Hidden Charged Dark Matter and Chiral Dark Radiation

In the light of recent possible tensions in the Hubble constant $H_0$ and the structure growth rate $\sigma_8$ between the Planck and other measurements, we investigate a hidden-charged dark matter (DM) model where DM interacts with hidden chiral fermions, which are charged under the hidden SU(N) and U(1) gauge interactions. The symmetries in this model assure these fermions to be massless. The DM in this model, which is a Dirac fermion and singlet under the hidden SU(N), is also assumed to be charged under the U(1) gauge symmetry, through which it can interact with the chiral fermions. Below the confinement scale of SU(N), the hidden quark condensate spontaneously breaks the U(1) gauge symmetry such that there remains a discrete symmetry, which accounts for the stability of DM. This condensate also breaks a flavor symmetry in this model and Nambu-Goldstone bosons associated with this flavor symmetry appear below the confinement scale. The hidden U(1) gauge boson and hidden quarks/Nambu-Goldstone bosons are components of dark radiation (DR) above/below the confinement scale. These light fields increase the effective number of neutrinos by $\delta N_{\rm eff}\simeq 0.59$ above the confinement scale for $N=2$, resolving the tension in the measurements of the Hubble constant by Planck and Hubble Space Telescope if the confinement scale is $\lesssim 1$ eV. DM and DR continuously scatter with each other via the hidden U(1) gauge interaction, which suppresses the matter power spectrum and results in a smaller structure growth rate. The DM sector couples to the Standard Model sector through the exchange of a real singlet scalar mixing with the Higgs boson, which makes it possible to probe our model in DM direct detection experiments. Variants of this model are also discussed, which may offer alternative ways to investigate this scenario.