{"id":"6770652f-2724-48f0-882d-6772a514d34a","arxiv_id":"2412.13288","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"During reheating, freeze-in from the gravitationally produced radiation bath can dominate the dark matter relic density for DM masses above the reheating temperature, with k- and n-dependent constraints.","lead":"This paper calculates how dark matter is produced just after inflation, adding a contribution from radiation generated by the inflaton's own gravitational scattering. Heavy dark matter can be made more efficiently by this 'gravitational bath' than by the usual decay bath, changing when freeze-in models match the observed abundance.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (16) is the reciprocal of the actual peak ratio from Eq. (15); via Eq. (49) it mis-scales every gravitational-bath freeze-in yield, so the printed quantitative basis for the central claim is not yet established.","rationale":"The central claim is quantitative: gravitational-bath freeze-in can dominate and saturate the relic density for m_chi > T_RH, and Lambda thresholds exist. The chain of formulas from Eq. (15) through Eq. (49) is the quantitative engine of the paper. The reader's verdict already flagged Eq. (16) in its rationale; I promote this to the load-bearing concern because it is an internally verifiable algebraic error rather than a model assumption: Eq. (17) uses the reciprocal of Eq. (16), so the inconsistency is not a matter of convention. The error propagates into every gravitational-bath abundance through Eq. (49), with an order-ten effect for k=2. The thermalization assumption identified as the reader's weakest point is real and should be revisited, but it is an explicit modeling assumption whose failure would require a separate phase-space calculation; the Eq. (16) error is testable immediately and affects the printed numbers. Since the reader's CONDITIONAL verdict already requires correcting Eq. (16) and quantifying these effects, my assessment leaves the verdict unchanged.","tokens_in":33018,"tokens_out":17224,"duration_ms":160986,"concrete_test":"Re-derive a_hmax/a_end by setting the derivative of the bracket in Eq. (15) with respect to ln a to zero. Confirm the result is ((6k-3)/(2k+4))^((k+2)/(8k-14)), not its reciprocal, then replace Eq. (16) in Eq. (49) and recompute the k=2, n=-2 and n=2 gravitational-bath relic-density curves in Figs. 6, 11, and 12. If the curves shift by more than a factor of about 10, the quantitative claim and the Lambda limits must be revised; if they are unchanged, the inversion is a local typo and the central claim stands.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Setting d ln rho_R^h / d ln a = 0 in Eq. (15) gives a_hmax/a_end = [(6k-3)/(2k+4)]^((k+2)/(8k-14)), which for k=2 is (9/8)^2 about 1.27. Equation (16) prints its reciprocal, (8/9)^2 about 0.79, implying the bath peaks before a_end. Equation (17) for T_hmax uses the correct reciprocal, so the paper is internally inconsistent. Equation (49) explicitly instructs using Eq. (16) for a_max/a_end; this ratio enters Eqs. (46), (53), (57), (59) and the reduced relic densities (47), (54), (60), (A.3), (A.4), (A.11). For k=2 the factor (a_max/a_RH) appears with exponent 9/2, so the printed gravitational-bath yields are suppressed by (0.79/1.27)^(9/2) about 1/13 relative to the corrected expressions. Because the headline claim, that gravitational-bath freeze-in can exceed the decay bath and set Omega_chi h^2 = 0.12 for m_chi > T_RH, is quantified with these formulas, the numerical support, including the Lambda upper limits, is not reliable as printed until Eq. (16) is corrected and propagated.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper analyzes dark-matter production during reheating from three sources: direct gravitational scattering of the inflaton condensate, freeze-in from the radiation bath produced by inflaton decay, and freeze-in from the radiation bath produced by gravitational scattering of the inflaton. The freeze-in rates are parameterized as R_chi proportional to T^{n+6}/Lambda^{n+2}, and the inflaton potential near its minimum is taken as V(phi) proportional to phi^k. The authors derive analytic relic-density expressions for each source and for the regimes m_chi < T_RH, m_chi > T_RH, and Lambda below the maximal bath temperature, and they compare the three production mechanisms in the (m_chi, T_RH) plane for k = 2, 4, 