Freeze-In Dark Matter Production

• Freeze-in production is a non-thermal mechanism that generates dark matter relics through extremely feeble portal couplings, ensuring particles never thermalize with the Standard Model.
• It employs coupled Boltzmann equations to determine the relic yield, with production processes dominated by either IR effects for renormalizable operators or UV effects for higher-dimension interactions.
• The framework connects cosmic thermal history with experimental probes, offering insights through astrophysical observations, collider experiments, and direct detection searches.

The freeze-in production mechanism is a non-thermal process for generating the relic abundance of dark matter (DM) and other feebly interacting particles in the early universe. Unlike the classic freeze-out scenario, where DM particles are initially in equilibrium with the Standard Model (SM) and then decouple as annihilation becomes inefficient, freeze-in operates with portal couplings so small that DM never thermalizes, and its abundance accrues gradually from rare bath processes. This paradigm unifies a broad family of models—including FIMPs (Feebly Interacting Massive Particles), axion-like particles, sterile neutrinos, and others—through a rigorous formalism rooted in coupled Boltzmann equations, with present-day observable consequences regulated both by particle interaction strength and cosmological thermal history.

1. Fundamental Principles and Boltzmann Formalism

The central physical condition for freeze-in is that the portal coupling between the DM candidate (X) and the SM (or a visible sector) is so feeble that the rate for X production is always sub-Hubble, i.e., $\Gamma_{\rm prod} \ll H$, so that $n_X \ll n_X^{\rm eq}$ at all times. The evolution of the number density $n_X$ is governed by the Boltzmann equation

$$\frac{dn_X}{dt} + 3H n_X = \mathcal{C}_{\rm prod}(T)\,,$$

where $\mathcal{C}_{\rm prod}$ is the sum of all relevant production terms (decay and/or scattering), and H is the Hubble rate. The comoving yield $Y_X = n_X / s$, with $s$ the entropy density, becomes a convenient object for relic density calculations.

For $2\to2$ scattering, production is: $$\frac{dY_X}{dT} = -\,\frac{\langle \sigma v \rangle \, n_{{\rm SM},1}^{\rm eq} \, n_{{\rm SM},2}^{\rm eq}}{s H T}\,,$$ integrated from some high scale (often reheating temperature $T_R$) down to temperatures well below the mass of X. For decay-dominated freeze-in, the collision term reads

$$\mathcal{C}_{\rm decay} = n_A^{\rm eq} \langle \Gamma_{A\to X Y} \rangle\,,$$

where A is a bath particle decaying into X.

The final yield is often IR-dominated—most production occurs near $T\sim m_X$ (for renormalizable interactions), and the result is insensitive to unknown early-universe conditions such as the reheat temperature, provided $T_R \gg m_X$ (0911.1120). However, for higher-dimension operators or if $m_X\gtrsim T_R$, the result can exhibit strong UV sensitivity.

2. Categories of Freeze-In Scenarios

Freeze-in production appears in several archetypal forms:

• Renormalizable (IR-dominated) freeze-in: Portal interactions are dimension-4 (e.g., small Yukawa, Higgs portal). Yield scales as $Y \sim \lambda^2 M_{\rm Pl}/m_X$ and is set mainly by $T\sim m_X$, nearly independent of $T_R$.
• Non-renormalizable (UV-dominated) freeze-in: Higher-dimension operators (suppressed by scale $\Lambda$) induce cross-sections scaling with temperature (e.g., $\langle \sigma v \rangle \sim T^{2n}/\Lambda^{2n}$), so $Y \propto T_R^{2n-1}/\Lambda^{2n}$ for $n\geq1$ (Benso et al., 14 Apr 2025, Cox et al., 2024).
• Temperature-suppressed freeze-in: If $T_R < m_X$, all production is Boltzmann suppressed, and the required portal can be significantly larger (Cosme et al., 2023, Arias et al., 28 Jan 2025).
• Semi-annihilation and forbidden channels: In "semi-production" (e.g., $\phi \chi \to \chi\chi$), the rate is proportional to the DM abundance and thus requires initial seeding and larger couplings; in "forbidden freeze-in" processes are only kinematically allowed at high temperature due to thermal corrections (Hryczuk et al., 2021, Konar et al., 2021).

An explicit model example is the singlet fermionic DM model with a feeble Yukawa and Higgs sector mixing, where the DM can be warm or cold, depending on parameters (Klasen et al., 2013).

3. Modifications from Cosmological Thermal History

Freeze-in is acutely sensitive to the cosmic expansion history:

• Non-instantaneous reheating: If reheating is not instantaneous, additional production may occur at temperatures above the standard $T_{\rm RH}$. Entropy production dilutes relic yields and can enhance parameter-space regions for freeze-in (Bernal et al., 10 Jun 2025, Dutra, 2019).
• Early matter-dominated or fast-expanding eras: If the universe underwent an early matter-dominated phase or a fast-expanding epoch (with $H \propto T^q$, $q>2$), freeze-in yields are suppressed, and required couplings must be orders of magnitude larger to compensate; couplings can become observable, with implications for LHC and direct detection (D'Eramo et al., 2017, Allahverdi et al., 2019).
• Phase transitions: In the presence of a first-order phase transition, "phase-in" production can dominate, with DM produced during the decay of a scalar field after supercooling; the DM relic density correlates with gravitational-wave peak frequency (Benso et al., 14 Apr 2025).

A comprehensive treatment requires solving coupled Boltzmann equations for DM, SM bath, and sometimes dark-sector temperature, especially if cannibal $2\to 3$ or $3\to 2$ processes are active (Bernal et al., 10 Jun 2025).

