Ref. [36] in the instantaneous-reheating limit; the treatment of the reheating duration explicitly brackets the uncertainty between the instantaneous case and the maximal-duration case allowed by the BICEP/Keck bound; and the conclusion that low-Trh scenarios require an increased κ is robust to the width of the bands shown in Fig. 3. The work is therefore a useful benchmark for interpreting future direct detection constraints in non-standard thermal histories.","major_comments":[],"minor_comments":[{"comment":"The parameterization assumes a fully thermalized SM bath for all temperatures between T_max and T_rh. This should be stated explicitly, and a brief comment on the effect of incomplete thermalization at the earliest stages of reheating would be useful; the infrared-dominated production makes the impact modest, but the assumption is load-bearing for the precise κ(mχ) curves.","section":"Section 2.2, Eqs. (2.9) and (2.13)"},{"comment":"The claim that the gray bands are 'generally narrow' is only supported visually. A quantitative statement of the fractional variation of κ across the band for representative masses and reheating temperatures would strengthen the argument that the results are insensitive to the duration of reheating.","section":"Section 3.2, Figures 3 and 4"},{"comment":"The modified FREEZEIN code is not provided and no tabulated values of the κ(mχ) curves are given. Releasing the code or providing a data table for the representative cases would allow the central quantitative results to be reproduced by other groups.","section":"Section 3 and Appendix A"},{"comment":"The first line of Eq. (A.15) contains a typographical artifact: 'exy' should read 'e^{xy}' (or the exponential should be typeset explicitly). The current rendering makes the equation difficult to parse.","section":"Appendix A, Eq. (A.15)"},{"comment":"The notation 'ϵ e′' used in the Introduction and in the sentence after Eq. (3.3) is not introduced as a combined quantity; the effective coupling κ ≡ ϵ e′/e is defined later. Using κ consistently from the beginning would avoid confusion.","section":"Section 2.1, Eq. (2.6) and footnote 1"},{"comment":"The statement that 'the production is not sensitive to the highest temperature during reheating Tmax' should be qualified: it holds in the infrared-dominated regime where T_max ≫ mχ, but for mχ above T_max the production is Boltzmann suppressed and the dependence on T_max reappears.","section":"Introduction, paragraph 4"}],"recommendation":"minor_revision","confidential_remarks":"The paper is a solid and timely contribution, and the central claim is robust. The main residual concern is reproducibility of the numerical curves, which I do not consider a blocker; encouraging the authors to release the modified code or a data table would strengthen the paper. The referee report agrees with the reader's assessment that no load-bearing technical flaw is present."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a solid, incremental phenomenology paper. It takes the standard minimal freeze-in dark photon model and works out the coupling kappa(mχ) needed to match the relic abundance when reheating is not instantaneous. The central result—low Trh requires larger kappa, and the size of the effect is controlled by the equation of state and temperature scaling—is robust and consistent with earlier work, but it is not a surprise. The paper earns its place by doing the calculation carefully.\n\nWhat is actually new: the full quantum-statistics collision term (a ~10% correction, largest for mχ above ~MeV), the explicit kappa(mχ) curves for matter domination (ω=0, α=3/8) and kination (ω=α=1), and a clear bracketing of the reheating duration uncertainty using the BICEP/Keck bound on HI. The instantaneous limit reproduces Ref. [36], which gives me confidence that the numerics are right. The appendix derivation of the statistical factors is clean and standard.\n\nSoft spots, in proportion. The reheating parameterization is a single power law with a fully thermalized SM bath from the start. That is a modeling assumption, and the paper says so; if the bath is not thermalized early or the expansion is not a single power law, the curves shift. I do not see this as a flaw, because the authors do not overclaim—they bracket the duration and present the dependence on (ω, α). The modified FREEZEIN code is not shipped, so no one has reproduced the numerical results; that is a minor but real gap for a paper whose main output is numerical curves. Also, the kination case is less dramatic: for ω=α=1 the required kappa only rises mildly, so the 'enhanced direct detection' punchline is really driven by the matter-dominated case. That is worth stating clearly, but it is in the paper.\n\nThe citation pattern is fine. The central calculation is a fit, not a prediction, and the paper is transparent about that. No circular reasoning: the direct detection rates follow from an independent scattering calculation using the fitted kappa.