No-go theorem for inflation in Ricci-inverse gravity

Abstract

We study a recent proposed Ricci-inverse gravity, which is a very novel type of fourth-order gravity. In particular, we are able to figure out both isotropically and anisotropically inflating universes to this model. More interestingly, these solutions are free from a singularity problem. However, stability analysis based on the dynamical system method shows that both isotropic and anisotropic inflation of this model turn out to be unstable against field perturbations. This result implies a no-go theorem for both isotropic and anisotropic inflation in the Ricci-inverse gravity.

15 pages, 2 figures. This is a minor revision, in which the title and abstract are modified in order to express more clearly the main result of this paper. In addition, discussions on some important results investigated by other people are added. Some relevant references are also added. All calculations and conclusions are not changed. Accepted for publication in EPJC. Comments are welcome

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• Ricci inverse gravity wormholes
• No-go theorem for inflation in an extended Ricci-inverse gravity model
• Can we bypass no-go theorem for Ricci-inverse Gravity?
• Cosmological constant Petrov type-N space-time in Ricci-inverse gravity
• Stationary BTZ space-time in Ricci-Inverse and $f(\mathcal{R})$ gravity theories
• Cylindrical black hole solutions in $f(\mathcal{R})$ and $f(\mathcal{R},\mathcal{A},A^{\mu \nu }{A}_{\mu \nu })$ modified 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