Abstract
The investigation of a cosmologically viable choice of a coupling function and scalar field potential is of great interest in scalar-tensor theories. The present work explores the form of the coupling function and scalar field potential using a Noether symmetry approach in a modified scalar-tensor gravity by including a nonminimal coupling of the scalar field with a torsion scalar. For this purpose, we consider locally rotational symmetric Bianchi I geometry in vacuum as well as nonvacuum cases and evaluate the corresponding conserved quantities for three different cases. By introducing cyclic variables, we find an exact solution of the corresponding field equations. We also discuss the expanding behavior of the resulting universe model through different cosmological parameters. Finally, we explore Noether gauge symmetry generators for Friedmann--Robertson--Walker and locally rotational symmetric Bianchi I universe models. It is concluded that in each case the symmetry generator as well as the conserved quantity exist, and the resulting solution is consistent with recent observations.
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