Low-Reheating Freeze-In Dark Matter

• Low-reheating-temperature freeze-in is a dark matter production mechanism relying on feeble interactions during a non-instantaneous reheating phase.
• It involves a precise interplay between Boltzmann-suppressed reaction rates, entropy injection, and modified cosmic expansion to shape the dark matter relic abundance.
• Enhanced couplings required in this regime open promising avenues for collider searches, direct detection experiments, and astrophysical constraints.

A low-reheating-temperature freeze-in scenario refers to dark matter (DM) production via feeble interactions in the early universe, where the Standard Model (SM) thermal bath is established at a temperature $T_\mathrm{RH}$ well below typical new-physics scales (such as the DM or mediator mass). In this regime, DM production is highly sensitive to the interplay between non-instantaneous reheating dynamics, Boltzmann-suppressed reaction rates, entropy injection, and the growing experimental accessibility arising from the associated coupling enhancements. The scenario is now a central focus in both phenomenological and model-building studies due to its relevance for direct detection, cosmological constraints, and collider signatures.

1. Freeze-In Mechanism at Low Reheating Temperature

In freeze-in, the DM population is produced out of equilibrium from the SM bath through extremely small couplings or high-dimensional operators. The number density $n_\chi$ evolves according to

$\dot n_\chi + 3H n_\chi = \mathcal{C}_\chi[T],$

where $\mathcal{C}_\chi[T]$ represents the production processes (decays or scatterings) and $H$ is the Hubble rate.

In the low-reheating-temperature regime ($T_\mathrm{RH} \ll m_\chi,~m_\text{med}$), DM production is generated predominantly during or just after reheating, when the plasma temperature is near $T_\mathrm{RH}$ and the production rate is exponentially (Boltzmann-)suppressed: $$Y_\chi^\infty \propto A\, M_\mathrm{Pl} \, T_\mathrm{RH}^n \exp(-p\,m/T_\mathrm{RH}),$$ with the power $n$ and exponent $p$ set by operator dimension and process kinematics. For example, in Higgs-portal or $n_\chi$0-mediated models, $n_\chi$1 for $n_\chi$2, while for UV-dominated higher-dimensional operators, the yield scales as $n_\chi$3 (Dalianis et al., 2023, Bernal et al., 2024, Monteux et al., 2015, Bélanger et al., 2024, Arias et al., 28 Jan 2025).

2. Boltzmann Equations and Cosmological Dynamics

The cosmological background during reheating is set by the inflaton or moduli field $n_\chi$4 decaying into SM radiation: $n_\chi$5 with $n_\chi$6 defined by $n_\chi$7, yielding

$n_\chi$8

For $n_\chi$9, the SM temperature scales as $\dot n_\chi + 3H n_\chi = \mathcal{C}_\chi[T],$0. This modified scaling accelerates the expansion rate, enhances entropy dilution, and shapes the relic abundance integrals (Bélanger et al., 2024, Dalianis et al., 2023, Becker et al., 2023).

The general freeze-in yield is

$\dot n_\chi + 3H n_\chi = \mathcal{C}_\chi[T],$1

where $\dot n_\chi + 3H n_\chi = \mathcal{C}_\chi[T],$2 is the entropy density and $\dot n_\chi + 3H n_\chi = \mathcal{C}_\chi[T],$3 encodes the relevant decay or annihilation source terms.

3. Exponential Suppression and Coupling Enhancement

When the reheating temperature is well below key mass thresholds, freeze-in production is dominated by rare events at $\dot n_\chi + 3H n_\chi = \mathcal{C}_\chi[T],$4, with rates suppressed $\dot n_\chi + 3H n_\chi = \mathcal{C}_\chi[T],$5 for process energy scales $\dot n_\chi + 3H n_\chi = \mathcal{C}_\chi[T],$6. To compensate for the reduced efficiency and match the observed DM relic density, the necessary portal or Yukawa couplings must be exponentially larger than in standard high-$\dot n_\chi + 3H n_\chi = \mathcal{C}_\chi[T],$7 freeze-in, while remaining small enough to preserve out-of-equilibrium conditions: $\dot n_\chi + 3H n_\chi = \mathcal{C}_\chi[T],$8 for representative scalar or vector freeze-in models (Cosme et al., 2023, Boddy et al., 2024, Bernal et al., 2024, Amiri et al., 26 Nov 2025).

These enhancements directly impact direct detection prospects by raising DM-nucleon or DM-electron cross sections into the experimentally accessible range. For instance, in minimal dark photon models, the electron-scattering cross-section can move from $\dot n_\chi + 3H n_\chi = \mathcal{C}_\chi[T],$9 cm$\mathcal{C}_\chi[T]$0 to $\mathcal{C}_\chi[T]$1 cm$\mathcal{C}_\chi[T]$2 as $\mathcal{C}_\chi[T]$3 is lowered from much above $\mathcal{C}_\chi[T]$4 to just a few MeV (Boddy et al., 2024, Bernal et al., 2024).

4. Non-Instantaneous Reheating and Entropy Dilution

A realistic treatment requires accounting for non-instantaneous reheating. The maximum bath temperature $\mathcal{C}_\chi[T]$5 can exceed $\mathcal{C}_\chi[T]$6, but most DM production is subsequently diluted by late entropy injection: $\mathcal{C}_\chi[T]$7 with the dilution factor scaling with either $\mathcal{C}_\chi[T]$8 or the (early) matter-dominated epoch duration. The effect is model- and operator-dependent, e.g., for UV-dominated operators: $\mathcal{C}_\chi[T]$9 but may be further suppressed during a prolonged matter epoch or cannibal phase in the dark sector (Dalianis et al., 2023, Bhattiprolu et al., 2022, Bernal et al., 10 Jun 2025, Bernal et al., 2024).

