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

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 $\mathcal{F}(R,A^{\mu \nu }{A}_{\mu \nu })$ where $\mathcal{F}$ 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.

V2: Version accepted in EPJ-Plus, 35 pages, 13 figures, 2 tables

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• Time-Machines Construct in $f(\mathcal{R},\mathcal{A},A^{\mu \nu }{A}_{\mu \nu })$ and $f(\mathcal{R})$ Modified Gravity Theories
• Cylindrical black hole solutions in $f(\mathcal{R})$ and $f(\mathcal{R},\mathcal{A},A^{\mu \nu }{A}_{\mu \nu })$ modified gravity