Cosmology of fractional gravity

Abstract This is a first study of the cosmology of classical fractional gravity, a nonlocal proposal endowed with self-adjoint fractional d'Alembertian operators which serves as the basis for an ultraviolet-complete theory of quantum gravity. We derive the classical covariant nonlocal equations of motion for an arbitrary fractional exponent γ and reduce them to the Friedmann equations on a homogeneous and isotropic cosmological background. We find that de Sitter is an exact stable solution and that hyperbolic cosine bouncing exact solutions are sustained by phantom ( w < -1) or ghost ( ρ < 0) fluids, in the latter case with a new type of finite-future singularity in the barotropic index. Working with a more general bouncing profile, we verify that the theory does support bounces where the null and weak energy conditions are respected for certain non-fine-tuned values of γ . On a branch of solutions, different representations of the form factor are equivalent, in line with the notion that fractional field theories are formulated on a universality class of form factors. We compare these preliminary results with what obtained in multi-fractional cosmological models mimicking the spacetime geometry of fractional quantum gravity.