Cotton Gravity: the cosmological constant as spatial curvature

Abstract

We derive Friedman-Lemaitre-Robertson-Walker (FLRW) models as non-trivial solutions of "Cotton Gravity" (CG), a recently proposed gravity theory alternative to General Relativity (GR) based on the Cotton tensor. Using an equivalent formulation, we show that CG leads to FLRW models with a modified expression for spatial curvature in terms of the Ricci scalar of hypersurfaces orthonormal to the 4-velocity. Considering models compatible with a well posed initial value formulation leads to operationally the same FLRW models in GR, but endowed with a precise covariant characterization of the positive/negative cosmological constant as the case with constant negative/positive spatial curvature. Under CG, the $\Lambda$CDM model becomes the unique FLRW dust model with constant negative spatial curvature.