Coincident General Relativity

TL;DR

This paper introduces a simplified, boundary-term-free formulation of General Relativity based on symmetric teleparallelism, which is more aligned with spin-2 field theory and offers new avenues for modified gravity and cosmological models.

Contribution

It proposes a novel, affine-structure-independent geometrical formulation of GR that simplifies the theory and connects it with spin-2 fields and double copy symmetry.

Findings

A boundary-term-free Hilbert action for GR

New self-accelerating cosmological solutions

Enhanced symmetry related to double copy structure

Abstract

The metric-affine variational principle is applied to generate teleparallel and symmetric teleparallel theories of gravity. From the latter is discovered an exceptional class which is consistent with a vanishing affine connection. Based on this remarkable property, this work proposes a simpler geometrical formulation of General Relativity that is oblivious to the affine spacetime structure, thus fundamentally depriving gravity of any inertial character. The resulting theory is described by the Hilbert action purged from the boundary term and is more robustly underpinned by the spin-2 field theory, where an extra symmetry is now manifest, possibly related to the double copy structure of the gravity amplitudes. This construction also provides a novel starting point for modified gravity theories, and the paper presents new and simple generalisations where analytical self-accelerating cosmological solutions arise naturally in the early and late time universe.