Stability investigations of isotropic and anisotropic exponential inflation in the Starobinsky-Bel-Robinson gravity

TL;DR

This study investigates the stability of exponential inflation solutions in Starobinsky-Bel-Robinson gravity, revealing that while some solutions are unstable, a modified model can produce a stable de Sitter inflationary solution.

Contribution

The paper derives exact inflationary solutions in Starobinsky-Bel-Robinson gravity and its modification, analyzing their stability and revealing conditions for stable inflation.

Findings

Exact de Sitter inflationary solution exists in the original model.

Bianchi type I inflationary solution does not exist in the original model.

A modified model admits a stable de Sitter inflationary solution.

Abstract

In this paper, we would like to examine whether a novel Starobinsky-Bel-Robinson gravity model admits stable exponential inflationary solutions with or without spatial anisotropies. As a result, we are able to derive an exact de Sitter inflationary to this Starobinsky-Bel-Robinson model. Furthermore, we observe that an exact Bianchi type I inflationary solution does not exist in the Starobinsky-Bel-Robinson model. However, we find that a modified Starobinsky-Bel-Robinson model, in which the sign of coefficient of $R^2$ term is flipped from positive to negative, can admit the corresponding Bianchi type I inflationary solution. Unfortunately, stability analysis using the dynamical system approach indicates that both of these inflationary solutions turn out to be unstable. Interestingly, we show that a stable de Sitter inflationary solution can be obtained in the modified Starobinsky-Bel-Robinson gravity.