Noether Symmetries of Some Homogeneous Universe Models in Curvature Corrected Scalar-Tensor Gravity

Abstract

We explore Noether gauge symmetries of FRW and Bianchi I universe models for perfect fluid in scalar-tensor gravity with extra term $R^{-1}$ as curvature correction. Noether symmetry approach can be used to fix the form of coupling function $\omega (\varphi )$ and the field potential $V(\varphi )$. It is shown that for both models, the Noether symmetries, the gauge function as well as the conserved quantity, i.e., the integral of motion exist for the respective point like Lagrangians. We determine the form of coupling function as well as the field potential in each case. Finally, we investigate solutions through scaling or dilatational symmetries for Bianchi I universe model without curvature correction and discuss its cosmological implications.

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Cited by in corpus (11)

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• Some Exact Solutions in $f(\mathcal{G},T)$ Gravity via Noether Symmetries
• Teleparallel dark energy model with a fermionic field via Noether symmetry
• Symmetries of geodesic motion in Gödel-type spacetimes
• Scalar-Tensor Teleparallel Gravity With Boundary Term by Noether Symmetries
• New exact solutions of Bianchi I, Bianchi III and Kantowski-Sachs spacetimes in scalar-coupled gravity theories via Noether gauge symmetries
• Noether Symmetries and Anisotropic Universe in Energy-Momentum Squared Gravity
• Exact Solutions and Conserved Quantities in f(R,T) Gravity
• Noether Symmetry Approach for Dirac-Born-Infeld Cosmology
• Dynamics of Potentials in Bianchi Type Scalar-Tensor Cosmology