Diffeomorphism Invariance Breaking in Gravity and Cosmological Evolution

TL;DR

This paper explores how small violations of diffeomorphism invariance, introduced in a modified gravity framework, affect cosmological evolution, finding that such violations do not lead to instabilities and smoothly connect to standard GR solutions.

Contribution

It provides a detailed analysis of cosmological solutions in a diffeomorphism-breaking gravity model with all leading two-derivative terms, including analytic and numerical solutions for various universe components.

Findings

Minor diffeomorphism violations do not cause instabilities in cosmological evolution.

Solutions smoothly connect to General Relativity in the limit of no symmetry breaking.

Numerical studies show no singular behavior in multi-component universes.

Abstract

Diffeomorphism invariance breaking has been investigated in the literature in several contexts, including emergent General Relativity (GR). If GR emerges from an underlying theory without diffeomorphism invariance, there may be small violations of this symmetry at low energies. Since such small violations should not cause instabilities in cosmological evolution, it is a suitable framework for examining such symmetry-breaking effects. In this paper, the cosmological evolution with broken diffeomorphism invariance is investigated in the (modified) FLRW spacetime in the effective theory framework. The GR Lagrangian is augmented with all diffeomorphism-breaking but Lorentz-invariant terms in the leading order, namely, those involving two derivatives. The magnitudes of (minor) violations are kept general modulo the conditions arising in the linearized theory. The analytic solutions of the scale factor in the full non-linear theory for the single-component universes are attempted; the radiation and vacuum solutions are found analytically, whereas the matter solution is worked out numerically since an analytic solution does not exist in the required form. It is observed that the solutions smoothly connect to those of GR in the limit of vanishing symmetry-breaking. The more realistic, two-component, and three-component universes are numerically studied, and no signs of singular behavior are observed: minor diffeomorphism-violating modifications to GR at the level of two derivatives do not cause instabilities in the basic cosmological evolution.