Ricci-inverse gravity: a novel alternative gravity, its flaws, and how to cure them

TL;DR

This paper introduces Ricci-inverse gravity based on the anticurvature tensor, derives its equations of motion, proves a no-go theorem against certain models driving cosmic acceleration, and discusses potential ways to overcome this limitation.

Contribution

It presents a new gravity theory using the inverse Ricci tensor, establishes a no-go theorem for certain Lagrangians, and explores possible solutions to this problem.

Findings

No Lagrangian with linear or power-law terms in anticurvature can produce cosmic acceleration.

The no-go theorem rules out many models of Ricci-inverse gravity.

Potential methods to circumvent the theorem are proposed.

Abstract

We introduce a novel theory of gravity based on the inverse of the Ricci tensor, that we call the anticurvature tensor. We derive the general equations of motion for any Lagrangian function of the curvature and anticurvature scalars. We then demonstrate a no-go theorem: no Lagrangian that contains terms linear in any positive or negative power of the anticurvature scalar can drive an evolution from deceleration to acceleration, as required by observations. This effectively rules out many realizations of this theory, as we illustrate in detail in a particular case. Finally, we speculate on how to circumvent the no-go theorem.