{"id":"1557ed30-5a68-4a18-9bc0-f17b57269993","arxiv_id":"1909.01457","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Dark matter freeze-in before an early matter-dominated epoch can dominate the relic abundance, and a broad early-equilibrium plateau makes the abundance nearly independent of the annihilation cross section.","lead":"This paper calculates how dark matter is produced in the radiation-dominated phase that precedes an early matter-dominated era, and shows this earlier production can dominate the final dark matter abundance. It matters because it changes the allowed dark matter mass and interaction strength in non-standard early universe cosmologies, and points to tests combining collider and cosmological observations.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Pre-EMD dominance and Eq. (9) assume a constant annihilation cross section; canonical FIMP freeze-in has <sigma_ann v> proportional to T^{-2}, which the paper's own Appendix excludes, so the claim that 'freeze-in' prior to EMD dominates does not carry over to the standard freeze-in realization.","rationale":"The paper is internally consistent and technically careful: the Boltzmann equations are standard, the analytic approximations are checked against numerical solutions, and the authors explicitly disclose in Section V that for n < -3/2, including the FIMP example with n = -2, pre-EMD production is no longer important. The reader's weakest_assumption correctly identifies this temperature dependence as the load-bearing restriction on the central claim. My read does not change the verdict: a CONDITIONAL decision is appropriate because the pre-EMD freeze-in dominance and the expanded parameter space are real only for a restricted class of models with a constant annihilation cross section, not for the canonical FIMP freeze-in scenario. The early-equilibrium plateau is a separate, internally valid result, although its presentation as part of a 'freeze-in' scenario is a terminological overclaim. No code or data are provided, but the analytic derivation is explicit and the main numerical results are reproducible in principle from Eqs. (8) and the stated thermal history. The concern is about scope and framing rather than an internal inconsistency, so I would keep the reader's conditional verdict unchanged.","tokens_in":16924,"tokens_out":4251,"duration_ms":45885,"concrete_test":"Use the same radiation/matter/DM Boltzmann system (8) with T_MAX = 10^12 GeV, T_O = 10^10 GeV, and T_R = 10 GeV, but set <sigma_ann v>_f = sigma_0 (T / m_chi)^{-2}, corresponding to the FIMP-like n = -2 case, and recompute the Omega h^2 = 0.12 contours in the m_chi - sigma_0 plane. If the pre-EMD regions 2 and 3, namely the horizontal early-equilibrium plateau and the low-cross-section branch, shrink or disappear, the constant-cross-section assumption is load-bearing and the paper's freeze-in framing needs a scope condition. For an analytic check, place the T^{-2} factor inside the integrals in Eq. (20) and confirm that the dominant contribution shifts from T_MAX to T ~ m_chi.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central results, namely the pre-EMD abundance formulas in Eq. (7), regions 2 and 3 of Fig. 2, and the inequality in Eq. (9), are derived under the assumption that <sigma_ann v>_f is constant over T_R < T < T_MAX. The Appendix's final paragraph shows that this is a special case: in the integrals of Eq. (20), early production is dominated by the upper integration limit only for n >= -1 for the radiation-dominated integral and n >= -3/2 for the memory-phase integral. For n < -3/2, the DM production rate peaks at T ~ m_chi rather than at the highest temperature, so the pre-EMD contribution no longer dominates. The paper explicitly names the FIMP scenario, where <sigma_ann v>_f is proportional to T^{-2}, as an important example of this failure. Since 'freeze-in' is commonly identified with feebly coupled FIMP models, the abstract's claim that freeze-in production prior to EMD opens vast parameter space for weak-scale dark matter does not apply to the canonical freeze-in realization; it applies only to the constant-cross-section case, for example dimension-5 operators with a mediator heavier than T_MAX. The early-equilibrium plateau is a valid but distinct hot-thermal-relic result, not freeze-in, and Eq. (9) should be framed as a result about that regime rather than about freeze-in generally.