Effectively nonlocal metric-affine gravity

TL;DR

This paper demonstrates that certain metric-affine gravity theories can be reformulated as effectively nonlocal gravity, providing insights into their geometric interpretation and potential cosmological applications.

Contribution

It shows how metric-affine theories can be recast as nonlocal gravity and analyzes their equivalences and boundary conditions at multiple levels.

Findings

Reformulation of metric-affine theories as nonlocal gravity

Identification of ghost-free, non-singular cosmological models

Analysis of boundary conditions and field redefinitions in nonlocal theories

Abstract

In metric-affine theories of gravity such as the C-theories, the spacetime connection is associated to a metric that is nontrivially related to the physical metric. In this article, such theories are rewritten in terms of a single metric and it is shown that they can be recast as effectively nonlocal gravity. With some assumptions, known ghost-free theories with non-singular and cosmologically interesting properties may be recovered. Relations between different formulations are analysed at both perturbative and nonperturbative levels taking carefully into account subtleties with boundary conditions in the presence of integral operators in the action, and equivalences between theories related by nonlocal redefinitions of the fields are verified at the level of equations of motion. This suggests a possible geometrical interpretation of nonlocal gravity as an emergent property of non-Riemannian spacetime structure.