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

We establish in a cosmological model based on Lyra's geometry a relationship between a displacement vector field $\phi_{\mu}$, 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.