5. Collider, Astrophysical, and Cosmological Constraints

Enhanced couplings in low-$H$0 freeze-in scenarios allow tests via multiple observables:

• Direct detection: Predicted cross-sections for DM–nucleon or DM–electron scattering overlap with and sometimes exceed current bounds (e.g., LZ, XENONnT, SENSEI, PandaX, DARWIN, Oscura), especially for $H$1 (Cosme et al., 2023, Boddy et al., 2024, Bernal et al., 2024, Amiri et al., 26 Nov 2025, Bhattiprolu et al., 2022).
• Long-lived particles: For freeze-in from decays, the required parent decay width is much larger at low $H$2, leading to decay lengths as short as $H$3mm–m (or less), testable in displaced-vertex searches at the LHC (HSCP, displaced leptons, non-pointing photons) (Becker et al., 2023, Arias et al., 21 Jul 2025).
• BBN and CMB: The minimum reheating temperature is bounded by Big Bang Nucleosynthesis considerations ($H$4–5 MeV). Contributions to $H$5 or late-time energy injection (e.g. from decays) are subject to CMB and structure-formation limits (Arias et al., 28 Jan 2025, Bhattiprolu et al., 2022, Cox et al., 2024, Berbig, 2022).
• Astrophysics and colliders: Stellar cooling (SN1987A), rare meson decays, and the existence of new particles (e.g., vector-like quarks or new charged scalars/fermions required by minimal UV completions) impose additional restrictions (Cox et al., 2024, Bhattiprolu et al., 2022).
• Gravitational waves: If freeze-in is associated with late reheaton decay, nonthermal preheating, or cosmic strings, the stochastic GW background can have distinctive signatures (e.g. a suppressed plateau at frequencies above $H$6), which future experiments may probe (Ghosh et al., 4 Nov 2025, Khan et al., 21 Sep 2025).

6. Model Implementations and Portal Realizations

A diverse set of concrete UV models realize low-$H$7 freeze-in:

• Higgs-portal scalars and pseudoscalars: DM produced via Higgs portals is subject to exponential suppression at $H$8 and requires $H$9 to match the relic density (Cosme et al., 2023, Amiri et al., 26 Nov 2025, Bernal et al., 10 Jun 2025, Bernal et al., 2024).
• Vector mediators ($T_\mathrm{RH} \ll m_\chi,~m_\text{med}$0 models): For both $T_\mathrm{RH} \ll m_\chi,~m_\text{med}$1 and $T_\mathrm{RH} \ll m_\chi,~m_\text{med}$2 scenarios, the coupling between DM and SM must be increased as $T_\mathrm{RH} \ll m_\chi,~m_\text{med}$3 lowers, moving models into regions testable by direct detection and displaced-vertex searches (Bélanger et al., 2024, Ghosh et al., 4 Nov 2025, Khan et al., 21 Sep 2025, Berbig, 2022).
• Ultralight dark photons: "Minimal" freeze-in models are particularly sensitive, as $T_\mathrm{RH} \ll m_\chi,~m_\text{med}$4 leads to an upward shift in the freeze-in coupling required for the correct $T_\mathrm{RH} \ll m_\chi,~m_\text{med}$5; parameter space already probed by low-threshold electron-recoil detectors (Boddy et al., 2024, Bernal et al., 2024).
• Hadrophilic and photonic freeze-in: Scenarios where production is via higher-dimensional operators (e.g., $T_\mathrm{RH} \ll m_\chi,~m_\text{med}$6 or pion fusion) yield cross-sections and couplings that are highly accessible if $T_\mathrm{RH} \ll m_\chi,~m_\text{med}$7 is close to the minimum allowed by BBN (Bhattiprolu et al., 2022, Cox et al., 2024).
• Exotic topologies: Models featuring DM production via cannibalization (2→3 or 3→2 dark-sector processes) are sensitive to $T_\mathrm{RH} \ll m_\chi,~m_\text{med}$8 and display nontrivial temperature and number-density histories, creating additional handles and phenomenology (Bernal et al., 10 Jun 2025).
• UV baryogenesis and EMD epochs: Early matter domination or late moduli decay can both suppress and dilute freeze-in signals, connecting inflationary observables ($T_\mathrm{RH} \ll m_\chi,~m_\text{med}$9, $T_\mathrm{RH}$0) to DM and baryon relics (Dalianis et al., 2023, Becker et al., 2023).

7. Phenomenological and Theoretical Implications

Allowing for a low-reheating-temperature phase generically expands the viable parameter space for freeze-in DM by decoupling the required relic density from the classic feeble-coupling regime, bridging toward "strong freeze-in" with potentially detectable couplings and decay signatures (Cosme et al., 2023, Amiri et al., 26 Nov 2025, Bernal et al., 2024). Conversely, arbitrarily lowering $T_\mathrm{RH}$1 can suppress the DM relic density below the observable window, even for superheavy DM (Khan et al., 21 Sep 2025).

This scenario also highlights the necessity of accurate cosmological modeling: instantaneous reheating or neglect of entropy injection can lead to order-of-magnitude misestimates for DM yield, decay lengths, and observable signatures (Becker et al., 2023, Bélanger et al., 2024, Bhattiprolu et al., 2022).

Key open directions include a systematic mapping of all viable reheating and dark-sector dynamics, refined CMB and BBN constraints, interplay with the gravitational wave spectrum, collider strategies for long-lived particles, and the role of model-dependent entropy injection or cannibalization in precise yield predictions. Upcoming direct detection and LHC searches are poised to explore much of the parameter space favored in low-reheating-temperature freeze-in scenarios.