On the initial conditions for inflation with plateau potentials: the $R+R^2$ (super)gravity case

TL;DR

This paper investigates how supergravity embedding of $R+R^2$ inflation models influences initial conditions, showing that auxiliary supergravity fields help reduce the homogeneity scale needed for inflation, with results depending on spatial curvature.

Contribution

It demonstrates that supergravity embedding naturally alleviates initial condition constraints for $R+R^2$ inflation by involving auxiliary fields, and explores curvature effects.

Findings

Supergravity auxiliary fields decrease the homogeneity size needed for inflation.

Initial conditions depend on background spatial curvature.

Embedding reduces the initial homogeneity problem for plateau potentials.

Abstract

We discuss the initial conditions problem for inflation driven by the vacuum energy of a plateau potential, and in particular the Starobinsky inflation. We show that the supergravity embedding of the $R+R^2$ theory naturally decreases the size of the acausal homogeneity, required for the low-scale inflation to occur, thanks to the presence of the dynamical pure supergravitational "auxiliary" fields. We examine the evolution of the $R+R^2$ fields within a FLRW Universe. We also find a dependence of the initial conditions problem on the background spatial curvature.