Cosmology of fractional gravity

TL;DR

This paper explores the cosmological implications of classical fractional gravity, deriving nonlocal equations of motion and analyzing solutions like de Sitter and bouncing universes within this novel framework.

Contribution

It introduces the first study of fractional gravity cosmology, deriving covariant nonlocal equations and analyzing their solutions, confirming universality across different form factors.

Findings

De Sitter solutions are stable in fractional gravity.

Bouncing solutions require phantom or ghost fluids.

Different form factor representations yield identical solutions.

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 $\gamma$ 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 bouncing exact solutions are sustained by phantom ($w<-1$) or ghost ($\rho<0$) fluids, in the latter case with a new type of finite-future singularity in the barotropic index. Different representations of the form factor give exactly the same solutions, thus confirming that the formulation of fractional field theories relies 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.