Phenomenology in type-I minimally modified gravity

TL;DR

This paper explores a class of minimally modified gravity theories with two local degrees of freedom, classifies them into type-I and type-II, and investigates their cosmological phenomenology, especially models with gravitational wave speed equal to light.

Contribution

It introduces a classification of minimally modified gravity theories into type-I and type-II and analyzes their cosmological implications, including models with standard gravitational wave speed.

Findings

Deviations from GR are characterized by two functions of an auxiliary variable.

A model with $c_T=1$ can have a dark energy equation-of-state different from -1.

Reconstruction of the theory is possible by choosing a specific dark energy evolution.

Abstract

We study cosmology in a class of minimally modified gravity (MMG) with two local gravitational degrees of freedom. We classify modified gravity theories into type-I and type-II: theories of type-I have an Einstein frame and can be recast by change of variables as general relativity (GR) with a non-minimal matter coupling, while theories of type-II have no Einstein frame. Considering a canonical transformation of the lapse, the 3-dimensional induced metric and their conjugate momenta we generate type-I MMG. We then show that phenomenological deviations from GR, such as the speed of gravitational waves $c_T$ and the effective gravitational constant for scalar perturbations $G_{\rm eff}$, are characterized by two functions of an auxiliary variable. We study the phenomenology of several models all having $c_T=1$. We obtain a scenario with $c_T=1$ in which the effective equation-of-state parameter of dark energy is different from $-1$ even though the cosmic acceleration is caused by a bare cosmological constant, and we find that it is possible to reconstruct the theory on choosing a selected time-evolution for the effective dark energy component.