Island of Stability for Consistent Deformations of Einstein's Gravity

TL;DR

This paper develops consistent deformations of Einstein's gravity that preserve key symmetries, are stable on curved backgrounds, and reduce to Einstein's theory in flat spacetime, offering a new class of viable modified gravity models.

Contribution

It explicitly constructs deformations of Einstein's gravity that are consistent, stable, and phenomenologically viable, especially on curved spacetimes, with unique symmetry properties.

Findings

Deformations respect cosmological backgrounds.

Existence of a curvature-induced self-stabilizing mechanism.

Deformations reduce to Einstein's theory on Minkowski spacetime.

Abstract

We construct explicitly deformations of Einstein's theory of gravity that are consistent and phenomenologically viable since they respect, in particular, cosmological backgrounds. We show that these deformations have unique symmetries in accordance with unitarity requirements, and give rise to a curvature induced self-stabilizing mechanism. As a consequence, any nonlinear completed deformation must incorporate self-stabilization on generic spacetimes already at lowest order in perturbation theory. Furthermore, our findings include the possibility of consistent and phenomenologically viable deformations of general relativity that are solely operative on curved spacetime geometries, reducing to Einstein's theory on the Minkowski background.