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

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.

32 pages, 3 figures. V3 with many discussions, calculations, and relevant references added. Accepted for publication by International Journal of Modern Physics D. Comments are welcome

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• Black holes in Starobinsky-Bel-Robinson Gravity and the breakdown of quasinormal modes/null geodesics correspondence
• Black hole solutions to Einstein-Bel-Robinson gravity
• Stability investigations of de Sitter inflationary solutions in power-law extensions of the Starobinsky model
• Effect of $R^2$ on the stability of de Sitter solution of the generalized Einsteinian cubic gravity
• On the stability of de Sitter inflationary solution in the Starobinsky-Bel-Robinson gravity