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 _ { \textrm { 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 .