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies dark matter production in a post-inflationary thermal history with a radiation-dominated (RD) epoch followed by an early matter-dominated (EMD) epoch. Assuming a constant velocity-averaged annihilation cross section <σannv>f over T_R ≲ T ≲ T_MAX, the authors derive analytic expressions for the DM relic abundance generated before the entropy-producing phase of EMD. Two regimes are identified: a decoupling regime in which production is dominated by the highest temperature T_MAX (first line of Eq. (7)) and an early-equilibrium regime in which DM starts in chemical equilibrium and decouples while relativistic, so the abundance is essentially independent of <σannv>f (second line of Eq. (7)). This leads to the upper bound m_χ ≲ 1.6 g_*dec (T_O/(10^9 T_R)) (1 GeV) in Eq. (9). Numerical solutions of the coupled Boltzmann equations (Eq. (8)) confirm the analytic formulas and map the allowed regions of the m_χ-<σannv>f plane for several thermal histories.","tokens_in":17206,"tokens_out":8778,"duration_ms":81903,"significance":"The analytic machinery is careful and the paper provides useful closed-form expressions for the pre-EMD contribution, including the memory phase, and these derivations are parameter-free in the sense that the observed relic abundance is used as a constraint rather than a fitted input. The early-equilibrium bound Eq. (9) is a clean relation between the DM mass and the duration of EMD, and the discussion of gravitational-wave and microhalo observables is a valuable addition. However, the paper's general claim that freeze-in prior to EMD dominates is not valid for the canonical FIMP realization, as the Appendix shows for n < -3/2; it applies only to constant or non-negative power-law cross sections. In addition, the early-equilibrium regime is physically a hot relativistic relic rather than freeze-in. These two issues affect the framing of the central results and require revision, but the underlying calculations should remain valid once the scope is stated accurately.","major_comments":[{"comment":"The central claim that pre-EMD production dominates in the freeze-in regime is derived under the assumption of a constant <σannv>f. The final paragraph of the Appendix shows that if <σannv>f ∝ T^n, the integrals in Eq. (20) are dominated by their upper limits only for n ≥ -1 in the RD phase and n ≥ -3/2 in the memory phase; for n < -3/2, in particular the canonical FIMP case n = -2, production is instead peaked near T ~ m_χ and the pre-EMD contribution no longer dominates. The paper does acknowledge this at the end of Section V, but the abstract, the introduction, Eq. (7), Eq. (9), and the description of regions 2 and 3 in Section III present the result as a general freeze-in statement. These statements should be explicitly restricted to constant <σannv>f (or n ≥ -1), and the FIMP case with n = -2 should be presented as a counterexample to the general claim.","section":"Section V and Appendix B, Eqs. (20) and (7)"},{"comment":"The 'early-equilibrium regime' is not freeze-in. In this regime DM particles begin in chemical equilibrium and decouple while relativistic, and the relic abundance is fixed by the equilibrium comoving density at decoupling (Eqs. (23) and (24)), exactly as in the standard hot-relativistic-relic case such as neutrino decoupling. Calling this a 'freeze-in analogue' and including it under the freeze-in label conflates two distinct production mechanisms. This matters because the plateau in region 2 of Fig. 2 and the inequality in Eq. (9) are hot-relic results, not freeze-in results. The terminology should be changed to 'early chemical decoupling' or 'hot relativistic relic,' and the abstract's statement that the paper focuses on freeze-in should be adjusted accordingly.","section":"Section II.B and Section IV"}],"minor_comments":[{"comment":"In the first paragraph, 'significant affect' should be 'significant effect.'","section":"Section I"},{"comment":"The statement that DM particles decouple 'during early matter domination' is imprecise; the body of the paper places decoupling at H_tran ≲ H ≲ H_MAX, which spans the prior RD phase and the memory phase of EMD. Please rephrase to 'prior to the entropy-producing phase of EMD.'","section":"Abstract and Section II.B"},{"comment":"Region 0 is defined only in the caption; the bulleted list in the text should also explain