Ultraviolet Freeze-In Mechanism

• Ultraviolet freeze-in is a non-thermal process that generates dark matter through feeble interactions mediated by non-renormalizable operators at high temperatures.
• It relies on effective operators whose production rates scale with reheating temperatures, making the relic yield highly sensitive to early universe thermal history.
• The mechanism links particle physics and cosmology, offering testable predictions via direct detection experiments, gravitational waves, and CMB constraints on light relics.

Ultraviolet (UV) freeze-in is a non-thermal mechanism for generating the cosmic abundance of dark matter (DM) or other relics. In this scenario, the DM candidate interacts with the Standard Model (SM) so feebly—typically via non-renormalizable effective operators suppressed by large mass scales—that it never thermalizes with the visible sector. The DM relic density is built up gradually through rare interactions in the early-universe plasma, with production rates that increase with temperature and are UV-sensitive. Unlike IR freeze-in, which is dominated at late times by weak, renormalizable couplings, UV freeze-in is governed by high-temperature physics, cosmological history, and the dimensionality of the connector operators between the SM and DM sectors. The resulting phenomenology is sharply dependent on both the microphysics (the operator structure, underlying mediators, or portals) and the macroscopic thermal history (particularly reheating dynamics, maximum temperatures, and possible kination or non-standard expansion epochs).

1. Theoretical Framework of Ultraviolet Freeze-in

UV freeze-in arises when the leading SM–DM couplings are described by non-renormalizable operators of mass dimension $d>4$, generically of the form

$$\mathcal{O}_d = \frac{1}{\Lambda^{d-4}}\, (\text{SM fields})\,(\text{DM fields}),$$

where $\Lambda$ is the heavy-mediator or portal mass scale. In this regime, the DM production rate in the early universe is proportional to a positive power of temperature: $\gamma(T) \propto T^{2d-4} / \Lambda^{2d-8},$ for generic $2 \to 2$ processes in the UV freeze-in regime (Elahi et al., 2014, Chen et al., 2017). As a result, DM production is dominated by the highest temperatures attained by the thermal bath—typically the reheating temperature $T_\mathrm{RH}$, or even the maximum temperature $T_{\max}$ reached during reheating if the process is not instantaneous.

The Boltzmann equation for the DM number density $n_\chi$ is given by

$\frac{d n_\chi}{dt} + 3 H n_\chi = \gamma(T),$

where $H$ is the Hubble parameter. The comoving yield $Y_\chi = n_\chi/s$ ($s$ is the entropy density) can be analytically integrated over temperature, yielding the relic density. For a leading operator of dimension $d$, the relic yield produced after reheating (in radiation domination) scales as

$$Y_\chi \propto \frac{m_\chi M_\mathrm{Pl} T_\mathrm{RH}^{2d-9}}{\Lambda^{2d-8}},$$

with $M_\mathrm{Pl}$ the reduced Planck mass (Chen et al., 2017, Elahi et al., 2014, Bernal et al., 8 Jan 2025).

Operators of larger dimension and higher $T_\mathrm{RH}$ (or $T_{\max}$) enhance the DM production, which is characteristic of the UV-dominated regime.

2. Cosmological Dependence and Reheating Dynamics

The thermal history of the universe, and specifically the details of the reheating era, are central to UV freeze-in phenomenology. Under instantaneous reheating, $T_{\max} = T_\mathrm{RH}$ and DM production is concentrated in a narrow temperature window. If reheating is non-instantaneous, entropy injection and higher initial temperatures ($T_{\max} \gg T_\mathrm{RH}$) can significantly alter the relic yield (Bernal et al., 2019, Bernal et al., 8 Jan 2025, Barman et al., 2022).

Analytic solutions describe three characteristic regimes, parametrized by the mass-dimension $n=2d-8$ of the operator, the effective equation of state $\omega$ during reheating, and the scaling of the temperature with scale factor $a$. There exists a critical dimension $d_c(\omega) = (3-\omega)/(1+\omega) + 5$ above which the relic yield gains a power-law enhancement proportional to $(T_{\max}/T_\mathrm{RH})^{2d-16}$; below this, the reheating period is subdominant and the IR contribution at $T_\mathrm{RH}$ dominates (Chen et al., 2017, Bernal et al., 2019, Bernal et al., 2020, Bernal et al., 8 Jan 2025).

