Existence of Bianchi type cosmological phantom universe with polytropic EoS parameter in Lyra's Geometry

This study explores the Bianchi type-V cosmological model with in the frame work of general relativity, featuring a perfect fluid governed by the polytropic equation in Lyra's Geometry, expressed $ p=\alpha \rho+k {\rho}^n $, as proposed at [1]. We considered the case representing phantom universe for $(1 + \alpha + k\rho^{n-1})\leqslant 0$, $ k < 0 $, where $\rho$ increases with the radius $a(t)$. The role of Lyra;s Geometry has been discussed/ The solution to Einsteins field equation have been derived, providing insights into the physical and cosmological attributes of this particular model.