In this paper, we investigate the newly developed f (R, T 2 ) theory (R is the Ricci scalar and T 2 = T αβ T αβ , T αβ demonstrates the energymomentum tensor) to explore some viable cosmological models. For this purpose, we use the Noether symmetry approach in the context of flat Friedmann-Robertson-Walker (FRW) universe. We solve the Noether equations of this modified theory for two types of models and obtain the symmetry generators as well as corresponding conserved quantities. We also evaluate exact solutions and investigate their physical behavior via different cosmological parameters. For the prospective models, the graphical behavior of these parameters indicate consistency with recent observations representing accelerated expansion of the universe. In the first case, we take a special model of this theory and obtain new class of exact solutions with the help of conserved quantities. Secondly, we consider minimal and non-minimal coupling models of f (R, T 2 ) gravity. We conclude that conserved quantities are very useful to derive the exact solutions that are used to study the cosmic accelerated expansion.

This paper investigates the dynamics of spherical collapse in the framework of energy–momentum squared gravity. This theory overcomes the big-bang singularity and provides viable cosmological consequences in the early time universe. We proceed our work by considering the nonstatic spherically symmetric space–time in the interior and static spherically symmetric metric in the exterior regions of the star. The Darmois junction conditions between interior and exterior geometries are derived. We construct dynamical equations through the Misner–Sharp technique to analyze the impact of matter variables and dark source terms on the collapsing phenomenon. A correlation among dark source terms, Weyl scalar and matter variables is also established. Due to the presence of multivariate function and its derivatives, space–time is no longer considered to be conformally flat. To obtain conformally flat space–time, we have considered a particular model of this gravity which yields conformally flat space–time and homogeneity of the energy density through the entire system. We conclude that positive dark source terms as well as negative pressure gradient provide the anti-gravitational behavior leading to the stability of self-gravitating objects and hence prevent the collapsing process.

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This paper investigates the dynamics of perfect fluid spherical collapse in curvature-matter coupled gravity. Using Darmois junction conditions, we derive smooth matching of both interior and exterior regions. The dynamical equations are formulated through Misner–Sharp formalism that give the collapse rate for both general and constant curvature terms. Finally, we formulate a relationship between correction terms, Weyl scalar and matter variables. For constant value of [Formula: see text], it is found that the metric is conformally flat if and only if energy density of the collapsing system is homogeneous while the positive correction terms decrease the collapse rate.