The recent observation of the the gravitational wave event GW170817 and of its electromagnetic counterpart GRB170817A, from a binary neutron star merger, has established that the speed of gravitational waves deviates from the speed of light by less than one part in 10 15 . As a consequence, many extensions of General Relativity are inevitably ruled out. Among these we find the most relevant sectors of Horndeski gravity. In its original formulation, mimetic gravity is able to mimic cosmological dark matter, has tensorial perturbations that travel exactly at the speed of light but has vanishing scalar perturbations and this fact persists if we combine mimetic with Horndeski gravity. In this work, we show that implementing the mimetic gravity action with higher-order terms that break the Horndeski structure yields a cosmological model that satisfies the constraint on the speed of gravitational waves and mimics both dark energy and dark matter with a non-vanishing speed of sound. In this way, we are able to reproduce the ΛCDM cosmological model
The near-simultaneous multi-messenger detection of the gravitational wave (GW) event GW170817 and its optical counterpart, the short γ-ray burst GRB170817A, implies that deviations of the GW speed from the speed of light are restricted to being of O(10 −15 ). In this note, we study the implications of this bound for mimetic gravity and confirm that in the original setting of the theory, GWs propagate at the speed of light, hence ensuring agreement with the recent multi-messenger detection. A higher-order extension of the original mimetic theory, appearing in the low-energy limit of projectable Hořava-Lifshitz gravity, is then considered. Performing a Bayesian statistical analysis where we compare the predictions of the higher-order mimetic model for the speed of GWs against the observational bound from GW170817/GRB170817A, we derive constraints on the three free parameters of the theory. Imposing the absence of both ghost instabilities and superluminal propagation of scalar and tensor perturbations, we find very stringent 95% confidence level upper limits of ∼ 7 × 10 −15 and ∼ 4 × 10 −15 on the coupling strengths of Lagrangian terms of the form ∇ µ ∇ ν φ∇µ∇ν φ and ( φ) 2 respectively, with φ the mimetic field. We discuss implications of the obtained bounds for mimetic theories. This work presents the first ever robust comparison of a mimetic theory to observational data.
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