1D Supergravity FLRW Model of Starobinsky

TL;DR

This paper explores supersymmetric extensions of the Starobinsky inflation model within $f(R)$ gravity, analyzing their dynamics and showing that inflation is driven by the $R^2$ term, with additional scalar fields remaining stable.

Contribution

It introduces N=1 and N=2 supersymmetric models of Starobinsky gravity with detailed classical and Hamiltonian analyses, extending previous non-supersymmetric models.

Findings

Inflation driven by $R^2$ term during high curvature

N=2 model includes a stable massive scalar field

Numerical solutions confirm inflationary dynamics

Abstract

We study two homogeneous supersymmetric extensions for the $f(R)$ modified gravity model of Starobinsky with the FLRW metric. The actions are defined in terms of a superfield $\mathcal{R}$ that contains the FLRW scalar curvature. One model has N=1 local supersymmetry, and its bosonic sector is the Starobinsky action; the other action has N=2, its bosonic sector contains, in additional to Starobinsky, a massive scalar field without self-interaction. As expected, the bosonic sectors of these models are consistent with cosmic inflation, as we show by solving numerically the classical dynamics. Inflation is driven by the $R^2$ term during the large curvature regime. In the N=2 case, the additional scalar field remains in a low energy state during inflation. Further, by means of an additional superfield, we write equivalent tensor-scalar-like actions from which we can give the Hamiltonian formulation.