Coincident general relativity

TLDR

The authors aim to formulate general relativity in a geometry that ignores affine structure, thereby removing inertial aspects and providing a foundation for modified gravity models with naturally self‑accelerating cosmologies. They employ a metric‑affine variational principle to derive teleparallel and symmetric teleparallel theories, ultimately yielding a Hilbert action without a boundary term that is grounded in spin‑2 field theory and exhibits an additional symmetry possibly linked to gravity amplitude double‑copy structures. The study identifies an exceptional class of theories with a vanishing affine connection and demonstrates that the resulting framework admits simple modified gravity extensions that produce analytical self‑accelerating solutions in both early‑ and late‑time cosmology.

Abstract

The metric-affine variational principle is applied to generate teleparallel and symmetric teleparallel theories of gravity. From the latter we discover 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 generalizations where analytical self-accelerating cosmological solutions arise naturally in the early- and late-time Universe.