We study the cosmic evolution of non-minimally coupled f ( R , T ) gravity in the presence of matter fluids consisting of collisional self-interacting dark matter and radiation. We study the cosmic evolution in the presence of collisional matter, and we compare the results with those corresponding to non-collisional matter and the Λ -cold-dark-matter ( Λ CDM) model. Particularly, for a flat Friedmann–Lema i ^ tre–Robertson–Walker Universe, we study two non-minimally coupled f ( R , T ) gravity models and we focus our study on the late-time dynamical evolution of the model. Our study is focused on the late-time behavior of the effective equation of the state parameter ω e f f and of the deceleration parameter q as functions of the redshift for a Universe containing collisional and non-collisional dark matter fluids, and we compare both models with the Λ CDM model. As we demonstrate, the resulting picture is well accommodated to the latest observational data on the basis of physical parameters.

In this paper, we discuss the cosmic evolution in a modified theory involving non-minimal interaction of geometry and matter, labeled as [Formula: see text] gravity, where [Formula: see text] is the non-minimal interaction term. First, we develop the dynamical [Formula: see text] field equations for Friedmann–Lemaitre–Robertson–Walker (FLRW) spacetime and then by using divergence of these equations, we explore its interesting outcome of non-conserved energy–momentum tensor (EMT). The presence of geometry matter coupling in such theories results in non-geodesic test particles motion and hence causes an additional force orthogonal to four-velocity of these particles. By taking these interesting features into account along with a particular choice of Lagrangian [Formula: see text], we explore the resulting expression of energy density. Further, the free model parameters are constrained using energy condition bounds where it is concluded that these values of free parameters are compatible with the recent data.

Here, we discuss the cosmic evolution in the presence of collisional matter (CM) with and without radiations within the framework of modified teleparallel theories. We opt f(T, B) theory (where T stands for torsion scalar and B represents the boundary term associated to the divergence of torsion 2∇ μ Tμ = B), which makes a good connection between f(R) (R for Ricci Scalar) and f(T) (T for torsion) theory under reasonable conditions. The power law and logarithmic f(T, B) models are selected to discuss the behavior of deceleration parameter q(z), Hubble parameter H(z), Equation of state (EoS) for dark energy (DE), and effective EoS. We found the great oscillations of EoS for DE across the phantom divide line. Effective EoS also crossed the phantom divide line without any oscillations. The graphs for H(z), q(z), effective EoS are alike for NCM with radiations, CM without radiaitons and CM with radiations.

An accelerated expansion phase is being experienced by the universe due to the presence of an unknown energy component known as dark energy (DE). To find out the cosmic evolution scientists ever tried to modify Einstein's gravitational theory and its unexplored parts. We also look forward to address the same problem with a different approach based on interaction between matter and geometry. For this purpose we consider f (R, T, Q) modified theory (where R is the Ricci Scalar, T is the trace of energy-momentum tensor (EMT) Tuv and Q = RuvT uv is interaction of EMT Tµν and Ricci Tensor Ruv). We formulate modified field equations in the background of Friedmann-Lemaître-Robertson-Walker (FLRW) model which is defined as ds 2 = dt 2 − a(t) 2 (dx 2 + dy 2 + dz 2 ), where a(t) represents the scale factor. In this formalism energy density is found using covariant divergence of modified field equations. ρ involves a contribution from non-minimal matter geometry coupling which helps to study different cosmic eras based on equation of state (EOS). Furthermore, we apply the energy bounds to constrain the model parameters establishing a pathway to discuss the cosmic evolution for best suitable parameters in accordance with recent observations.

The purpose of this work is to examine the cosmic evolution in the presence of collisional matter (CM) with and without radiations in a modified Teleparallel theory involving a generic function [Formula: see text] which depends on the scalar torsion [Formula: see text] and the boundary term associated to the divergence of torsion [Formula: see text]. We select seven novel [Formula: see text] models including power law, logarithmic models and exponential models, some of these reported in [S. Bahamonde, M. Zubair and G. Abbas, Phys. Dark Univ. 19 (2018) 78; S. Bahamonde and S. Capozziello, The Eur. Phys. J. C. 77 (2017) 107; C. Escamilla-Rivera and J. L. Said, Class. Quantum Grav. 37 (2020) 165002] and discuss the evolutionary scenario. The behavior of deceleration parameter [Formula: see text], Hubble parameter [Formula: see text], Equation-of-state (EoS) for dark energy (DE) and effective EoS is presented. [Formula: see text]CDM epoch and crossing of phantom divide line (approaching to phantom era) is observed in scenarios like noncollisional matter (NCM) with radiation, CM with and without radiation. Results are found to be adequate with recent cosmic observations.