  In the framework of axion-gauge fields models, primordial gravitational wave
perturbations could be generated during the inflationary epoch from not only
the quantum fluctuation of gravitons but also the dynamics of hidden gauge
fields coupled with an axion field. We investigate the evolution of the axion
and the gauge field of an additional hidden SU(2) gauge group and those energy
densities during and after the inflation. We show that the extra radiation
component of the hidden gauge bosons produced by the axion decay can be sizable
in the cases where the gauge fields sourced additional gravitational waves is
subdominant. We point out that future measurements of the dark radiation
energy, such as CMB-S4, can impose significant constraints on this cosmological
scenario.
