Ultraviolet Freeze-in and Non-Standard Cosmologies

TL;DR

This work shows that UV freeze-in dark matter production is not limited to radiation-dominated reheating; the pre-reheating equation of state $ ext{ω}$ and the maximum bath temperature $T_{max}$ can dramatically alter the DM yield through a boost factor that depends on the operator dimension $n$ and the ratio $T_{max}/T_{RH}$. By developing a model-independent treatment of reheating beyond the instantaneous decay approximation, the authors derive how the critical dimension $n_c=2\frac{3-\omega}{1+\omega}$ and the boost exponent shift with $ ext{ω}$, leading to enhanced DM production for $n>n_c$ in several concrete portals. They illustrate this with gravitino production, spin-2, moduli, and Higgs portals, showing that non-standard cosmologies can reconcile underproduced DM scenarios or produce sizeable relic densities without adjusting microphysical couplings. The results motivate considering early-universe dynamics—such as a kination phase or other $ ext{ω}$-dominated epochs—in DM phenomenology, and they suggest potential indirect probes via primordial gravitational waves from the reheating era. Overall, the paper provides a coherent framework linking UV freeze-in, non-standard cosmologies, and specific portal models, highlighting when and how the relic density can be substantially boosted by the cosmological history prior to radiation domination.

Abstract

A notable feature of UV freeze-in is that the relic density is strongly dependent on the highest temperatures of the thermal bath, and a common assumption is that the relevant 'highest temperature' should be the reheating temperature after inflation $T_\text{RH}$. However, the temperature of the thermal bath can be significantly higher in certain scenarios, reaching a value denoted T max , a fact which is only apparent away from the instantaneous decay approximation. Interestingly, it has been shown that if the operators are of sufficiently high mass dimension then the dark matter abundance can be enhanced by a 'boost factor' depending on ($T_\text{max}/T_\text{RH}$) relative to naive estimates assuming instantaneous reheating. We highlight here that in non-standard cosmological histories the critical mass dimension of the operator above at which the instantaneous decay approximation breaks down, and the exponent of the boost factor, depend on the equation of state $ω$ prior to reheating. We highlight four examples in which the dark matter abundance receives a significant enhancement in the context of gravitino dark matter, the moduli portal, the Higgs portal, and the spin-2 portal (as might arise in bimetric gravity models). We comment on the transition from kination domination to radiation domination as a motivated example of non-standard cosmologies.

Figures (5)

• Figure 1: Evolution of the energy densities (upper panels) and Standard Model thermal bath temperature (lower panels) for $T_\text{RH}=10^6$ GeV and $T_\text{max}=10^8$ GeV. The left panels depict the case $\omega=-1/3$, central panels $\omega=0$ and right panels $\omega=2/3$. The dotted lines corresponding to $a=a_\text{max}$, $a_\text{RH}$ and $a_\times$ (from left to right) and $T=T_\text{max}$, $T_\text{RH}$ and $T_\times$ (from top to bottom) are overlaid.
• Figure 2: Evolution of the DM comoving number density $N$ as a function of the scale factor (upper panels) and the DM yield $Y$ as a function of $T$ (lower panels), for values $\omega=0$, $T_\text{RH}=10^6$ GeV, $T_\text{max}=10^8$ GeV and $m=100$ GeV. The left panels correspond to $n=4$ and $\Lambda=1.4\times 10^9$ GeV, the central panels to $n=6$ and $\Lambda=2.8\times 10^8$ GeV and the right ones to $n=8$ and $\Lambda=1.6\times 10^8$ GeV. The values for $\Lambda$ were chosen in order to fit the observed DM abundance with the red bands showing the observed DM relic abundance today. The horizontal dotted lines depict the approximate numerical solutions $Y_\text{rh}$ and $Y_\times$. The dotted vertical lines correspond to $a=a_\text{max}$, $a_\text{RH}$, $a_\times$ and $T=T_\text{max}$, $T_\text{RH}$, $T_\times$ respectively. The arrows in the lower panels are directed to indicate the evolution with time.
• Figure 3: Contours in the $\Lambda-\omega$ space that generates the observed DM abundance for $m=100$ GeV, $T_\text{RH}=10^6$ GeV, $T_\text{max}=10^8$ GeV for $n=4$ (left), $n=6$ (central) and $n=8$ (right). The dashed blue lines correspond to $n=n_c$ (or equivalently to $\omega=\omega_c$), and the red dotted lines indicate $\omega=1$, since value $\omega>1$ are based on certain special classes of cosmological models, e.g. DEramo:2017gplGardner:2004inChoi:1999xnDutta:2016htzOkada:2004ncMeehan:2014bya.
• Figure 4: Taking $T_\text{max}/T_\text{RH}=100$ we show a contour plot of the boost factor $B$ in the $\omega-n$ plane, where $n$ corresponds to the temperature dependence of the cross section $\langle\sigma v\rangle\sim T^n/\Lambda^{2+n}$. Equivalently the exponent value $n$ corresponds to UV freeze-in via an effective operator of mass dimension $5+n/2$. For ease of conversion, the right hand axis gives the corresponding mass dimension of the portal operator for each value of $n$. The boost factor $B$ characterizes the enhancement to the relic density due to reheating effects by normalizing to the expectations from instantaneous reheating as discussed in Section \ref{['ss:boost']}. The dashed blue lines correspond to the critical threshold $n=n_c$, beyond which (for $n>n_c$) the DM relic density due to UV freeze-in via an operator of mass dimension $n>n_c$ is parametrically enhanced. The vertical line indicates $\omega=1$.
• Figure 5: Contours of the boost factor $B$ in the $\omega-T_\text{max}/T_\text{RH}$ plane, where $\omega$ is the equation of state prior to reheating. We present plots for three different choices of the cross section temperature dependence $\langle\sigma v\rangle\sim T^n/\Lambda^{2+n}$, for $n=4$, 6, 8. The dashed vertical line corresponds to $\omega=1$.