Cosmic Expansion and Noether Gauge Symmetries in $f(R,T,R_{\mu\nu}T^{\mu\nu})$ Gravity

TL;DR

This paper investigates cosmic evolution in a modified gravity theory with non-minimal coupling, identifying symmetries, deriving solutions, and confirming their viability and compatibility with observational data, ultimately supporting accelerated expansion.

Contribution

It introduces new models of $f(R,T,R_{ ueta}T^{ ueta})$ gravity, analyzes their symmetries, and demonstrates their stability and observational consistency.

Findings

Identified temporal and scaling symmetries leading to conserved quantities.

Derived exact cosmological solutions compatible with observational data.

Models favor accelerated cosmic expansion and are stable and viable.

Abstract

The present work explores different evolutionary phases of isotropically homogeneous and flat cosmos filled with dust fluid in non-minimally coupled gravity. We consider different models of this gravity to discuss the presence of symmetry generators together with conserved integrals using Nother Gauge symmetry scheme. In most of the cases, we obtain temporal and scaling symmetries that yield conservation of energy and linear momentum, respectively. In the absence of contracted Ricci and energy-momentum tensors, we obtain maximum symmetries but none of them correspond to any standard symmetry or conservation law. We formulate exact solutions and construct graphical analysis of standard cosmological parameters. We observe realistic nature of new models via squared speed of sound, viability conditions suggested by Dolgov-Kawasaki instability and state-finder parameters. We investigate the behavior of fractional densities and check the compatibility with Planck 2018 observational data. The new models are stable and viable preserving compatibility with $\Lambda$CDM and Chaplygin gas models. It is concluded that most of the solutions favor accelerated cosmic expansion.