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In this paper, we study cosmic evolutionary stages in the background ofmodified theory admitting non-minimal coupling between Ricci scalar, trace ofthe energy-momentum tensor, contracted Ricci and energy-momentum tensors. Fordust distribution, we consider isotropic, homogeneous and flat cosmic model todetermine symmetry generators, conserved integrals and exact solutions usingNoether symmetry scheme. We find maximum symmetries for non-minimallyinteracting Ricci scalar and trace of the energy-momentum tensor but none ofthem correspond to any standard symmetry. For rest of the models, we obtainscaling symmetry with conserved linear momentum. The graphical analysis ofstandard cosmological parameters, squared speed of sound, viability conditionssuggested by Dolgov-Kawasaki instability and state-finder parameters identifyrealistic nature of new models compatible with Chaplygin gas model,quintessence and phantom regions. The fractional densities relative to ordinarymatter and dark energy are found to be consistent with Planck 2018observational data. It is concluded that the constructed non-minimally coupledmodels successfully explore cosmic accelerated expansion.

Isotropic Exact Solutions via Noether Symmetries in $f(R,T,R_{\mu\nu}T^{\mu\nu})$ Gravity