Non-Local Cosmology: From Theory to Observations

Abstract

We examine the key aspects of gravitational theories that incorporate non-local terms, particularly in the context of cosmology and spherical symmetry. We thus explore various extensions of General Relativity, including non-local effects in the action through the function F(R,□−1R), where R denotes the Ricci curvature scalar and the operator □−1 introduces non-locality. By selecting the functional forms using Noether Symmetries, we identify exact solutions within a cosmological framework. We can thus reduce the dynamics of these chosen models and obtain analytical solutions for the equations of motion. Therefore, we study the capability of the selected models in matching cosmological observations by evaluating the phase space and the fixed points; this allows one to further constrain the non-local model selected by symmetry considerations. Furthermore, we also investigate gravitational non-local effects on astrophysical scales. In this context, we seek symmetries within the framework of f(R,□−1R) gravity and place constraints on the free parameters. Specifically, we analyze the impact of non-locality on the orbits of the S2 star orbiting SgrA*.