4. Advanced Phenomenology: Dark Sector Dynamics and Constraints

• Self-interactions and cannibalization: If dark-sector self-interactions (e.g., $2\leftrightarrow3$ or $3\to2$) are active, the internal dark temperature and number density evolution are profoundly altered. Number-changing processes can induce a period of "cannibalization", changing the temperature scaling and modifying the final relic density. In $\mathbb{Z}_3$ models with cubic couplings, such effects become critical (Bernal et al., 10 Jun 2025).
• Direct detection at large and small couplings: For large $\lambda$ (accessible via Boltzmann-suppressed freeze-in), direct detection experiments (e.g., LZ, XENONnT) now probe parameter space associated with freeze-in (Cosme et al., 2023, Hambye et al., 2018). For light mediators, direct detection and self-interaction cross sections can be connected.
• Astrophysical and cosmological probes: Constraints arise from warm DM limits (structure formation, Lyman-$\alpha$), supernova cooling, BBN, CMB. For axion-like or sterile-neutrino DM, the misalignment mechanism can compete with freeze-in and must be parameterized and subtracted where necessary (Arias et al., 28 Jan 2025, Bae et al., 2017). Dark photon decay, ALP warmness, and hidden-sector signatures at $B$-factories are also relevant (Arias et al., 28 Jan 2025).
• Gravitational waves: Gravitational bremsstrahlung during freeze-in induces a high-frequency stochastic GW background, peaking typically in the 10–100 GHz regime and providing a potential signal for future high-frequency detectors, particularly for UV-dominated freeze-in with $T_R\sim 10^{16}$ GeV (Wang et al., 14 Aug 2025, Benso et al., 14 Apr 2025).

5. Phase Space, Relic Abundance, and Non-Thermal Spectra

Freeze-in scenarios often produce non-thermal DM phase-space distributions distinct from the standard relics of freeze-out:

• Phase-space treatment: The single-particle distribution $f(p,t)$ for DM, governed by the full collision integral, can yield spectra that are sub-thermal ("colder"), multi-modal, or otherwise distinctive, impacting small-scale structure formation (Du et al., 2021, Bae et al., 2017).
• Warm vs. cold transition: The DM mass and production mechanism set the velocity distribution. For e.g. 7 keV axino DM, phase-space details and entropy events (such as saxion decay) can shift Ly-$\alpha$ limits, enabling viable parameter space even for relatively warm DM species (Bae et al., 2017).
• Analytic relic abundance: The final abundance is $\Omega_X h^2 = (m_X s_0/\rho_c) Y_X^{\infty}$, with $Y_X^\infty$ computed via the aforementioned Boltzmann integrals. For forbidden channels, the kinematic thresholds and thermal corrections must also be incorporated (Konar et al., 2021).

6. Representative Models and Experimental Signatures

A broad class of scenarios have been analyzed in the freeze-in context, each with specific portal operators and phenomenological signatures:

• Axion/dark photon portals: Dimension-5 operators coupling axion-like particles to photons and dark photons ($$g_{\phi\gamma\gamma'}\,\phi F_{\mu\nu} \tilde F'^{\mu\nu}$$) realize both weak and strong freeze-in, with strong coupling regions accessible to $B$-factory searches (Arias et al., 28 Jan 2025).
• Photonic freeze-in: Pure $F_{\mu\nu}F^{\mu\nu}$ portal via a loop of TeV-scale charged states, yielding UV-dominated yields $\propto T_R^4/\Lambda_s^4$ for scalar DM and subject to direct detection, LHC, SN1987A, and structure-formation constraints (Cox et al., 2024).
• Spin-1/spin-2 portals: Feeble $U(1)'$ (with Chern-Simons connection to gluons) or Planck/intermediate-scale spin-2 mediators yield strong $T_R$-dependence and can be dramatically enhanced by a non-instantaneous reheating phase (Dutra, 2019).
• Higgs portal and variants: Majorana/Dirac DM with $1/\Lambda$-suppressed Higgs coupling; the interplay of EWSB, resonance effects at $m_\chi\sim m_h/2$, and the nature of reheating phase determine the abundance (Mondal et al., 26 Mar 2025).
• Semi-annihilation and semi-production: In $\mathbb{Z}_3$-stabilized models with $\phi \chi^3$ couplings, semi-production ($\phi\chi\to\chi\chi$) freeze-in can yield indirect-detection observable rates, in contrast with standard FIMP where the late-time annihilation is negligible (Hryczuk et al., 2021).

Predictions for direct/indirect detection depend crucially on whether the required portal couplings fall into the observable regime, as can be achieved with either suppressed production temperature (Boltzmann suppression), fast expansion, or in semi-production scenarios.

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This hierarchy of mechanisms, underpinned by precise numerical and analytic Boltzmann analyses, establishes freeze-in as a mature and predictive framework for dark matter genesis—one in which the cosmic, particle, and astrophysical input parameters are intertwined, and where upcoming advances in both laboratory and cosmological observation will further delineate and test the allowable parameter space (0911.1120, Arias et al., 28 Jan 2025, Mondal et al., 26 Mar 2025, Cosme et al., 2023, Hambye et al., 2018, Cox et al., 2024, Bernal et al., 10 Jun 2025, Wang et al., 14 Aug 2025, Benso et al., 14 Apr 2025, Allahverdi et al., 2019, D'Eramo et al., 2017, Klasen et al., 2013, Bae et al., 2017, Hryczuk et al., 2021, Du et al., 2021, Konar et al., 2021, Das et al., 2021, Heeba et al., 2018, Dutra, 2019).