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

TL;DR

This paper explores cosmological models within Lyra's geometry, establishing relationships between key variables and deriving exact solutions that include the $ ext{Lambda}$CDM and power-law expansion scenarios.

Contribution

It introduces a novel framework linking the displacement vector, Hubble parameter, and matter density via an arbitrary function in Lyra's geometry, leading to exact cosmological solutions.

Findings

Derived exact solutions for $ ext{Lambda}$CDM and power-law expansion models.

Established a relationship between displacement vector, Hubble parameter, and matter density.

Demonstrated how the effective equation of state depends on the arbitrary function $eta(t)$.

Abstract

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.