  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.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics;High Energy Physics - Theory