it explicitly alongside regions 1-3.","section":"Section III, Fig. 2 caption"},{"comment":"The phrase 'freeze-in analogue to the WIMP miracle' should be removed in favor of a hot-relic description, given the reclassification suggested in the major comment.","section":"Section IV"},{"comment":"The factors (10^9 T_MAX T_R / T_O) and (10^9 T_R / T_O) would benefit from an explicit statement that T_MAX, T_O, and T_R are in GeV.","section":"Section II.B, Eq. (7)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a solid calculation but the abstract overstates the scope. The authors should be asked to reclassify the early-equilibrium regime as a hot relativistic relic and to add explicit caveats about the constant-cross-section assumption. The self-citation to [26] is appropriate for the temperature-evolution formulas, and the paper is within the scope of the journal."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. The paper's genuinely new piece is pre-EMD production of dark matter in a radiation-dominated phase followed by an early matter-dominated epoch, and it works out the analytics: the decoupling-regime yield growing with T_MAX, and the plateau where DM starts in chemical equilibrium and decouples while relativistic, making the relic abundance nearly independent of the annihilation cross section. The mapping in Figs. 2-5 and the inequality m_chi <~ 1.6 g_*dec (T_O / 10^9 T_R) GeV are clean and useful. The Boltzmann treatment and the temperature evolution for RD, memory phase, and decay-driven EMD are internally coherent, and the paper gives explicit models with dimension-5 operators that realize constant <sigma v>.\n\nThe soft spots are two, and the second one is load-bearing. First, the early-equilibrium regime is a hot thermal relic, not freeze-in. The authors know this—they explicitly compare it to neutrino decoupling—but they still present it as part of the freeze-in scenario and advertise it as a way to test the elusive freeze-in scenario. That is a terminological overclaim. Second, the pre-EMD dominance and Eq. (9) rely on <sigma v>_f being constant over T_R < T < T_MAX. The paper's own Appendix shows that if <sigma v>_f ~ T^n with n < -3/2, the early production integrals peak at T ~ m_chi, not at the highest temperature, and the expanded parameter space collapses. The canonical FIMP, with n = -2, is exactly that case. So the abstract's claim that freeze-in production before EMD opens vast parameter space for weak-scale DM does not hold for the standard freeze-in realization; it holds for constant-cross-section models, which the paper does give concrete examples of. That does not kill the paper—the constant-cross-section case is real and the examples are explicit—but the framing should be corrected.\n\nThe math and the citation pattern look fine. The temperature-evolution formulas come from the authors' earlier paper, but that is a parameter-free derivation, so the self-citation is legitimate. No code or data are shipped, but the analytic expressions are checkable and the numerical results agree with them.\n\nWho is this for? People working on non-standard thermal histories and freeze-in/freeze-out will want it as a reference, though they should read Section V and the Appendix first. It deserves a serious referee: the calculation is solid, the result is useful, and the main fix is an honest reframing. I'd accept it for review, and I'd tell the authors to change the language before publication.","headline":"Solid extension of EMD freeze-in to pre-EMD production, but the 'freeze-in' label is stretched: the early-equilibrium plateau is a hot relic, and the headline results assume a constant annihilation cross section.","tokens_in":17772,"tokens_out":1875,"would_cite":true,"duration_ms":17138,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["95.35.