6 and several values of n. The central claims are that freeze-in from the gravitationally produced bath can exceed that from the conventional decay bath for m_chi > T_RH, and that for each interaction there is a BSM scale Lambda above which direct gravitational production from the inflaton dominates thermal freeze-in.","tokens_in":33296,"tokens_out":11699,"duration_ms":108311,"significance":"If the quantitative results are correct, the paper makes a useful and timely contribution: it identifies an often-neglected third source of FIMP dark matter during reheating and shows that it can be the dominant source in a non-negligible part of parameter space. The analytic framework is a strength: the appendix collects the n- and k-dependent relic-density formulas, and the structure of the Boltzmann-equation solutions is transparent enough for independent checks. The predicted Omega_chi h^2 contours and the Lambda upper limits are falsifiable and directly relevant for model-building. The main caveat is that the numerical realization of the headline claim currently rests on an internally inconsistent set of formulas, so the quantitative support must be re-established after correction.","major_comments":[{"comment":"The printed expression for a_hmax/a_end is the reciprocal of the value implied by Eq. (15). Setting d ln rho_R^h / d ln a = 0 in Eq. (15) gives a_hmax/a_end = [(6k-3)/(2k+4)]^{(k+2)/(8k-14)}, whereas Eq. (16) prints the inverse base. For k = 2 this gives 0.79 instead of 1.27, so the printed peak occurs before a_end even though Eq. (15) vanishes at a_end and rises afterwards. Because Eq. (49) explicitly instructs the reader to substitute Eq. (16) into the scale-factor ratios, the printed forms of Eqs. (46), (53), (54), and the k = 2 result (47) inherit a suppression factor [(8/9)/(9/8)]^{9/2} ≈ 1/13 for k = 2. At the same time, Eqs. (17), (57), and (A.3) already use the correct ratio, so the paper is internally inconsistent rather than uniformly mis-scaled. The authors should correct Eq. (16), re-derive every expression that substitutes it, and re-evaluate the affected figures and parameter-space statements.","section":"Section II.A, Eq. (16)"},{"comment":"Because the corrected and printed forms of the gravitational-bath density differ by an order of magnitude in the k = 2 regime, the numerical results in Section III need to be recomputed or explicitly mapped to the corrected expressions. For example, Eq. (47) is the k = 2 gravitational-bath relic density for n > n_h^c; if evaluated using Eq. (49) with the printed Eq. (16), the resulting Omega_h values are suppressed by about a factor of 13. However, Eq. (57) already contains (9/8)^9, which corresponds to the corrected peak ratio. It is therefore unclear which expressions were used to generate each panel in Figs. 10-12 and 15-19. The authors should state the formula used for each figure and, where Eq. (16) was used, correct the curves and the associated discussion of gravitational-bath dominance and upper limits on Lambda.","section":"Section III, numerical implementation"}],"minor_comments":[{"comment":"The instantaneous-thermalization assumption is stated in the paragraph on the decay bath, but the gravitational bath is also treated as a thermal bath with temperature T_h in the freeze-in rate R_chi(T); please state explicitly that the same assumption is made for the gravitational bath and comment on its regime of validity.","section":"Section II.A"},{"comment":"In Figs. 2 and 3, the quantities y_max and T_RH^max are used in the captions but are only defined in the surrounding text; please add definitions in the captions for readability.","section":"Figure captions"},{"comment":"The heading of Eq. (A.12) says \"For the decay bath with T_h^max > Lambda > m_chi > T_RH,\" but the decay bath's maximum temperature is T_y^max; the notation should be corrected.","section":"Appendix A.12"},{"comment":"The bracket in the second line of Eq. (52) is missing a closing parenthesis; please check the parentheses and the displayed formula.","section":"Equation (52)"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the journal's scope and the central idea is worth pursuing. The main uncertainty is whether the figures were generated with the corrected peak ratio despite the typo in Eq. (16); I would ask the authors to specify which formulas were used for each figure and to supply corrected versions of the affected expressions and plots. If the numerical results turn out to be unchanged because the plots used the correct ratio, the revision can be modest; otherwise the quantitative conclusions in the gravitational-bath-dominated regions may shift by about an order of magnitude."