Further investigation about inflation and reheating stages based on the Planck and WMAP-9

Abstract

The potential [Formula: see text] is responsible for the inflation of the universe as scalar field [Formula: see text] oscillates quickly around some point where [Formula: see text] has a minimum. The end of this stage has an important role on the further evolution stages of the universe. The created particles are responsible for reheating the universe at the end of this stage. The behavior of the inflation and reheating stages are often known as power law expansion [Formula: see text], [Formula: see text], respectively. The reheating temperature ([Formula: see text]) and [Formula: see text] give us valuable information about the reheating stage. Recently, people have studied about the behavior of [Formula: see text] based on slow-roll inflation and initial condition of quantum normalization. It is shown that there is some discrepancy on [Formula: see text] due to the amount of [Formula: see text] under the condition of slow-roll inflation and quantum normalization [M. Tong, Class. Quantum Grav. 30 (2013) 055013.]. Therefore, the author is believed in [M. Tong, Class. Quantum Grav. 30 (2013) 055013.] that the quantum normalization may not be a good initial condition but it seems that, we can remove this discrepancy by determining the appropriate parameter [Formula: see text] and hence the obtained temperatures based on the calculated [Formula: see text] are in favor of both mentioned conditions. Then from given [Formula: see text], we can calculate [Formula: see text], tensor-to-scalar ratio [Formula: see text] and parameters [Formula: see text] based on the Planck and WMAP-9 data. The observed results of [Formula: see text] and [Formula: see text] have consistency with their constrains. Also the results of [Formula: see text] are in agreement with its general range and special range based on the DECIGO and BBO detectors.