\n\nBottom line: this is a useful reference for anyone working on freeze-in with non-standard cosmological histories. It deserves a serious referee and should be published after minor comments, mostly requesting the code release and a bit more discussion of the kination case. I would accept it myself. Send it to review.","headline":"A careful, honest freeze-in calculation for non-instantaneous reheating; the main result holds up but is incremental, not groundbreaking.","tokens_in":18650,"tokens_out":2470,"would_cite":true,"duration_ms":24410,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper argues that if the early universe reheated at or below the dark matter mass, the minimal freeze-in dark photon model requires a larger dark-visible coupling, which pushes it into the reach of next-generation direct detection…","keywords":["freeze-in dark matter","dark photon","low reheating temperature","reheating dynamics","direct detection","kination","matter domination","FIMP"],"falsifier":"A null result from a direct-detection campaign whose sensitivity covers the full low-reheating band mapped here—electron-recoil searches across the MeV-to-GeV range and nuclear-recoil searches across the 10 GeV-to-TeV range—would rule out those reheating histories for minimal freeze-in dark matter, because the relic abundance would then require a coupling above the experimental bound.","tokens_in":17591,"feed_emoji":"🌌","tokens_out":10486,"duration_ms":93989,"temperature":0.7,"pith_summary":"This paper argues that the minimal freeze-in dark matter model—a fermion of mass $m_\\chi$ coupled to the standard model through a nearly massless dark photon—cannot be assessed without specifying the reheating history. When the reheating temperature $T_{\\rm rh}$ is at or below $m_\\chi$, production from the thermal plasma is Boltzmann suppressed, so reproducing the observed relic abundance requires a larger portal coupling $\\kappa\\equiv\\epsilon e'/e$. That increase moves the model into parameter space already constrained by direct detection and largely reachable by next-generation experiments over the scanned range $10^{-2}\\,\\mathrm{MeV} \\lesssim m_\\chi \\lesssim 10^3\\,\\mathrm{TeV}$. The paper quantifies this for instantaneous reheating, for a matter-dominated inflaton that decays with entropy injection, and for a kination-like phase, and finds that low-temperature reheating shifts the required coupling by orders of magnitude while full quantum statistics shift it by only a few percent.","feed_headline":"Low reheating pushes dark matter coupling into detector range","feed_subtitle":"Cool reheating raises the needed dark-matter coupling, putting it in next-gen detectors' reach.","key_machinery":"The central object is the minimal freeze-in dark photon model: a Dirac fermion $\\chi$ carrying a dark $U(1)'$ charge, with a very light dark photon $A'$ that kinetically mixes with the standard-model hypercharge, characterized by the portal coupling $\\kappa\\equiv\\epsilon e'/e$. The argument is carried by the freeze-in production rate $\\langle\\sigma v\\rangle n_{\\rm eq}^2$ integrated over a reheating era described by a power-law temperature profile $T(a)=T_{\\rm rh}(a_{\\rm rh}/a)^\\alpha$ and a Hubble rate set by an inflaton equation of state $\\omega$, with the maximal duration of reheating fixed by the CMB tensor-mode bound on the inflationary Hubble scale. That setup lets the yield be computed both during and after reheating, with quantum statistics included for all initial states, and lets the required $\\kappa$ be compared with current and projected direct-detection bounds.","core_discovery":"The central claim is that the coupling needed to fit $\\Omega h^2\\simeq 0.12$ is not a single function of $m_\\chi$: for $T_{\\rm rh}\\gg m_\\chi$ it follows the usual freeze-in curve, but for $T_{\\rm rh}\\lesssim m_\\chi$ it rises steeply, because only the high-velocity tail of the standard-model bath has enough energy to create dark matter. The rise is mostly independent of the highest temperature reached during reheating, since the production is infrared-dominated with a cross section scaling as $1/T^2$; allowing $T_{\\rm max}$ to vary from $T_{\\rm rh}$ up to its maximum set by the CMB tensor-mode bound brackets the required coupling into a band. For a massive inflaton decaying with a constant width ($\\omega=0$, $\\alpha=3/8$), the band is narrow because the entropy released during reheating dilutes any dark matter produced early, while for kination ($\\omega=\\alpha=1$) the dominant effect is a faster expansion and only a modest rise in $\\kappa$. In both cases the larger $\\kappa$ demanded by low reheating makes the model more visible to electron- and nuclear-recoil searches, and the paper maps which parts of the $(m_\\chi,\\kappa)$ plane are already excluded and which lie within projected sensitivities.","pith_inferences":["Beyond the paper, the same infrared-dominated logic should apply to any freeze-in portal whose production peaks near $T\\sim m_\\chi$, so the