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things you should know. First, the physics is genuinely worth your time: it systematically adds the gravitationally-produced SM bath to the freeze-in-during-reheating calculation, and the Section II.E treatment of Lambda < Tmax (where n changes as the bath temperature drops below the mediator scale) is new, even for the decay bath. The arbitrary-k,n formulas in the appendix are thorough, and the comparison of the three production channels is useful. Second, there is a concrete error: Eq. (16) gives a_hmax/a_end = [(2k+4)/(6k-3)]^{(k+2)/(8k-14)}, which is less than 1 for k = 2, 4, 6. Eq. (15) gives rho_R^h = 0 at a_end and the bracket has a maximum at a > a_end; differentiating Eq. (15) gives a_hmax/a_end = [(6k-3)/(2k+4)]^{(k+2)/(8k-14)} = 1.27 for k = 2. So Eq. (16) prints the reciprocal. Because Eq. (49) instructs you to use this ratio as a_max/a_RH, the error propagates into Eqs. (46), (53), and all the gravitational-bath relic densities in the text and appendix. For k = 2 the factor appears with a high power, so the printed gravitational-bath yields are suppressed by roughly an order of magnitude relative to the corrected expressions. The headline claim—that the gravitational bath can exceed the decay bath and set Omega h^2 = 0.12 for m_chi > T_RH—rests on those numbers, so the quantitative support is not there as printed. The error is simple to locate and likely a typo (Eq. (17) seems to use the correct ratio), but the authors need to fix Eq. (16), propagate it, and confirm the plots and Lambda limits. The instantaneous-thermalization assumption is a softer spot: it is stated clearly but not quantified, and it matters for heavy DM where the gravitational bath's early-time history is the whole story. The paper otherwise reads carefully; the self-cited inputs from Refs. [9,10,31] are published, and the derivations do not use the observed relic density as an input. This paper is for FIMP/dark-matter model-builders and reheating phenomenologists. I think it deserves a serious referee: the framework is a real extension of the freeze-in program, and the fix is straightforward. If I were handling it, I would send it out with a request to correct Eq. (16) and re-run the numbers.","headline":"A well-motivated extension of freeze-in during reheating with a real error in Eq. (16) that undermines the printed numbers; worth refereeing after a simple fix.","tokens_in":33894,"tokens_out":5979,"would_cite":false,"duration_ms":46792,"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":"During reheating, freeze-in from the gravitationally produced radiation bath can dominate over the conventional decay bath and alone set the dark matter relic density when $m_{\\chi}>T_{\\rm RH}$.","keywords":["gravitational portal","freeze-in","reheating","dark matter relic density","inflaton condensate","gravitational radiation bath","T-model inflation","BSM scale"],"falsifier":"Identify a stable scalar dark matter candidate in a T-model reheating scenario with $k=4$ and $m_{\\chi}\\gtrsim128$ GeV: the paper predicts direct gravitational inflaton scattering alone overproduces such particles, so a confirmed stable scalar at that mass would contradict the framework. Alternatively, in a parameter region where the gravitational bath should dominate, for example $m_{\\chi}>T_{\\rm RH}$ with $\\Lambda\\sim10^{10}$-$10^{12}$ GeV, a precision measurement of the dark matter relic density that matches only the decay-bath prediction would falsify the claim that the gravitational bath is a required third production source.","tokens_in":32749,"feed_emoji":"⚛️","tokens_out":10369,"duration_ms":89456,"temperature":0.7,"pith_summary":"This paper asks how dark matter is produced in the first moments after inflation, while the inflaton condensate is still dominating the universe and reheating it. It shows that three production routes must be tracked together: direct gravitational scattering of the inflaton, freeze-in from the radiation bath produced by inflaton decay, and freeze-in from a second, often neglected radiation bath that the inflaton itself creates through gravitational scattering. The