The more investigation of inflation and reheating stages based on the Planck and WMAP-9

Abstract

The potential $V(\phi)=\lambda \phi^{n}$ is responsible for the inflation of the universe as scalar field $\phi$ oscillates quickly around some point where $V(\phi)$ 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 behaviour of the inflation and reheating stages are often known as power law expansion $S(\eta) \varpropto \eta^{1+\beta}$, $S(\eta) \varpropto \eta^{1+\beta_{s}}$ respectively. The reheating temperature ($T_{rh}$) and $\beta_{s}$ give us valuable information about the reheating stage. Recently people have studied about the behaviour of $T_{rh}$ based on slow-roll inflation and initial condition of quantum normalization. It is shown that there is some discrepancy on $T_{rh}$ due to amount of $\beta_{s}$ under the condition of slow-roll inflation and quantum normalization \cite{acq}. Therefore the author is believed in \cite{acq} 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 favour of both mentioned conditions. Then from given $\beta_{s}$, we can calculate $T_{rh}$, 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 $T_{rh}$ are in agreement with its general range and special range based on the DECIGO and BBO detectors.