New Modified Mimetic Gravity
A modified Mimetic gravity (MMG) is proposed as a generalization of general relativity. The model contain a physical metric which is function of an auxiliary (unphysical) metric and a Lyra's metric. We construct different kinds of conformally invariant models in different levels of the expansion parameter $\lambda$. This model phenomenologically has been extended to higher order forms. Cosmology of a certain class of such models has been investigated in details. A cosmological solution has been proposed in inhomogeneous form of scalar field. For homogenous case, energy conditions are widely investigated. We have shown that the system evaluated at intervals shorter than a certain time $T_c$ meets all the energy conditions.