$\Lambda$CDM and Power-Law Expansion in Lyra's Geometry

Abstract

We establish in a cosmological model based on Lyra's geometry a relationship between a displacement vector field ${\varphi }_{\mu }$, the Hubble parameter and the matter energy density ${\rho }_m$ (with a constant equation of state $0\le {\omega }_m<1$) via an arbitrary function $\alpha (t)$. For a pressureless matter (${\omega }_m=0$) the effective equation of state ${\omega }_{eff}$ is completely determined by $\alpha (t)$. We subsequently investigate and find exact solutions in models yielding the $\Lambda$CDM and a power-law expansion.

11 pages, references added