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

TL;DR

This paper investigates an extended Ricci-inverse gravity model with a second order correction and demonstrates, through a stability analysis, that stable inflationary solutions are not possible in this framework.

Contribution

The paper introduces a second order correction to Ricci-inverse gravity and proves a no-go theorem for stable inflation within this extended model.

Findings

No stable inflationary solutions exist in the extended Ricci-inverse gravity model.

The stability analysis reveals a fundamental limitation of the extended model.

Inflation cannot be achieved in this extended gravity framework.

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.