Noether and some other dynamical symmetries in Kantowski–Sachs model

The forms of coupling of the scalar field with gravity, appearing in the induced theory of gravity, and that of 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 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.