Stability and singularity analysis of the cosmologies with different scenarios for deceleration parameter in the presence of torsion

In the current paper, path deviation equations in absolutely parametric parallel geometries are derived. It is considered as a geodesic deviation equation. Additionally, it is modified by a torsion term. It proposes the deviation path equation that describes the trajectory deviation of a particle under the influence of the gravitational field. To examine the singularity of the Cosmological models, the modified version of the Raychaudhuri equation is utilized. The generalized law of the variation of Hubble's parameter is utilized to achieve some Cosmological models.