+d","98.80.Cq"],"model":"deepseek-v4-flash","headline":"Dark matter produced before an early matter-dominated era can account for the full observed relic abundance, even for weak-scale masses and very small annihilation cross sections.","keywords":["dark matter","freeze-in","early matter domination","relic abundance","chemical equilibrium","non-standard thermal history","FIMP","Boltzmann equations"],"falsifier":"Compute the temperature exponent $n$ in $\\langle\\sigma_{\\rm ann}v\\rangle_{\\rm f}\\propto T^n$ for a concrete particle model. For $n < -3/2$, as in the FIMP case with a mediator lighter than the dark-matter particle, the paper's own appendix shows that early production in the radiation and memory phases is suppressed and the expanded parameter regions vanish. Alternatively, an independent measurement of $m_\\chi$, $T_O$, and $T_R$ that violates $m_\\chi < 1.6\\,g_{*\\mathrm{dec}}\\,(T_O/10^9\\,T_R)\\,\\mathrm{GeV}$ would imply overproduction in the early-equilibrium regime.","tokens_in":16698,"feed_emoji":"🌌","tokens_out":10706,"duration_ms":98799,"temperature":0.7,"pith_summary":"The paper tries to establish that, in a post-inflationary universe that first passes through a radiation-dominated phase and then through an early matter-dominated (EMD) phase, dark matter produced during that earlier radiation phase can supply most of today's dark matter. This matters for weak-scale masses and for annihilation cross sections too small for ordinary freeze-out, the regime known as freeze-in, where particles are slowly built up from the hot bath. The pre-EMD contribution depends on the full thermal history—the maximum temperature after reheating ($T_{\\rm MAX}$), the temperature at the onset of matter domination ($T_O$), and the reheat temperature at its end ($T_R$)—so the allowed parameter space cannot be read off from the EMD era alone. In a broad early-equilibrium regime, dark matter starts in chemical equilibrium while relativistic and decouples later, making the final abundance nearly independent of the annihilation cross section; avoiding overproduction then forces $m_\\chi \\lesssim 1.6\\,g_{*\\mathrm{dec}}\\,(T_O/10^9\\,T_R)\\,\\mathrm{GeV}$.","feed_headline":"Pre-matter-era dark matter can set the relic abundance","feed_subtitle":"The relic abundance can be fixed before the early matter era, opening new weak-scale mass regions.","key_machinery":"The machinery is the temperature-history map of the non-standard era, fixed by the three temperatures $T_{\\rm MAX}$, $T_O$, and $T_R$, with scaling laws $T\\propto H^{1/2}$ during radiation domination, $T\\propto H^{2/3}$ during the memory phase, and $T\\propto H^{1/4}$ during the entropy-producing part of EMD. Inserted into the coupled Boltzmann equations for radiation, the decaying matter component, and the dark-matter number density, these scalings show that the DM production rate falls more slowly than the Hubble rate at early times, so the dominant contribution comes from the highest temperature in each pre-EMD phase. The threshold separating the two regimes is $\\langle\\sigma_{\\rm ann}v\\rangle_{\\rm f} \\sim g_{*\\mathrm{MAX}}^{1/2}/(M_P T_{\\rm MAX})$; below it dark matter never equilibrates, above it dark matter decouples while relativistic, and the second branch is what makes the abundance cross-section-independent.","core_discovery":"The central discovery is that production prior to the EMD era—both in the radiation-dominated phase and in the 'memory phase' at the start of EMD, when leftover radiation still dominates over decay products—can dominate the dark-matter relic abundance. Working with a thermally averaged annihilation cross section $\\langle\\sigma_{\\rm ann}v\\rangle_{\\rm f}$ that is constant between $T_R$ and $T_{\\rm MAX}$, the authors show that the pre-EMD contribution is the largest at the highest temperature in each phase. When $\\langle\\sigma_{\\rm ann}v\\rangle_{\\rm f}$ is so small that dark matter never reaches equilibrium, the relic abundance is set at $T_{\\rm MAX}$; when it is larger, dark matter begins in chemical equilibrium and decouples while relativistic, leaving a comoving number density determined by the decoupling temperature and by $T_O$. In that early-equilibrium regime the relic abundance is essentially independent of the cross section, and not overproducing dark matter gives the inequality $m_\\chi \\lesssim 1.6\\,g_{*\\mathrm{dec}}\\,(T_O/10^9\\,T_R)\\,\\mathrm{GeV}$.","pith_inferences":["The same 'look before the non-standard epoch' logic should apply to other early phases with a high-temperature radiation stage, such as kination or a burst of fast expansion; computing freeze-in there would show whether the $T_O/T_R$ bound generalizes.","In the early-equilibrium regime dark-matter particles decouple while relativistic, so their momentum distribution may carry memory of the pre-EMD epoch; the paper does not examine consequences for structure formation or direct-detection kinematics.","The inequality $m_\\chi < 