No-go theorem for inflation in an extended Ricci-inverse gravity model

Abstract

In this paper, we propose an extension of the Ricci-inverse gravity, which has been proposed recently as a very novel type of fourth-order gravity, by introducing a second order term of the so-called anticurvature scalar as a correction. The main purpose of this paper is that we would like to see whether the extended Ricci-inverse gravity model admits the homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker metric as its stable inflationary solution. However, a no-go theorem for inflation in this extended Ricci-inverse gravity is shown to appear through a stability analysis based on the dynamical system method. As a result, this no-go theorem implies that it is impossible to have such stable inflation in this extended Ricci-inverse gravity model.

14 pages, 3 figures. Updated version with additional discussions on the Minkowskian limit. All calculations are not modified. Matches the published version. Comments are welcome

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• Cylindrical black hole solutions in $f(\mathcal{R})$ and $f(\mathcal{R},\mathcal{A},A^{\mu \nu }{A}_{\mu \nu })$ modified gravity
• Cosmic structures in Ricci-inverse theories of gravity
• Stability investigations of de Sitter inflationary solutions in power-law extensions of the Starobinsky model