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

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.

arXiv comment9 pages, 4 figures

References in corpus (16)

• Planck 2015 results. XIII. Cosmological parameters
• Extended Theories of Gravity
• The Complete Light-curve Sample of Spectroscopically Confirmed Type Ia Supernovae from Pan-STARRS1 and Cosmological Constraints from The Combined Pantheon Sample
• Nonlocal Cosmology
• First Cosmology Results using Type Ia Supernovae from the Dark Energy Survey: Constraints on Cosmological Parameters
• On the Unification Problem in Physics
• Probing cosmic isotropy with a new X-ray galaxy cluster sample through the $L_{\text{X}}-T$ scaling relation
• Tension between the power spectrum of density perturbations measured on large and small scales
• Lectures on the Cosmological Constant Problem
• Nonlocal Models of Cosmic Acceleration
• The Cosmology of Ricci-Tensor-Squared Gravity in the Palatini Variational Approach
• Structure formation in a nonlocally modified gravity model
• Nonlocal Gravity and Structure in the Universe
• Nonlocal Cosmology II --- Cosmic acceleration without fine tuning or dark energy
• Structure formation in the Deser-Woodard nonlocal gravity model: a reappraisal
• Observational Constraints in Nonlocal Gravity: the Deser-Woodard Case

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