Restricted f(R) Gravity and Its Cosmological Implications

TL;DR

This paper explores a modified f(R) gravity theory with broken diffeomorphism symmetry, revealing its equivalence to a low-energy limit of Horava-Lifshitz gravity and analyzing its cosmological solutions, including de Sitter space.

Contribution

It introduces a new form of f(R) gravity with broken symmetry and demonstrates its equivalence to a known gravity model, providing insights into its cosmological implications.

Findings

De Sitter solutions exist in the broken symmetry f(R) gravity.

The theory is equivalent to the low-energy limit of non-projectable f(R) Horava-Lifshitz gravity.

Cosmological models exhibit specific asymptotic behaviors.

Abstract

We investigate the f(R) theory of gravity with broken diffeomorphism due to the change of the coefficient in front of the total divergence term in the (3+1)-decomposition of the scalar curvature. We perform the canonical analysis of this theory and show that its consistent, i.e. with no unphysical degrees of freedom, form is equivalent to the low-energy limit of the non-projectable f(R) Horava-Lifshitz theory of gravity. We also analyze its cosmological solutions and show that the de Sitter solution can be obtained also in the case of this broken symmetry. The consequences of the proposed theory on the asymptotic solutions of a few specific models in the cosmological context are also presented.