In this paper, we investigate the evolution of the equation of state of the interacting viscous dark energy in [Formula: see text] gravity. We first consider the case when the dark energy does not interact with the dark matter and after, the case where there is a coupling between these dark components. The viscosity and the interaction between the two fluids are parameterized by constants [Formula: see text] and [Formula: see text] respectively for which a detailed investigation on the cosmological implications has been done. In the later part of the paper, we explore some bulk viscosity models with Little and Pseudo Rip infinite time singularities within [Formula: see text] modified gravity. We obtain analytic expressions for characteristic properties of these cosmological models.

We have studied in this paper, the stability of dynamical system in f (R) gravity. We have considered the f (R) γ-gravity and explored its dynamical analysis. We found six critical points among which only one describes a universe filled of both matter and dominated dark energy. It is shown that these critical points present specific phase spaces described by the corresponding fluids. Furthermore, we have investigated the stability conditions of these critical points and find that these conditions are dependent of the model parameters. We also study the stability of a new power-law f * (R) model with de Sitter and power law solutions.

We investigate the turbulence effect in dark fluid universe with linear inhomogeneous equation of state. Attention is attached to two physical situations. First, we perform the perturbative analysis of turbulence and check its effects around the Big Rip. Later, treating the turbulence energy density as a part of total dark fluid, we study the stability of the system. The result shows that the stability is achieving as the energy density of turbulence decreases, changing into heat (the radiation), in perfect agreement with the avoidance of the Big Rip.

In this work, we investigate the Rastall–Maxwell theory around the strange quark matter (SQM) in the presence of a quintessence field and a quintessence dark energy having a characteristic parameter [Formula: see text] such that [Formula: see text]. The SQM is governed by the simplified MIT bag model equation of state: [Formula: see text], with [Formula: see text] the bag constant, in the presence of a load distribution given by [Formula: see text]. We find some solutions by using the modified Tolman–Oppenheimer–Volkoff (TOV) equation in the framework of Rastall gravity. We investigate the energy condition, the mass–radius relation, modified TOV equation, redshift and the stability of the system is checked by exploring the adiabatic index, the compactification factor and the causality condition for verifying the physical consistency of our model. We notify that for physical values of Rastall parameter, the stellar system is more massive compared to its size. Hence, it is revealed that the alternative Rastall theory is appropriate to explain the behavior of massive stellar objects. The presence of dark energy motivates us to consider that the existing strange stars are a mixture of both ordinary matter and quintessence matter in different proportions. The incorporation of quintessence matter with the real one describes the well-known SQM.

Inflationary cosmology was the subject of an investigation in the [Formula: see text] gravity context, for which [Formula: see text] stands for the torsion scalar while [Formula: see text] is the trace of the energy–momentum tensor using three different class of inflation potentials well known in the literature. In order to find the range of geometry-matter coupling parameter to describe cosmological inflation scenario, we determined the slow-roll parameters and predict the scalar spectral index [Formula: see text], the tensor to scalar ratio [Formula: see text] and tensor spectral index [Formula: see text] in function in inflation potential parameters. The results show that the range of geometry-matter coupling parameter found is in agreement with the PLANCK 2018 data and WMAP data.