Dark radiation in spectator axion-gauge models

In the framework of axion-gauge field 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-field-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.