Induced non-local cosmology

We nvestigate the cosmological implications of an effective gravitational action, inspired by Sakharov’s idea of induced gravity, containing non-local contributions from the operator (□ + β)−1 R. The β term is a novel feature in the panorama of non-local models of gravity, and arises naturally within Sakharov theory from the potential of a non-minimally coupled scalar field after a spontaneous symmetry breaking takes place. In this class of models the non-local contribution can acquire an oscillatory behaviour, thereby avoiding the divergence of the Hubble parameter at late times, which is another characteristic feature of the non-local models treated in the literature. Furthermore, the effective gravitational coupling Geff inherits the oscillatory behaviour, resulting in alternating epochs of stronger and weaker gravity. This framework is argued to have potentially interesting implications for the H0 and the σ8 tensions.