strong enhancement of the required coupling for $T_{\\rm rh}\\lesssim m_\\chi$ is likely a general feature rather than a peculiarity of the dark photon.","Beyond the paper, a detection in the low-reheating band would not by itself identify the reheating history; independent observables, such as the primordial gravitational-wave spectrum, would be needed to separate $\\omega$, $\\alpha$, and $T_{\\rm rh}$.","Beyond the paper, the assumption that the standard-model bath is fully thermalized during reheating could be relaxed; computing freeze-in with non-thermal early distributions would show how much the required coupling curves shift."],"forward_implications":["For $T_{\\rm rh}\\lesssim m_\\chi$, the portal coupling required to fit the relic density rises steeply, moving the model into regions already bounded by nuclear and electron recoil searches.","In a matter-dominated reheating with a decaying inflaton, entropy injection dilutes early dark matter, so the required coupling stays close to the instantaneous-reheating value and the uncertainty band is narrow.","In a kination-like phase with no entropy injection, the required coupling is only slightly above the high-reheating curve, because the main new effect is the enhanced Hubble expansion.","The low-reheating enhancement extends the reach of next-generation direct detection to essentially the whole scanned mass range, while the range $m_\\chi\\lesssim3\\times10^{-2}\\,\\mathrm{MeV}$ is already excluded by red-giant cooling.","Quantum statistical corrections change the required coupling by about 2--10\\%, much less than the orders-of-magnitude shifts produced by low reheating."],"supporting_citations":[{"why":"Establishes the low-reheating freeze-in benchmark with instantaneous reheating that this work generalizes to non-instantaneous histories.","marker":"[36]"},{"why":"Defines the dark-photon portal coupling and the basic freeze-in production channels for this model.","marker":"[30]"},{"why":"Supplies the plasmon decay contribution and in-medium photon mass effects that dominate production for $m_\\chi$ below the electron mass.","marker":"[31]"},{"why":"Provides the relation between the maximal temperature during reheating, the reheating temperature, and the inflationary Hubble scale.","marker":"[35]"},{"why":"Supplies the power-law temperature and Hubble parameterization for non-instantaneous reheating used throughout the scan.","marker":"[57]"},{"why":"Gives the CMB tensor-mode upper bound on the inflationary Hubble scale that fixes the maximal possible duration of reheating.","marker":"[64]"},{"why":"Provides the numerical freeze-in calculation, including plasmon decay, that the paper modifies to include full quantum statistics.","marker":"[69]"},{"why":"Supplies the nuclear-recoil direct-detection limits that exclude part of the high-mass parameter space.","marker":"[117]"},{"why":"Supplies electron-recoil limits that approach the freeze-in curve for sub-GeV dark matter.","marker":"[118]"},{"why":"Defines the projected sensitivity of a next-generation direct-detection experiment used to map the future reach.","marker":"[119]"}],"fun_headline_variants":["Low reheating boosts freeze-in DM coupling into view","Cool cosmic reheating raises dark matter coupling reach","Low reheating lifts freeze-in dark matter into detector sights","Reheating chill bumps dark matter coupling to detectable","Freeze-in dark matter: low reheating sharpens detection odds"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes the standard-model bath stays fully thermalized while its temperature falls as a single power law throughout reheating, so if actual reheating has a different thermal or expansion history, the required coupling curves and detection reach would shift.","fun_headline_variants_meta":{"raw":{"variants":["Low reheating boosts freeze-in DM coupling into view","Cool cosmic reheating raises dark matter coupling reach","Low reheating lifts freeze-in dark matter into detector sights","Reheating chill bumps dark matter coupling to detectable","Freeze-in dark matter: low reheating sharpens detection odds"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000161,"raw_usage":{"total_tokens":1264,"prompt_tokens":1000,"completion_tokens":264,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":616,"completion_tokens_details":{"reasoning_tokens":185}},"tokens_in":616,"tokens_out":264,"duration_ms":3359,"temperature":1.0,"reasoning_tokens":185,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T21:24:05.027838+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A null result from a direct-detection campaign whose sensitivity covers the full low-reheating band mapped here—electron-recoil searches across the MeV-to-GeV range and nuclear-recoil searches across the 10 GeV-to-TeV range—would rule out those reheating histories for minimal freeze-in dark matter, because the relic abundance would then require a coupling above the experimental bound.","supporting_citations":[],"review_version":1}