Non-local Metric-Affine Gravity

TL;DR

This work extends non-local gravity into the metric-affine framework, treating the metric and independent connection as fundamental and exploring both UV- and IR-type non-local formalisms. The authors show that for actions of the form $R F(\Box)R$ and $R F(\Box^{-1})R$, the metric and connection equations admit analytical solutions, and the on-shell dynamics reduce to higher-derivative Scalar-Tensor theories on a Riemannian background, generalizing previous metric-based results. They also introduce a novel non-Riemannian non-local theory that involves torsion and non-metricity in a way with no Riemannian analogue, yielding propagating geometric degrees of freedom and a vector-tensor-like sector. Cosmological applications illustrate non-local MAG can drive early-universe behavior such as superexponential expansion in simple setups, indicating rich cosmological dynamics and promising avenues for further study. Overall, the paper broadens the scope of non-local gravity by embedding it in MAG, highlighting both technical tractability (via connection solving and equivalence to Scalar-Tensor theories) and new geometric degrees of freedom with potential physical relevance.

Abstract

Non-local gravity can potentially solve several problems of gravitational field both at Ultra-Violet and Infra-Red scales. However, such an approach has been formulated mainly in metric formalism. In this paper, we discuss non-local theories of gravity in the metric-affine framework. In particular, we study the dynamics of metric-affine analogue of some well-studied non-local theories, by treating the metric and the connection as independent fields. The approach gives the opportunity to deal with non-local gravity under a more general standard. Furthermore, we introduce some novel non-local metric-affine theories with no Riemannian analogue and investigate their dynamics. Finally we discuss some cosmological applications of our development.