Universality of Einstein's General Relativity

TL;DR

This paper demonstrates that Einstein's general relativity is essentially unique among relativistic gravity theories, as small deviations either replicate its physics or lead to unstable, physically untenable models.

Contribution

It provides a comprehensive analysis showing the near-universality of general relativity by relating scalar-tensor and f(R) theories to it and discussing their physical equivalence or instability.

Findings

Scalar-tensor and f(R) theories are equivalent to general relativity plus a scalar field.

Small deviations from general relativity either replicate its physics or cause instability.

General relativity is an isolated point in the space of gravity theories.

Abstract

Among relativistic theories of gravitation the closest ones to general relativity are the scalar-tensor ones and these with Lagrangians being any function f(R) of the curvature scalar. A complete chart of relationships between these theories and general relativity can be delineated. These theories are mathematically (locally) equivalent to general relativity plus a minimally coupled self-interacting scalar field. Physically they describe a massless spin-2 field (graviton) and a spin-0 component of gravity. It is shown that these theories are either physically equivalent to general relativity plus the scalar or flat space is classically unstable (or at least suspected of being unstable). In this sense general relativity is universal: it is an isolated point in the space of gravity theories since small deviations from it either carry the same physical content as it or give rise to physically untenable theories.