Thermal inflation model in semiclassical quantum gravity

We study the thermal inflation model of a massive inflaton in the semiclassical quantum gravity which consists of the semiclassical Friedmann equation and the time-dependent functional Schrodinger equation. We find that when the mass is below the critical value, the inflaton in an initial thermal equilibrium leads to the quasi-exponential expansion whose rate is entirely determined by the mass, temperature and ground state energy. It is further found that the inflaton in high temperature thermal equilibrium enhances the amount of quasi-exponential expansion. The duration of inflation continues until the inflaton undergoes dynamically the quantum transition from an effective tunneling motion during the exponential expansion period to an under-damped oscillatory motion during the power-law expansion period.