Topological inflation from the Starobinsky model in supergravity

TL;DR

This paper investigates how higher order corrections in the Starobinsky supergravity model affect inflation, finding that positive $R^4$ corrections can enable topological inflation consistent with observations.

Contribution

It demonstrates that positive $R^4$ corrections create a potential suitable for topological inflation within supergravity, aligning with recent observational constraints.

Findings

Positive $R^4$ correction allows topological inflation.

Constraints on the $R^4$ coupling from Planck data.

Inflation is possible with certain coupling values.

Abstract

We consider the ghost-free higher order corrections to the Starobinsky model in the old minimal supergravity. In general, higher order corrections cannot be forbidden by symmetries, which likely violate the flatness of the scalaron potential and makes inflation difficult to explain the present Universe. We find a severe constraint on the dimensionless coupling of the $R^4$ correction as $-5.5 \times 10^{-8}<s<9.1 \times 10^{-8}$ from the recent results of the Planck observation. If we start from the chaotic initial condition, the constraint becomes much severer. However, in the case where the coupling of the $R^4$ correction is positive, the scalaron potential has a local maximum with two local minimum at the origin and infinity, which admits topological inflation. In this case, inflation can take place naturally if the coupling satisfies the observational constraints.