Reheating in inflation models with the inflaton decaying into radiation

The physics of reheating can provide additional predictions for inflationary models and thus has spurred an increasing deal of interest. In this paper, by considering a special function for the decay of the inflaton into radiation, which renders the effective equation of state (EoS) parameter to be time varying during reheating, we investigate the constraints on reheating from the cosmic microwave background observations and the effect of reheating on the predictions for inflationary models. Our work is different from previous ones where a constant EoS parameter is assumed. Taking the power-law inflationary models as concrete examples, we find that the time-varying EoS parameter during reheating entails a non-negligible effect on the reheating predictions.

Figure 1

Evolutions of the effective EoS parameter $w_{\mathrm{eff}}$ during reheating for power-law potential with $p=2/3$, $4/3$, 1, and 2. The dashed line corresponds to $1/3$.

Figure 2

The $N_{\mathrm{re}}-n_s$, ${\mathrm{Log}}_{10}[T_{\mathrm{re}}/\mathrm{GeV}]-n_s$ and $N_{*}-n_s$ for power-law inflationary models. In the left and middle column panels, the different colored solid lines correspond to different values of $\delta$, and the different colored dashed lines are the results of different values of $w_{\mathrm{re}}$. In the right column panels the green lines are the results with $\delta$ varying in the allowed regions given in Eq. (36). The brown region indicates the $1\sigma$ bound on the spectral index from the Planck 2018 TT, TE, $\mathrm{EE}+\mathrm{lowE}+\mathrm{lensing}$ data [12]. The gray region shows that temperatures are below the electroweak scale, ${10}^2\mathrm{GeV}$, and temperatures below $T_{\mathrm{re}}<{10}^{-2}\mathrm{GeV}$ shown as the green region are ruled out by the BBN.

Figure 3

The green lines show the predicted $r$ against $n_s$ for the power-law inflationary models with $\delta$ varying in the allowed regions given in Eq. (36). The blue and light blue regions are the $1\sigma$ and $2\sigma$ observational constraints at the pivot scale $k_{*}=0.002{\mathrm{Mpc}}^{-1}$ from the Planck 2018 TT, TE, $\mathrm{EE}+\mathrm{lowE}+\mathrm{lensing}$ data [12].