Can we bypass no-go theorem for Ricci-inverse Gravity?

TL;DR

This paper investigates Ricci-inverse gravity models, demonstrating through numerical and theoretical analysis that these models cannot explain late-time cosmic acceleration, thus confirming the no-go theorem in this context.

Contribution

The study introduces two classes of Ricci-inverse gravity models and proves, both numerically and via reduced action, that they cannot account for late-time cosmic acceleration, reinforcing the no-go theorem.

Findings

Models fail to produce late-time acceleration.

Numerical solutions show no transition to accelerated expansion.

Reduced action analysis confirms the no-go theorem.

Abstract

Recently, Amendola et al. proposed a geometrical theory of gravity containing higher-order derivative terms. The authors introduced anticurvature scalar $(A)$, which is the trace of the inverse of the Ricci tensor ($A^{\mu\nu} = R_{\mu\nu}^{-1}$). In this work, we consider two classes of Ricci-inverse -- Class I and Class II -- models. Class I models are of the form $f(R, A)$ where $f$ is a function of Ricci and anticurvature scalars. Class II models are of the form ${\cal F}(R, A^{\mu\nu}A_{\mu\nu})$ where ${\cal F}$ is a function of Ricci scalar and square of anticurvature tensor. For both these classes of models, we numerically solve the modified Friedmann equations in the redshift range $1500 < z < 0$. We show that the late-time evolution of the Universe, i.e., evolution from matter-dominated epoch to accelerated expansion epoch, \emph{can not} be explained by these two classes of models. Using the reduced action approach, we show that we \emph{can not bypass} the no-go theorem for Ricci-inverse gravity models. Finally, we discuss the implications of our analysis for the early-Universe cosmology.