Specific non-standard post-inflationary eras—such as kination domination ($\omega=1$)—can dramatically boost UV freeze-in yields by sustaining high temperatures for longer with minimal entropy injection (Bernal et al., 2020). In warm-inflation scenarios, dark matter can even be generated efficiently during inflation itself, with enhancements scaling steeply with the operator dimension (Freese et al., 2024).

3. Relic Abundance Calculations and Scaling Relations

The relic abundance in UV freeze-in is highly sensitive to four parameters: the DM mass $m_\chi$, the portal scale $\Lambda$, the highest bath temperature $T_\mathrm{RH}$ (or $T_{\max}$), and the operator dimension $d$. For a dimension-$d$ operator,

$$\Omega_\chi h^2 \simeq C_d \, (m_\chi/\mathrm{GeV}) \, (M_\mathrm{Pl}/\Lambda)^{2n} \, (T_\mathrm{RH}/M_\mathrm{Pl})^{2n-1},$$

where $n = d - 4$, and $C_d$ is an $\mathcal{O}(10^8)$ coefficient fixed by phase-space and statistical factors (Elahi et al., 2014). Important regimes include:

• $m_\chi \ll T_\mathrm{RH}$: No Boltzmann suppression; yield is UV-dominated.
• $m_\chi \gg T_\mathrm{RH}$ and $m_\chi < T_{\max}$: Boltzmann suppression, with $Y \propto e^{-2m_\chi/T_*}$, and $T_* = T_{\max}$ in non-instantaneous cases (Bernal et al., 1 Oct 2025, Chen et al., 2017).
• $m_\chi > T_{\max}$: Yield is exponentially suppressed; DM production is inefficient (Bernal et al., 1 Oct 2025).

Non-instantaneous reheating and stiff EoS ($\omega > 1/3$) further amplify production, especially for operators with $d>6$, leading to parametric enhancements of the yield (Bernal et al., 2020, Bernal et al., 2019).

4. Portal Models and Concrete Realizations

UV freeze-in is realized in a variety of BSM frameworks:

• Axion, Z$^\prime$, and Higgs Portals: UV freeze-in via dimension-5 or 6 operators, e.g., $S^\dagger S \bar\chi\chi / \Lambda$ or $(H^\dagger H) \bar\chi\chi / \Lambda$ (Elahi et al., 2014, Chen et al., 2017).
• Gluonic Portals: Hidden Yang–Mills sectors produce glueball DM via gauge or Higgs field strength operators, with operator dimensions $d=6,8$ (Kang, 2019).
• Dilaton Portal: Spontaneously broken scale-invariance leads to dimension-5/6 portals connecting SM and DM via the dilaton field, with relic yields scaling as $Y_\chi \propto T_{\max}^3/f^4$ for scalar/vector DM (Ahmed et al., 2021).
• UV-Complete Frameworks: Extensions such as left–right symmetric models provide loop-suppressed or heavy-portal-induced UV freeze-in with DM mass in the keV–TeV range (Biswas et al., 2018).
• Gravitino, Moduli, Spin-2, and Neutrino-Portal Models: Various BSM sectors, including high-scale SUSY, generate DM via higher-dimension operators and are subject to specific cosmological and laboratory constraints (Bernal et al., 2019, Chen et al., 2017).

All these models share the common feature that the UV freeze-in mechanism is insensitive to the strength of the dimensionless couplings (provided they avoid thermalization), but highly sensitive to the UV scale, operator dimension, and thermal history.

5. Baryogenesis, Asymmetry, and Light Relics

Extensions of UV freeze-in scenarios accommodate baryogenesis and dark sector asymmetries. Out-of-equilibrium, CP-violating $2\to2$ scatterings via non-renormalizable operators can simultaneously yield the observed baryon asymmetry and dark matter density, provided the parameters support efficient CP-violating interference and suppression of wash-out processes. These mechanisms typically require operator dimensions $d=5$ or $6$, heavy mediators, and DM in the $1$–$10^2$ keV range for cogenesis (Goudelis et al., 2022, Asadi et al., 28 May 2025, Dong et al., 24 Jul 2025).

