Light dark photon and fermionic dark radiation for the Hubble constant and the structure formation

TL;DR

This paper addresses the $H_0$ and $\sigma_8$ tensions by proposing a dark sector in which DM interacts with fermionic DR via a light dark photon. The framework yields $\delta N_{\rm eff} \approx 0.5$, helping reconcile Planck and HST measurements, while DM-DR diffusion damping suppresses the matter power spectrum, reducing $\sigma_8$. The model features a local $U(1)_X$ with DM $\chi$, DR $\psi$, and mediator dynamics, linking relic density, $\delta N_{\rm eff}$, and late kinetic decoupling to observable cosmological signals. Numerical results using CLASS demonstrate a $\sim$10% suppression in $P(k)$ and a corresponding reduction in $\sigma_8$ for $m_\chi \sim 100$ GeV and $g_X^2 \sim 10^{-8}$, illustrating the viability of this approach to alleviate cosmological tensions.

Abstract

Motivated by the tensions in the Hubble constant $H_0$ and the structure growth $σ_8$ between $Planck$ results and other low redshift measurements, we discuss some cosmological effects of a dark sector model in which dark matter (DM) interacts with fermionic dark radiation (DR) through a light gauge boson (dark photon). Such kind of models are very generic in particle physics with a dark sector with dark gauge symmetries. The effective number of neutrinos is increased by $δN_{eff} \sim 0.5$ due to light dark photon and fermionic DR, thereby resolving the conflicts in $H_0$. The elastic scattering between DM and DR induces suppression for DM's density perturbation, but without acoustic oscillations. For weakly-interacting DM around $100$GeV, the new gauge coupling should be $\sim 10^{-4}$ to have sizable effect on matter power spectrum in order to relax the tension in $σ_8$.

Figures (1)

• Figure 1: Illustration on matter power spectrum $P(k)$ with $m_\chi\simeq 100\mathrm{GeV}$ and $g^2_X\simeq 10^{-8}$. The black solid lines are for $\Lambda$CDM and the blue dashed lines for interacting DM-DR case. We can easily see that $P(k)$ is suppressed for modes that enter horizon at radiation-dominant era.