Bianchi Type I Cosmology in Generalized Saez-Ballester Theory via Noether Gauge Symmetry

In this paper, we investigate the generalized Saez-Ballester scalar-tensor theory of gravity via Noether gauge symmetry (NGS) in the background of Bianchi type I cosmological spacetime. We start with the Lagrangian of our model and calculate its gauge symmetries and corresponding invariant quantities. We obtain the potential function for the scalar field in the exponential form. For all the symmetries obtained, we determine the gauge functions corresponding to each gauge symmmetry which include constant and dynamic gauge. We discuss cosmological implications of our model and show that it is compatible with the observational data.