Z' portal dark matter from post-inflationary reheating: WIMPs, FIMPs, and UFOs

TL;DR

This paper investigates dark matter production via a heavy $Z'$ portal during the post-inflationary reheating epoch, unifying freeze-in, ultra-relativistic freeze-out (UFO), and WIMP-like freeze-out (FO) within a single framework. It analyzes non-instantaneous reheating with $T_{ m max}$ and $T_{ m RH}$, derives production rates for vector and axial-vector couplings, and solves the Boltzmann equations to obtain the relic abundance across FI, UFO, and FO regimes. A key finding is that UFO can dominate much of the viable parameter space for $M_{Z'}$ in the range $10^4$–$10^{10}$ GeV and $m_\chi$ from $10^{-7}$–$10^7$ GeV, producing cold DM despite initial relativistic decoupling, and allowing stronger couplings than standard FI. The work also characterizes how the DM relic density depends on the reheating temperature and mediator mass, extends the viable DM mass/coupling space beyond conventional FI/FO, and highlights potential detectability due to larger interaction strengths in UFO relative to FI.

Abstract

We investigate the production of dark matter (DM) via a heavy $Z'$ mediator during the post-inflationary reheating epoch. In particular, we study production from three mechanisms which are smoothly connected to one another: WIMP-like freeze-out, FIMP-like freeze-in, and ultra-relativistic freeze-out (UFO). This is the first systematic study of $Z'$ portal DM which includes UFO. We find that much of the available parameter space for keV to TeV DM lies in the UFO regime for $ 1 \text{ TeV}\lesssim M_{Z'} \lesssim 1 \text{ PeV}$. When the mediator mass $M_{Z'}$ is greater than both the DM mass and the reheating temperature, UFO is a robust mechanism for producing cold DM. Although UFO DM is initially "hot" after freeze-out, it can easily become cold before structure formation if freeze-out occurs during post-inflationary reheating. Compared to standard freeze-in, UFO can accommodate significantly stronger interaction strengths (stronger couplings and/or smaller mediator masses).

Figures (7)

• Figure 1: Evolution of the energy densities of the oscillating inflaton condensate and the SM radiation bath during and after the reheating period (left panel). Evolution of the co-moving number of SM radiation and the co-moving DM equilibrium number densities (right panel) for two choices of DM mass, $m_\chi=1$ GeV ($m_\chi<T_{\rm RH}$) and $m_\chi=10^4$ GeV ($m_\chi>T_{\rm RH}$). $T_{\rm RH}=100$ GeV in both panels. The co-moving SM radiation number density, $Y_{R}$, in the right panel has been normalized to that of a representative fermionic SM bath species (e.g. electron) for direct comparison with fermionic DM.
• Figure 2: The evolution of the co-moving DM number density $Y_\chi$ for WIMP-like FO (solid red), UFO (dotted blue), and FI (dashed purple) when DM production occurs during reheating (top panel, focus of this study) or during radiation domination (bottom panel, standard scenario). Parameter choices are $M_{Z'}=10$ TeV, $m_{\chi}=100$ GeV for both panels. For the top panel, $T_{\rm RH}=1$ GeV and the couplings are $V_\chi=1$ (red), $V_\chi=0.1$ (blue), and $V_\chi=0.01$ (purple). For the bottom panel, $T_{\rm RH}=10^{10}$ GeV and the couplings are $V_\chi=1$ (red), $V_\chi=0.01$ (blue), and $V_\chi=10^{-5}$ (purple). The horizontal gray dashed lines indicate the correct final abundance. The thin vertical line in the top panel corresponds to $T=\frac{2}{13}m_\chi$, which is the natural boundary between non-relativistic and relativistic FO during reheating.
• Figure 3: The $(m_{\chi},T_{\rm RH})$ plane showing contours (black) for which $\Omega_{\chi}h^2=0.12$. Three choices of $M_{Z'}$ are displayed in separate figures illustrating the regions of parameter space associated with UFO (blue), WIMP-like FO (red), and freeze-in (purple) (top left: $M_{Z'}=10^4$ GeV, top right: $M_{Z'}=10^6$ GeV, bottom left: $M_{Z'}=10^8$ GeV). In the bottom right panel, contours corresponding to the correct abundance are overlaid for four choices of $M_{Z'}$. Couplings were chosen to be $V_{f}=V_{\chi}=1$ and $A_{f}=A_{\chi}=0$. The thin gray lines correspond to $m_{\chi}=T_{\rm RH}$. The shaded region at the bottom of each plot is excluded due to the lower bound on $T_{\rm RH}$ from BBN ($T_{\rm RH}>4$ MeV).
• Figure 4: Comparison of contours in the $(m_\chi,T_{\rm RH})$ plane for different values of the coupling $V_\chi$ for $M_{Z'}=10^6$ GeV. Each contour corresponds to the correct relic abundance $\Omega_\chi h^2=0.12$. The thin gray line corresponds to $m_\chi=T_{\rm RH}$.
• Figure 5: Comparison of the viable parameter space for vector vs. axial vector couplings for $M_{Z'}=10^6$ GeV. Contours in the $(m_{\chi},T_{\rm RH})$ correspond to $\Omega_{\chi}h^2=0.12$. The left panel displays the entire parameter space, while the right panel is a zoom of the left plot which depicts the regime where the two coupling contours differ. The gray lines in each panel correspond to $m_{\chi}=T_{\rm RH}$.