Non-minimally coupled scalar field in Kantowski--Sachs model and symmetry analysis

TL;DR

This paper investigates a non-minimally coupled scalar field in Kantowski--Sachs cosmology, deriving specific coupling and potential functions through symmetry analysis, leading to simplified equations and cosmological solutions relevant to universe evolution.

Contribution

It introduces a method to determine coupling and potential functions via Noether symmetry in anisotropic cosmology, providing new exact solutions.

Findings

Derived specific forms of coupling and potential functions.

Obtained cosmological solutions consistent with universe evolution.

Simplified equations through variable transformation and conserved quantities.

Abstract

The paper deals with a non--minimally coupled scalar field in the background of homogeneous but anisotropic Kantowski--Sachs space--time model. The form of the coupling function of the scalar field with gravity and the potential function of the scalar field are not assumed phenomenologically, rather they are evaluated by imposing Noether symmetry to the Lagrangian of the present physical system. The physical system gets considerable mathematical simplification by a suitable transformation of the augmented variables $(a, b, \phi)\rightarrow (u, v, w)$ and by the use of the conserved quantities due to the geometrical symmetry. Finally, cosmological solutions are evaluated and analyzed from the point of view of the present evolution of the Universe.