Noether symmetries of LRS Bianchi type-I spacetime in f (R, φ, χ) gravity

This paper investigates the Noether symmetry approach in modified f (R, phi, chi) theory of gravity, where R is the Ricci scalar, phi is a scalar field and chi is the kinetic energy term. For this purpose, we consider Locally Rotationally Symmetric (LRS) Bianchi Type-I spacetimes. The cosmological solutions are developed through Noether symmetry approach. The determining equations are computed in the context of a point-like Lagrangian for f (R, phi, chi) gravity. In particular, three different cases are taken into account for the LRS Bianchi Type-I spacetimes. Some important conserved quantities for the Lagrangian in this modified theory of gravity are worked out through the determining equations. In this scenario, the graphical behavior of energy density, pressure component and equation of state parameter are reported and analyzed with the help of first integrals of motion. The negative trends of the strong energy conditions actually suggest. that the said theory supports expanding Universe with dark energy.