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

TL;DR

This paper numerically calculates the e-fold number in a two-inflaton hilltop inflation model, demonstrating parameter sets that produce realistic inflation durations consistent with observations.

Contribution

It introduces a numerical method to compute e-folds in a two-inflaton hilltop model and identifies parameter ranges that yield viable inflationary predictions.

Findings

E-fold number can be in the range 50-60 with suitable parameters.

Inflation parameters consistent with BICEP2 observations.

Numerical approach effectively explores initial conditions and parameter space.

Abstract

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.