paper

Cosmology of fractional gravity

arXiv:2604.28188 · doi:10.1088/1475-7516/2026/09/033

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 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 () or ghost () 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.

22 pages + appendices and references, 6 figures. v2: analysis of the bounce and of de Sitter improved, new bouncing solutions with ordinary matter found, comparison of representations and concept of universality classes clarified, figures and references added, section 5 reorganized and updated, conclusions strengthened, appendix on bounces in local gravity added

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