Decoupling of Asymmetric Dark Matter During an Early Matter Dominated Era

TL;DR

This work investigates asymmetric dark matter (ADM) that decouples during an early matter-dominated era, developing a model-independent Boltzmann framework for an $s$-wave ADM and showing how a nonstandard expansion history and entropy injection from a decaying field alter the relic yield. It quantifies the evolution of the dark matter and anti-dark matter abundances, introduces the fractional asymmetry $F$, and derives how the final relic density depends on the initial asymmetry $\eta_{\chi}$, the annihilation cross section, and the dilution factor $\zeta$ from the transition to radiation domination. The authors then embed this scenario in an SO(10) GUT context with a long-lived RH neutrino driving the matter-dominated epoch and a Higgs-portal scalar dark matter candidate, illustrating viable parameter space under current experimental constraints and showing how $T_{RH}$ controls the dilution. The analysis demonstrates that entropy injection can enable superheavy ADM (up to $\sim 10^{11}$ GeV for certain $T_{*}$) by suppressing the symmetric component and relaxing unitarity bounds, with implications for cosmology and astrophysical objects.

Abstract

In models of Asymmetric Dark Matter (ADM) the relic density is set by a particle asymmetry in an analogous manner to the baryons. Here we explore the scenario in which ADM decouples from the Standard Model thermal bath during an early period of matter domination. We first present a model independent analysis for a generic ADM candidate with s-wave annihilation cross section with fairly general assumptions regarding the origin of the early matter dominated period. We contrast our results to those from conventional ADM models which assume radiation domination during decoupling. Subsequently, we examine an explicit example of this scenario in the context of an elegant SO(10) implementation of ADM in which the matter dominated era is due to a long lived heavy right-handed neutrino. In the concluding remarks we discuss the prospects for superheavy ADM in this setting.

Figures (4)

• Figure 1: Evolution of the abundances of dark matter $Y^{+}$ and anti-dark matter $Y^{-}$ as functions of $x = m_{\chi}/T$, assuming radiation domination (RD) and matter dominated (MD), for an annihilation cross-section $\sigma_{0} = 2~{\rm pb}$ and an initial dark matter asymmetry $\eta_{\chi}= 10^{-10}$. We assume that matter domination occurs at a temperature of $10^{5}~{\rm GeV}$ in the case of decoupling during a matter dominated era. Observe that for the same particular choices of particle physics parameters (masses, couplings), radiation dominated decoupling implies an ADM scenario with the late time abundance set by $\eta_{\chi}$, while the matter dominated case leads to symmetric dark matter. Thus cosmology can play a role in determining the late time dark matter scenario.
• Figure 2: Contours for which the observed relic density $\Omega_{\rm relic}h^{2}\approx 0.12$ is obtained as functions of the initial asymmetry $\eta_{\chi}^{\rm initial}$ and the mass of dark matter $m_{\chi}$ for different entropy dilution factor $\zeta$ as indicated. With $\sigma_{0}$ as in eq. \ref{['eq:MIsigma']}, the plot shows the case of two different values of the coupling constant $\kappa_{\chi}=0.3$ and 0.05 as indicated by solid and dashed lines, respectively. We cut off matter domination case for $m_{\chi}>25\times T_\star$ since $m_{\chi}/25$ is the characteristic freeze-out point and thus beyond this the dark matter freezes out in a radiation domination regime prior to $\phi$ matter domination.
• Figure 3: The present fractional asymmetry $F_{f}$ as function of the cross-section $\sigma_{0}$ relative to the traditional WIMP cross section $\sigma_{0,{\rm WIMP}}$. One can observe variations of the late time fractional asymmetry $F_{f}$ with $\sigma_{0}/\sigma_{0,{\rm WIMP}}$, for a fixed mass (left panel) and for a fixed asymmetry $\eta_{\chi}$ (right panel) for two different dark matter masses $m_{\chi} = 1.0\times 10^{4}~{\rm GeV}$ (solid line) and $m_{\chi} = 1.5\times 10^{4}~{\rm GeV}$ (dashed line). The case of decoupling in the radiation dominated era is shown as the black curve.
• Figure 4: An entropy injection dilutes the dark matter after freeze-out introducing a new parameter for calculating the dark matter relic density, the energy from the entropy injection sets the reheat temperature of the Standard Model radiation bath to $T_{\rm RH}$. We show contours of $T_{\rm RH}$ for which $F_f=Y_{\overline{\rm DM}}/Y_{\rm DM}=10^{-2}$ evaluated at freeze-out, thus the dark matter is asymmetric and reproduces the observed relic density for couplings on or above a given contour. The model under consideration is a complex scalar dark matter annihilating through the Higgs portal, as motivated by the SO(10) model discussed here. Experimental constraints are shown from XENON1T Aprile:2018dbl (dashed red), LUX Akerib:2016vxi (dashed orange), Fermi-LAT Ackermann:2015zua (dashed purple) and the invisible Higgs width Escudero:2016gzxKhachatryan:2016whc (dashed brown). The grey shaded region indicates where the theoretical analysis breaks down, corresponding to the assumption of a matter dominated universe. The neutrino floor is shown as the dashed green curve. We assume that the onset of matter domination occurs at $T_{\rm MD} = M_N/100\sim 10^{8}~{\rm GeV}$, as might arise for $T_\star\sim M_N$ with the fraction of energy in $N_1$ at $T=T_\star$ being $r=0.01$, cf. eq. (\ref{['MDD']}). The white space in each panel is viable parameter space in which the dark matter relic density is correct while evading experimental limits for an appropriate choice of $T_{\rm RH}$ (it is, however, below the neutrino floor). We note that reducing $F_f$ by an order of magnitude or two leads to quite similar plots.