Corrections to general relativity with higher-order invariants and cosmological applications

Abstract

In this paper, we review the main features of modified theories of gravity containing higher-order curvature invariants in the action. After summarizing the main features of these theories, we consider their applications to cosmology, pointing out the differences with respect to general relativity that can eventually solve issues exhibited by the latter at low and high energy scales. Specifically, we explore a gravitational action that incorporates both the Ricci scalar [Formula: see text] and the topological Gauss–Bonnet term, denoted as [Formula: see text]. Our investigation revolves around the cosmological properties of a specific category of modified gravity theories, chosen upon symmetry considerations. Within the framework of a spatially flat, homogeneous and isotropic cosmic background, we demonstrate that it is possible to account for the presently observed acceleration of the Universe by means of the extra geometric terms carried by the selected [Formula: see text] model. This approach offers a way to address the issues associated with the cosmological constant. To achieve this, we first examine the energy conditions and find that, under certain choices for the values of the cosmographic parameters, these conditions are all violated. In the second part of the work, to assess the feasibility of the selected [Formula: see text] model, we place observational constraints on its free parameters through a Bayesian Monte Carlo technique applied to late-time cosmic data. Our findings reveal that the [Formula: see text] model can effectively reproduce observations at low redshifts, providing an alternative to the standard [Formula: see text]CDM scenario.