Noether and some other dynamical symmetries in Kantowski-Sachs model

TL;DR

This paper investigates dynamical symmetries in the Kantowski-Sachs cosmological model, identifying conditions for Noether symmetry and alternative methods to find symmetries that avoid degeneracy, leading to inflationary solutions.

Contribution

It introduces a new approach to identify dynamical symmetries in the Kantowski-Sachs model, including non-degenerate cases, and analyzes the resulting inflationary solutions.

Findings

Derived forms of scalar coupling and potential under Noether symmetry.

Found inflationary solutions in the degenerate Lagrangian case.

Identified additional symmetries through field equation analysis.

Abstract

The forms of coupling of the scalar field with gravity, appearing in the induced theory of gravity, and the potential are found in the Kantowski-Sachs model under the assumption that the Lagrangian admits Noether symmetry. The form thus obtained makes the Lagrangian degenerate. The constrained dynamics thus evolved due to such degeneracy has been analysed and a solution has also been presented which is inflationary in behaviour. It has further been shown that there exists other technique to explore the dynamical symmetries of the Lagrangian and that is simply by inspecting the field equations. Through this method, Noether along with some other dynamical symmetries are found, which do not make the Lagrangian degenerate.