central result is that this gravitational bath can be the dominant source of freeze-in dark matter and can by itself account for the observed relic density, provided the dark matter mass exceeds the reheating temperature and certain $k$- and $n$-dependent conditions are met. The paper also derives, for each freeze-in interaction, an upper limit on the new-physics scale $\\Lambda$ above which direct gravitational production from the inflaton beats thermal freeze-in. A complete calculation of the dark matter relic abundance during reheating therefore has to include the gravitational bath, not just the decay bath.","feed_headline":"Gravity's own radiation bath can dominate dark matter freeze-in","feed_subtitle":"A third dark-matter source during reheating can set the relic density when dark matter is heavier than the reheating temperature.","key_machinery":"The central object is the gravitational bath: Standard Model radiation produced by graviton exchange from the oscillating inflaton condensate, $\\phi\\phi\\to h_{\\mu\\nu}\\to$ SM fields, whose energy density redshifts as $\\rho^h_R\\propto a^{-4}$ and peaks at a temperature $T^h_{\\max}\\simeq 1.0\\times10^{12}$ GeV for $k=2$. It is compared with the decay bath produced by inflaton decay. The argument is carried by closed-form Boltzmann-equation solutions parameterized by $k$, the power of the inflaton potential about its minimum, and $n$, the temperature power of the freeze-in rate $R_{\\chi}\\propto T^{n+6}/\\Lambda^{n+2}$, together with the crossing temperature $T_{\\times}$ at which the two bath densities are equal; for $m_{\\chi}>T_{\\times}$, freeze-in is fed by the gravitational bath even for interactions whose production is otherwise dominated by late, low-temperature times. The analytic results hinge on critical values $n_c^h=-6/(k+2)$ and $n_c^y=(10-2k)/(k-1)$ that separate production dominated by early, high-temperature times from production dominated by late, low-temperature times.","core_discovery":"The paper's central claim is that a complete account of dark matter production during reheating must include three sources, and that the newly emphasized one, freeze-in from the gravitational bath, can dominate. For a general inflaton potential $V(\\phi)\\propto\\phi^k$ about its minimum and a general freeze-in rate $R_{\\chi}\\propto T^{n+6}/\\Lambda^{n+2}$, the paper derives analytic relic densities for all three sources for arbitrary $k$ and $n$ and compares them. It finds that when $m_{\\chi}>T_{\\rm RH}$, freeze-in from the gravitational bath can exceed the decay-bath contribution and saturate $\\Omega_{\\chi}h^2=0.12$, subject to $k$- and $n$-dependent constraints; for $k=4$ and $n=2$, for instance, the gravitational bath provides the dominant source at reheating temperatures $T_{\\rm RH}\\lesssim 60$ GeV. Conversely, for each interaction there is an $m_{\\chi}$- and $T_{\\rm RH}$-dependent upper bound on $\\Lambda$ above which direct gravitational production from the inflaton condensate exceeds ordinary freeze-in, so freeze-in studies using high BSM scales must be re-examined.","pith_inferences":["The same gravitational bath should source any very weakly coupled relic produced at temperatures near $T^h_{\\max}\\sim10^{12}$ GeV, including gravitinos, axions, or a baryon asymmetry; those channels would inherit the same competition between direct and bath production.","The derived upper limits on $\\Lambda$ imply that freeze-in parameter scans assuming $\\Lambda\\gtrsim10^{10}$ GeV should be rerun with direct gravitational production included, and experimental bounds on mediator masses may need to be reinterpreted as bounds on where freeze-in applies at all.","If thermalization of the gravitational bath is not instantaneous, the effective crossing temperature $T_{\\times}$ and the $m_{\\chi}>T_{\\rm RH}$ dominance region would shift; a dedicated treatment of delayed thermalization could sharpen or relax the conclusions for $k=2$ and $k=4$."],"forward_implications":["A complete freeze-in relic calculation during reheating must include the gravitational bath as a third source; for $m_{\\chi}>T_{\\rm RH}$ it can dominate and alone give $\\Omega_{\\chi}h^2=0.12$ under $k$- and $n$-dependent conditions.","For every freeze-in interaction considered, there is an $m_{\\chi}$- and $T_{\\rm RH}$-dependent upper limit on the BSM scale $\\Lambda$ above which direct gravitational production from the