Numerical calcultaion of e-fold number from hilltop with two inflatons

Abstract

We consider a cosmological inflation with two inflatons, $\varphi$ and $X$. The inflation potential is a hilltop form in the $\varphi$ space and $X$ is a sideway down-fall field in the region $\varphi \ge m$. In this model, we calculate the $e$-fold number numerically starting from the intitial point which is in the vicinity of the hilltop point. Firstly, by varying parameters and initial conditions the inflaton path field $\phi$ for the BICEP2 point, ${\phi }_{BCP2}$, is found to give $n_s\simeq 0.96$ and $r\simeq 0.16$. Next, from the point ${\phi }_{BCP2}$ to the end of inflation the e-fold number is obtained. We find a reasonable set of parameters allowing the e-fold number in the range 50-60.