Stability of Axially Symmetric Cosmological Model in Lyra Geometry

The present study concerns an examination of a cosmological model that exhibits axially symmetric and incorporates perfect fluid within the context of Lyra geometry. The field equations are solved by utilising the relation between the metric coefficients and the equation of state for a stiff fluid. The physical and kinematic properties, namely the Hubble parameter, the deceleration parameter, the energy density, and the pressure, have been examined, and their graphical behaviour has been analysed. Furthermore, we examined several additional parameters, including the redshift and the Om(z) diagnostic, and verified the stability of the model by utilising the sound speed ratio and perturbation technique.