Noether symmetries of some homogeneous universe models incurvature corrected scalar-tensor gravity

Abstract

We explore Noether gauge symmetries of FRW and Bianchi I universemodels for perfect fluid in scalar-tensor gravity with extra termR−1 as curvature correction. Noether symmetry approach can beused to fix the form of coupling function ω(ϕ) and thefield potential V(ϕ). It is shown that for both models, theNoether symmetries, the gauge function as well as the conservedquantity, i.e., the integral of motion exist for the respectivepoint like Lagrangians. We determine the form of coupling functionas well as the field potential in each case. Finally, we investigatesolutions through scaling or dilatational symmetries for Bianchi Iuniverse model without curvature correction and discuss itscosmological implications.