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, which exposes in the low-energy
limit of projectable Ho\v{r}ava-Lifshitz gravity. Thence, we specify the
parametric space of three parameters of our model ($a$, $b$, and $c$ )
utilizing the observational constraint from GW170817-GRB170817A on $C_{T}$,
beside 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 latest observational value for the age of the
Universe) in addition to the previous ones. 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 addition to the
erstwhile ones. In consequence, we attain a viable HOMimG model with four
parameter ($a$, $b$, $c$, and $\lambda$) 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.
