Thermodynamics of warm axionic Abelian gauge inflation

Inflationary spectral index from the Langevin equation is calculated under the frame of warm inflationary scenario with inflaton interacting with U(1) gauge fields through the Chern-Simons coupling proportional to phi F mu nu F similar to mu nu/f . Under the strong dissipative condition, the spectral index is calculated in terms of the ratio of Hubble parameter to temperature H/T. Then relation between H/T and other cosmic parameters is analytically expressed, based on which a spectral index related to the Chern-Simons coupling strength is further obtained. Numerical results show that cosmic temperature T closes to a constant during inflation and decreases after inflation without a reheating process. Meanwhile, the ratio H/T tends to a constant if the gauged coupling constant is less than a threshold. This phenomenon shows that cosmic temperature may be an important physical parameter with a special value and adiabatic approximation still holds. We obtain the estimate H/T <= 0.3377 during inflation from Planck data and other constraint conditions.