Equilibrium thermodynamics of axion inflation

Thermal effects from the ensemble average and thermal mass are analyzed in the model of axionic inflaton interacting with U(1) gauge fields through the Chern-Simons coupling proportional to phi F mu nu F mu nu/f under equilibrium. The ensemble average eliminates the divergence of radiational spectral density. The cosmic temperature is controlled by the parameter xi=(center dot)phi/(2Hf) and the renormalization coefficient alpha T. It is found that the adiabatic approximation is always corresponding to a slow-roll approximation in the (quasi-)de Sitter universe. The equilibrium condition and backreaction constrain the parameter in a range of 2.47 < xi < 6.52, and the axion becomes thermalized if xi similar or equal to 4.0. Thermal mass leads to the correlation of scalar perturbation and tensor perturbation, which may be a potential method to distinguish different cosmological models. In addition, the tensor-to-scalar ratio is suppressed in a form proportional to H/T if the fields become thermal in the Standard Model. On the other hand, the condition xi<3.0 is the same as cold inflation, i.e., r similar or equal to 16 & varepsilon;, although thermal effects are taken into consideration.