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

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 t...

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Bibliographic Details
Published inPhysics letters. B Vol. 811; p. 135923
Main Authors Amendola, Luca, Giani, Leonardo, Laverda, Giorgio
Format Journal Article
LanguageEnglish
Published Elsevier B.V 10.12.2020
Elsevier
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Summary: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.
ISSN:0370-2693
1873-2445
DOI:10.1016/j.physletb.2020.135923