  This article examines the analytic solutions of isotropic spacetime with the
minimal coupling of scalar field and matter in the context of energy-momentum
squared gravity. The scalar field includes quintessence and phantom dark energy
models. We evaluate solutions of a physical system through the Noether symmetry
approach that provide some viable constraints to choose the cosmological models
on the basis of current observations. We consider different models of this
theory to establish Noether equations, symmetry generators and corresponding
conserved quantities. We compute analytic solutions and examine their graphical
representation for various cosmological quantities. The behavior of these
quantities is found to be consistent with current observations implying that
this theory shows expanding behavior of the universe. We find that symmetry
generators and their conserved parameters exist in all cases.
