Covariant Horava-like and mimetic Horndeski gravity: cosmological solutions and perturbations

TL;DR

This paper introduces a covariant Horava-like gravity model with a mimetic scalar field, addressing stability issues, exploring cosmological solutions, and analyzing perturbations with a focus on non-zero sound speed in a modified higher derivative framework.

Contribution

It extends Horava-like gravity to include mimetic scalar fields via Lagrange multipliers, and investigates perturbations with higher derivatives to ensure well-defined sound speed.

Findings

The fluid behaves as an irrotational fluid with zero sound speed.

Adding higher derivatives yields a non-zero sound speed, enabling sensible perturbation analysis.

The model reproduces various cosmological scenarios and reduces to GR in the IR.

Abstract

We consider a variant of the Nojiri-Odintsov covariant Horava-like gravitational model, where diffeomorphism invariance is broken dynamically via a non-standard coupling to a perfect fluid. The theory allows to address some of the potential instability problems present in Horava-Lifshitz gravity due to explicit diffeomorphism invariance breaking. The fluid is instead constructed from a scalar field constrained by a Lagrange multiplier. In fact, the Lagrange multiplier construction allows for an extension of the Horava-like model to include the scalar field of mimetic gravity, an extension which we thoroughly explore. By adding a potential for the scalar field, we show how one can reproduce a number of interesting cosmological scenarios. We then turn to the study of perturbations around a flat FLRW background, showing that the fluid in question behaves as an irrotational fluid, with zero sound speed. To address this problem, we consider a modified version of the theory, adding higher derivative terms in a way which brings us beyond the Horndeski framework. We compute the sound speed in this modified higher order mimetic Horava-like model and show that it is non-zero, which means that perturbations therein can be sensibly defined. Caveats to our analysis, as well as comparisons to projectable Horava-Lifshitz gravity, are also discussed. In conclusion, we present a theory of gravity which preserves diffeomorphism invariance at the level of the action but breaks it dynamically in the UV, reduces to General Relativity in the IR, allows the realization of a number of interesting cosmological scenarios, is well defined when considering perturbations around a flat FLRW background, and features cosmological dark matter emerging as an integration constant.