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

摘要

The potential V (phi) = lambda phi(n) is responsible for the inflation of the universe as scalar field f oscillates quickly around some point where V (f) 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 S(eta) proportional to+ eta(1 + beta), S(eta) proportional to+ eta(1 + beta s), respectively. The reheating temperature (T-rh) and beta s give us valuable information about the reheating stage. Recently, people have studied about the behavior of Trh based on slow-roll inflation and initial condition of quantum normalization. It is shown that there is some discrepancy on Trh due to the amount of beta s 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 beta s and hence the obtained temperatures based on the calculated beta s are in favor of both mentioned conditions. Then from given beta s, we can calculate Trh, tensor-to-scalar ratio r and parameters beta, n based on the Planck and WMAP-9 data. The observed results of r, beta s, beta and n have consistency with their constrains. Also the results of Trh are in agreement with its general range and special range based on the DECIGO and BBO detectors.