  In this paper we study a homothetic vector field of a Bianchi type-I model
based on Lyra geometry. The cases when a displacement vector is function of $t$
and when it is constant are considered. In both two cases we investigate the
equation of state. A comparison between the obtained results, using Lyra
geometry, and that have obtained previously in the context of General
Relativity, based on Riemannian geometry, will be given.

General Relativity and Quantum Cosmology