The UV freeze-in paradigm also applies to the production of feebly coupled light relics—such as axion-like particles, dark photons, or right-handed neutrinos—which contribute to the effective number of relativistic degrees of freedom, $\Delta N_\mathrm{eff}$. The predictivity of UV freeze-in for light relics makes next-generation CMB experiments (CMB-S4, CMB-HD) especially sensitive to the highest temperature and portal dimension (Caloni et al., 2024).

6. Phenomenological Probes and Experimental Prospects

Direct detection prospects for UV freeze-in dark matter depend critically on the underlying portal model and couplings. In the case of low-scale hadrophilic UV freeze-in mediated by a scalar, predicted DM–nucleon cross sections can approach $\sigma_{\chi n} \sim 10^{-45}$–$10^{-42}$ cm$^2$ for $m_\chi \sim 0.2\,\mathrm{keV}$–$100\,\mathrm{MeV}$ and reheating temperatures as low as $T_\mathrm{RH} \sim 6$–$16\,\mathrm{MeV}$, making them accessible to future low-threshold recoil experiments. Collider constraints on mediators impact the allowed coupling strength and, by extension, the minimal direct-detection cross section (Bhattiprolu et al., 2022).

Gravitational wave (GW) signatures arise in UV freeze-in due to graviton bremsstrahlung in SM-DM scatterings. The resulting high-frequency stochastic GW background peaks at $f_\mathrm{peak} \sim 5 \times 10^{10}\,$Hz with $\Omega_\mathrm{GW} h^2 \lesssim 10^{-16}$, outside current GW detector sensitivities but potentially accessible via future high-frequency detectors (Wang et al., 14 Aug 2025).

CMB constraints on $\Delta N_\mathrm{eff}$ from freeze-in production of light relics can surpass many astrophysical and laboratory limits, probing parameter regions inaccessible to direct searches, especially for higher-dimension operators and large $T_\mathrm{RH}$ (Caloni et al., 2024).

For asymmetric DM or baryogenesis via UV freeze-in, structure-formation and X-ray bounds constrain the viable mass ranges (e.g., $24$–$1000$ keV for DM in oscillation baryogenesis), and future small-scale structure or line searches may provide definitive tests (Asadi et al., 28 May 2025, Dong et al., 24 Jul 2025).

7. Summary of Core Formulas and Parameter Dependence

A compact summary of key scaling relations relevant for UV freeze-in is presented in the following table:

Operator Dimension $d$	Production Rate $\gamma(T)$	Yield $Y_\chi$ Scaling	Sensitivity to $T_{\max}$
$d \leq 8$	$T^{2d-4}/\Lambda^{2d-8}$	$M_\mathrm{Pl} T_\mathrm{RH}^{2d-9}/\Lambda^{2d-8}$	No (IR dominated)
$d > 8$	$T^{2d-4}/\Lambda^{2d-8}$	$M_\mathrm{Pl} T_{\max}^{2d-9}/\Lambda^{2d-8}$	Yes (UV dominated)

For $d \leq 8$ (e.g., dimension-5 to 8 operators), the freeze-in abundance is set by $T_\mathrm{RH}$, making cosmological probes (BBN, CMB) and collider bounds on portal scales critical. For $d > 8$, the abundance acquires significant sensitivity to $T_{\max}$ and the details of reheating, making UV freeze-in a probe of the universe's earliest dynamics (Chen et al., 2017, Bernal et al., 2019).

In conclusion, UV freeze-in is a robust and predictive mechanism for generating DM and light relic abundances in the early universe, controlled by portal operator structure, smoothing dynamics of reheating, and the highest attainable temperatures after inflation. It produces a broad array of signatures—ranging from enhanced direct detection prospects at low mass, unique GW backgrounds, and characteristic cosmological imprints in $\Delta N_\mathrm{eff}$—and connects diverse experimental and observational frontiers (Elahi et al., 2014, Chen et al., 2017, Bhattiprolu et al., 2022, Bernal et al., 8 Jan 2025, Bernal et al., 1 Oct 2025, Caloni et al., 2024, Wang et al., 14 Aug 2025).