Numerical calcultaion of e-fold number from hilltop with two inflatons
  We consider a cosmological inflation with two inflatons, $\phi$ and $X$. The
inflation potential is a hilltop form in the $\phi$ space and $X$ is a sideway
down-fall field in the region $\phi\ge m$. 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 $\varphi$ for the BICEP2 point,
$\varphi_{\rm BCP2}$, is found to give $ n_s\simeq 0.96$ and $r\simeq 0.16$.
Next, from the point $\varphi_{\rm BCP2}$ 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.