inflaton exceeds thermal freeze-in, so freeze-in studies with high $\\Lambda$ must include that source.","For $k=4$, stable scalar dark matter heavier than about 128 GeV, and fermionic dark matter above about $1.8\\times10^9$ GeV, are overproduced by direct gravitational inflaton scattering regardless of reheating temperature.","When $\\Lambda<T^h_{\\max}$, the effective interaction index $n$ jumps by 4 once the bath cools below $\\Lambda$; for the gravitational bath this makes production peak near $T\\sim\\Lambda$ rather than at $T_{\\max}$ or $T_{\\rm RH}$, a regime that is unique to the gravitational bath.","For $k=6$, freeze-in from the gravitational bath never exceeds the decay bath for any allowed reheating temperature above the big-bang nucleosynthesis limit of about 4 MeV, so whether the gravitational bath matters at all is controlled by the inflaton potential's $k$."],"supporting_citations":[{"why":"Supplies the gravitational-bath energy density, its peak temperature, and the direct gravitational production rates for scalar and fermionic dark matter used throughout the comparison.","marker":"[31]"},{"why":"Supplies the inflaton oscillation frequency, Fourier coefficients, and the k-dependent evolution of the radiation baths and inflation parameters.","marker":"[10]"},{"why":"Provides the decay-bath freeze-in number density and the integration method that the paper extends to the gravitational bath.","marker":"[9]"},{"why":"Defines the freeze-in mechanism and the conversion from number density to relic density.","marker":"[5, 6]"},{"why":"Establishes gravitational-portal production of dark matter from the inflaton, the starting point for the direct-production comparison.","marker":"[27]"},{"why":"Supplies the inflaton-fragmentation bound that rules out low reheating temperatures for k=6 and higher.","marker":"[44]"},{"why":"Provides the big-bang-nucleosynthesis gravitational-wave constraint used to restrict attention to k=2, 4, and 6.","marker":"[74]"}],"fun_headline_variants":["Gravitational bath freeze-in can dominate dark matter relic density","Dark matter from gravity's own radiation bath during reheating","Freeze-in from gravitational bath beats decay bath for heavy DM","Gravitational portals set relic density for heavy DM","Reheating bath from gravity can dominate dark matter freeze-in"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes that the gravitationally produced Standard Model radiation thermalizes instantaneously into a bath with a well-defined temperature $T_h$, so that freeze-in rates written as functions of temperature apply throughout reheating; if thermalization is delayed or incomplete, the early production history and all comparisons between the gravitational and decay baths change.","fun_headline_variants_meta":{"raw":{"variants":["Gravitational bath freeze-in can dominate dark matter relic density","Dark matter from gravity's own radiation bath during reheating","Freeze-in from gravitational bath beats decay bath for heavy DM","Gravitational portals set relic density for heavy DM","Reheating bath from gravity can dominate dark matter freeze-in"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000562,"raw_usage":{"total_tokens":2740,"prompt_tokens":1090,"completion_tokens":1650,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":706,"completion_tokens_details":{"reasoning_tokens":1567}},"tokens_in":706,"tokens_out":1650,"duration_ms":10312,"temperature":1.0,"reasoning_tokens":1567,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T13:18:28.541583+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Identify a stable scalar dark matter candidate in a T-model reheating scenario with $k=4$ and $m_{\\chi}\\gtrsim128$ GeV: the paper predicts direct gravitational inflaton scattering alone overproduces such particles, so a confirmed stable scalar at that mass would contradict the framework. Alternatively, in a parameter region where the gravitational bath should dominate, for example $m_{\\chi}>T_{\\rm RH}$ with $\\Lambda\\sim10^{10}$-$10^{12}$ GeV, a precision measurement of the dark matter relic density that matches only the decay-bath prediction would falsify the claim that the gravitational bath is a required third production source.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the decay-bath freeze-in number density and the integration method that the paper extends to the gravitational bath."}],"review_version":1}