Speaker
Description
Fitting cosmic observations with General Relativity and the Cosmological Principle requires assuming the existence of a dark sector that dominates gravitational dynamics and whose fundamental properties are still unknown. This fact has motivated the search for alternative gravity theories, which so far has given mixed results. In particular, 4th-order theories are mathematically intractable and are plagued by inconsistencies. To address this problem, we derived a second-order theory, “Schouten-Codazzi” (SC) gravity, that resembles GR and does not violate Lovelock’s theorem. Keeping the same energy momentum tensor as in GR, the geometric sector of SC is constructed as the sum of the Schouten curvature tensor and a second order tensor that must comply with the two following properties: (1) it is defined through diffeomorphisms applied to a generic tensor constructed from the invariant eigenvalues and eigenvectors of the Ricci tensor and (2) the diffeomorphisms must satisfy the Codazzi differential constraint. Applying SC gravity to standard FLRW cosmology leads naturally to the cosmological constant and adds free parameters that allow for a possible geometric interpretation for the dark sector. At the same time, the extra parameters remain consistent with solar system data and black hole horizons described by the Schwarzschild-like SC solution. The potential for a geometric interpretation for dark matter also arises from the application of SC gravity to static fluid solutions. Although SC gravity is still under development and further testing is necessary, it seems so far to be an appropriate candidate for an alternative theory.