---
title: Low-Reheating Freeze-In Dark Matter
url: https://www.emergentmind.com/topics/low-reheating-temperature-freeze-in-scenario
type: topic
---

# Low-Reheating Freeze-In Dark Matter

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 $Z'$-mediated models, $Y_\chi^\infty \propto T_\mathrm{RH} \, e^{-2m_\chi/T_\mathrm{RH}}$ for $m_\chi \gg T_\mathrm{RH}$, while for UV-dominated higher-dimensional operators, the yield scales as $Y_\chi \propto T_\mathrm{RH}^{2n-1}$ [2304.07345, 2412.04550, 1505.03149, 2412.12303, 2501.17234].

## 2. Boltzmann Equations and Cosmological Dynamics

The cosmological background during reheating is set by the inflaton or moduli field $\phi$ decaying into SM radiation:
\[
\begin{aligned}
\dot\rho_\phi + 3H\rho_\phi &= -\Gamma_\phi \rho_\phi,\\
\dot\rho_R + 4H\rho_R &= +\Gamma_\phi \rho_\phi,
\end{aligned}
\]
with $T_\mathrm{RH}$ defined by $\rho_R(T_\mathrm{RH}) = \rho_\phi(T_\mathrm{RH})$, yielding
\[
T_\mathrm{RH} = \left[\frac{90}{\pi^2 g_*(T_\mathrm{RH})}\right]^{1/4}\sqrt{\Gamma_\phi M_P}.
\]
For $a < a_\mathrm{RH}$, the SM temperature scales as $T(a) \propto a^{-3/8}$. This modified scaling accelerates the expansion rate, enhances entropy dilution, and shapes the relic abundance integrals [2412.12303, 2304.07345, 2306.17238].

The general freeze-in yield is
\[
Y_\chi(\infty) = \int_{T_0}^{T_\mathrm{max}} \frac{C_\chi(T)}{s(T)H(T)T}\,dT,
\]
where $s(T)$ is the entropy density and $C_\chi(T)$ 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 $T \sim T_\mathrm{RH}$, with rates suppressed $\propto \exp(-p\,m/T_\mathrm{RH})$ for process energy scales $m$.
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-$T_\mathrm{RH}$ freeze-in, while remaining small enough to preserve out-of-equilibrium conditions:
\[
\lambda_{\min} \sim e^{m_\chi / T_\mathrm{RH}} \quad \text{or} \quad \kappa \propto e^{m_\chi / T_\mathrm{RH}}
\]
for representative scalar or vector freeze-in models [2306.13061, 2405.06226, 2412.04550, 2511.21520].

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 $\sim 10^{-51}$ cm$^2$ to $10^{-45}$ cm$^2$ as $T_\mathrm{RH}$ is lowered from much above $m_\chi$ to just a few MeV [2405.06226, 2412.04550].

## 4. Non-Instantaneous Reheating and Entropy Dilution

A realistic treatment requires accounting for non-instantaneous reheating. The maximum bath temperature $T_\mathrm{max}$ can exceed $T_\mathrm{RH}$, but most DM production is subsequently diluted by late entropy injection:
\[
Y_\chi^{\text{final}} = Y_\chi^{\text{init}} / \Delta_\text{dilution},
\]
with the dilution factor scaling with either $T_\mathrm{max}/T_\mathrm{RH}$ or the (early) matter-dominated epoch duration. The effect is model- and operator-dependent, e.g., for UV-dominated operators:
\[
Y_\chi^{\text{non-inst}} \propto T_R^7 \qquad \text{(for $d=5$ dimension operator)}
\]
but may be further suppressed during a prolonged matter epoch or cannibal phase in the dark sector [2304.07345, 2210.15653, 2506.09155, 2412.04550].

## 5. Collider, Astrophysical, and Cosmological Constraints

Enhanced couplings in low-$T_\mathrm{RH}$ 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 $T_\mathrm{RH}\lesssim m_\chi$ [2306.13061, 2405.06226, 2412.04550, 2511.21520, 2210.15653].

- **Long-lived particles**: For freeze-in from decays, the required parent decay width is much larger at low $T_\mathrm{RH}$, leading to decay lengths as short as $\sim$mm–m (or less), testable in displaced-vertex searches at the LHC (HSCP, displaced leptons, non-pointing photons) [2306.17238, 2507.15930].

- **BBN and CMB**: The minimum reheating temperature is bounded by Big Bang Nucleosynthesis considerations ($T_\mathrm{RH}\gtrsim 4$–5 MeV). Contributions to $\Delta N_{\rm eff}$ or late-time energy injection (e.g. from decays) are subject to CMB and structure-formation limits [2501.17234, 2210.15653, 2412.17308, 2203.04276].

- **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 [2412.17308, 2210.15653].

- **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 $f_R \sim T_\mathrm{RH}$), which future experiments may probe [2511.02184, 2509.17129].

## 6. Model Implementations and Portal Realizations

A diverse set of concrete UV models realize low-$T_\mathrm{RH}$ freeze-in:

- **Higgs-portal scalars and pseudoscalars**: DM produced via Higgs portals is subject to exponential suppression at $T_\mathrm{RH} \ll m_h, m_\phi$ and requires $\lambda \sim e^{m_\phi/T_\mathrm{RH}}$ to match the relic density [2306.13061, 2511.21520, 2506.09155, 2412.04550].

- **Vector mediators ($Z'$ models)**: For both $U(1)_D$ and $U(1)_{B-L}$ scenarios, the coupling between DM and SM must be increased as $T_\mathrm{RH}$ lowers, moving models into regions testable by direct detection and displaced-vertex searches [2412.12303, 2511.02184, 2509.17129, 2203.04276].

- **Ultralight dark photons**: "Minimal" freeze-in models are particularly sensitive, as $T_\mathrm{RH} < m_\chi$ leads to an upward shift in the freeze-in coupling required for the correct $\Omega h^2$; parameter space already probed by low-threshold electron-recoil detectors [2405.06226, 2412.04550].

- **Hadrophilic and photonic freeze-in**: Scenarios where production is via higher-dimensional operators (e.g., $\gamma\gamma \to \chi\bar{\chi}$ or pion fusion) yield cross-sections and couplings that are highly accessible if $T_\mathrm{RH}$ is close to the minimum allowed by BBN [2210.15653, 2412.17308].

- **Exotic topologies**: Models featuring DM production via cannibalization (2→3 or 3→2 dark-sector processes) are sensitive to $T_\mathrm{RH}$ and display nontrivial temperature and number-density histories, creating additional handles and phenomenology [2506.09155].

- **UV baryogenesis and EMD epochs**: Early matter domination or late moduli decay can both suppress and dilute freeze-in signals, connecting inflationary observables ($n_s$, $r$) to DM and baryon relics [2304.07345, 2306.17238].

## 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 [2306.13061, 2511.21520, 2412.04550]. Conversely, arbitrarily lowering $T_\mathrm{RH}$ can suppress the DM relic density below the observable window, even for superheavy DM [2509.17129].

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 [2306.17238, 2412.12303, 2210.15653].

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.

Source: https://www.emergentmind.com/topics/low-reheating-temperature-freeze-in-scenario