Inhomogeneous cosmology with quasi-vacuum effective equation of state on Lyra manifold

A class of inhomogeneous Lema？tre-Tolman cosmological models is obtained in the context of Lyra’s geometry. Cosmological models in Lyra’s geometry are studied under the condition of the minimal coupling of matter with the displacement vector field and the varying Λ term. Exact solutions to the model equations are obtained subject to the quasi-vacuum effective equation of state. As a result, the displacement field as well as the cosmological term can be expressed in terms of the energy density of matter. The rate of expansion and the deceleration parameter of the model are also studied