  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.
