Mutated hybrid inflation on brane and reheating temperature

Abstract.

In the mutated hybrid-inflation standard case, the spectral index $n_{\rm s}$ is constrained by the e-folds number N, and the gravitational waves are negligible $(r\sim 10^{-4})$. Therefore, we propose to study this model in the framework of the Randall-Sundrum II braneworld scenario. Using the latest observational measurements from Planck data, we have shown that the inflation observables ( $n_{\rm s}$, r, and $\frac{{\rm d} n_{\rm s}}{{\rm d} \ln k}$ depend on all parameters. On the other hand, from the observed central value of the power spectrum perturbation $P_{\rm R}(k)$, we have determined the energy scale which must be $V_{0}^{1/4} \succsim 10^{14}$ GeV and we evaluate the brane tension value $\lambda$. We showed that the spectral index takes the central value $n_{\rm s}\sim 0.96$ and the gravitational waves becomes important $r\sim 2\times 10^{-2}$. Furthermore the running $\frac{{\rm d} n_{\rm s}}{{\rm d} \ln k}$ is perfectly in agreement with the recent observations. For the reheating phase, we have determined the value of reheating temperature $T_{\rm re}\sim 10^{9}$ GeV.