Higher order mimetic gravity after GW170817

On the 17th of August 2017, the thriving discovery of gravitational waves event GW170817 and its optical counterpart GRB170817A, owing to coalescing of two neutron starts divulged a very small amount of difference around ${\cal O}(10^{-16})$ between traveling speed of light and the velocity of gravitational waves ($C_{T}$). This small deviation can be used as a strong constraint on modified gravity models. We concentrate on the Higher-Order expansion of Mimetic Gravity (HOMimG) model to specify the parametric space of three parameters of our model ($a$, $b$, and $c$ ) utilizing the observational constraint from GW170817-GRB170817A on $C_{T}$, besides two theoretical constraints on $C_{T}^{2}$ and $C_{s}^{2}$ due to assurance of the stability of the model and subluminal promulgation of the scalar and tensor perturbations. Thereafter, we increase the accuracy of the parametric space with the aid of imposing further limitation of $\gamma$ parameter (related to the age of the Universe). In pursuance of determining the other parameter of the model ($\lambda$), the potential of the model is specified, and another observational bound related to the Equation of State (EoS) parameter of dark energy is taken into account. In consequence, we attain a viable HOMimG model confined to numbers of observational and theoretical constraints. At the end, regarding the concluded numerical ranges for the model parameters, and cogitating two different potential (quadratic and quartic potentials) to specify $\lambda$ parameter, we illustrate that the values of the model parameters are independent of the form of potential.