Nonlocal Gravity: Fundamental Tetrads and Constitutive Relations

TL;DR

This paper reformulates nonlocal gravity to directly relate measurable quantities through a constitutive relation, aligning with recent proposals, and demonstrates that de Sitter spacetime is not a solution within this framework.

Contribution

It introduces a reformulation of nonlocal gravity that directly connects measurable quantities via a specific constitutive relation, aligning with recent theoretical suggestions.

Findings

De Sitter spacetime is not a solution of nonlocal gravity.

The constitutive relation in NLG coincides with recent proposals.

The reformulation links nonlocal gravity more closely to observable data.

Abstract

Nonlocal gravity (NLG) is a classical nonlocal generalization of Einstein's theory of gravitation based on a certain analogy with the nonlocal electrodynamics of media. The history dependence enters NLG through a constitutive relation involving a causal kernel that should ultimately be determined via observational data. The purpose of this paper is to reformulate nonlocal gravity such that the nonlocal aspect of the constitutive relation directly connects measurable quantities as in the nonlocal electrodynamics of media. The resulting constitutive relation turns out to coincide with the recent suggestion of Puetzfeld, Obukhov, and Hehl [25]. With the new constitutive relation of NLG, it is possible to show that de Sitter spacetime is not a solution of NLG.