Gravity in mimetic scalar-tensor theories after GW170817

TL;DR

This paper derives the most general mimetic scalar-tensor theories consistent with gravitational wave speed constraints from GW170817, analyzing linear perturbations to understand modifications to gravity and dark energy effects.

Contribution

It provides a comprehensive derivation of mimetic scalar-tensor theories under GW170817 constraints, including linear perturbation analysis and effective gravitational constant calculations.

Findings

In minimally coupled models, the effective gravitational constant matches that of General Relativity with dark matter and dark energy.

For ΛCDM backgrounds, the effective gravitational constant is indistinguishable from standard ΛCDM at linear order.

Non-minimally coupled models exhibit a non-zero gravitational slip and a different effective gravitational constant from standard ΛCDM.

Abstract

We derive the most general mimetic scalar-tensor theory assuming a healthy "seed" action and accounting for the constraints on the speed of gravitational-wave propagation arising from the GW170817 event. By analysing linear perturbations around a flat FLRW background in this model, we obtain a suitable form of the Poisson equation, which allows us to calculate the effective gravitational constant felt by "ordinary" matter. By restricting to a minimally coupled model, such an effective gravitational constant is equivalent to that obtained within General Relativity, with cold dark matter plus a perfect fluid dark energy component, with vanishing sound speed. Assuming, further, a $\Lambda$CDM background, the effective gravitational constant cannot be distinguished from that of the standard $\Lambda$CDM model, at linear order. For the full non-minimally coupled mimetic gravity model we obtain a non-vanishing gravitational slip and an effective gravitational constant which always differs from that of standard $\Lambda$CDM.