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

Motivated by the tensions in the Hubble constant $H_0$ and the structure growth $\sigma_8$ 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 $\delta N_{eff} \sim 0.5$ 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 $\sigma_8$.