1.6\\,g_{*\\mathrm{dec}}\\,(T_O/10^9\\,T_R)\\,\\mathrm{GeV}$ can be read in reverse as a falsifiable prediction: once gravitational-wave or CMB experiments pin down $T_O/T_R$, a stable weak-scale particle found above the bound would rule the early-equilibrium branch out."],"forward_implications":["The allowed $m_\\chi$–$\\langle\\sigma_{\\rm ann}v\\rangle_{\\rm f}$ plane gains large regions at very small cross sections, down to values that the EMD-only freeze-in analysis would exclude.","In the early-equilibrium regime, the dark-matter relic abundance is set almost entirely by $m_\\chi$ and the ratio $T_O/T_R$, so measuring $m_\\chi$ at a collider plus cosmological bounds on that ratio can test the scenario even if direct and indirect detection see nothing.","The pre-EMD contribution scales linearly with $m_\\chi$ and only mildly with $T_R$, in contrast to the steep $m_\\chi^{-5}$ of late-EMD freeze-in, so changing the thermal history reshuffles which masses are viable.","If the cross section grows with temperature ($n>0$), pre-EMD production can dominate even for very small cross sections at the mass scale, while for $n<-3/2$ (for example the FIMP with $n=-2$) the newly opened parameter space disappears."],"supporting_citations":[{"why":"Supplies the standard formula for freeze-in during the entropy-producing phase of EMD, the baseline that pre-EMD production is compared against.","marker":"[7]"},{"why":"Gives the late-EMD freeze-in abundance used to draw the baseline curve and quantifies the indirect-detection boost from microhalos.","marker":"[8]"},{"why":"Provides the temperature-versus-Hubble relations for the memory phase of EMD used to compute the pre-EMD contribution.","marker":"[26]"},{"why":"Defines the FIMP with $n=-2$, the example that shows when the constant-cross-section early-production dominance fails.","marker":"[55]"},{"why":"Presents an explicit dimension-5 operator model that realizes a constant annihilation cross section over the relevant temperature range.","marker":"[56]"}],"fun_headline_variants":["Pre-EMD production dominates relic abundance","Dark matter abundance set before matter domination","Early freeze-in sets dark matter density","Pre-matter-era production fixes relic abundance","Dark matter forms before early matter era"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the dark-matter annihilation cross section stays constant over the whole temperature interval from $T_R$ to $T_{\\rm MAX}$; if it falls steeply as the universe cools, the early pre-matter-era production that the paper relies on is suppressed and the newly opened parameter space disappears.","fun_headline_variants_meta":{"raw":{"variants":["Pre-EMD production dominates relic abundance","Dark matter abundance set before matter domination","Early freeze-in sets dark matter density","Pre-matter-era production fixes relic abundance","Dark matter forms before early matter era"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000995,"raw_usage":{"total_tokens":4249,"prompt_tokens":1017,"completion_tokens":3232,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":633,"completion_tokens_details":{"reasoning_tokens":3169}},"tokens_in":633,"tokens_out":3232,"duration_ms":22140,"temperature":1.0,"reasoning_tokens":3169,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T05:17:13.652962+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the temperature exponent $n$ in $\\langle\\sigma_{\\rm ann}v\\rangle_{\\rm f}\\propto T^n$ for a concrete particle model. For $n < -3/2$, as in the FIMP case with a mediator lighter than the dark-matter particle, the paper's own appendix shows that early production in the radiation and memory phases is suppressed and the expanded parameter regions vanish. Alternatively, an independent measurement of $m_\\chi$, $T_O$, and $T_R$ that violates $m_\\chi < 1.6\\,g_{*\\mathrm{dec}}\\,(T_O/10^9\\,T_R)\\,\\mathrm{GeV}$ would imply overproduction in the early-equilibrium regime.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the standard formula for freeze-in during the entropy-producing phase of EMD, the baseline that pre-EMD production is compared against."},{"cited_title":"Unified TeV Scale Picture of Baryogenesis and Dark Matter","cited_arxiv_id":"hep-ph/0612357","evidence_quote":"Presents an explicit dimension-5 operator model that realizes a constant annihilation cross section over the relevant temperature range."}],"review_version":1}