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 ∝ ϕ F μ ν F ∼ μ ν / 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.