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In this paper, we investigate the late-time accelerated universe evolution in a flat, homogeneous and isotropic model in the context of [Formula: see text] gravity, where [Formula: see text] and [Formula: see text] are non-metricity scalar and trace of energy–momentum tensor, respectively. The scale factor, by construction, yields ekpyrotic contraction era followed by a non-singular bounce. The expanding era of the universe yields late-time dark energy era preceded by matter-dominating decelerating era. The model unifies an ekpyrotic, non-singular bounce with the present dark energy-dominated epoch. The model parameters in the functional form of [Formula: see text] gravity affect the dynamical evolution of the equation of state (EoS) parameter. The theoretical value of EoS parameter is found to be [Formula: see text] for [Formula: see text], respectively, and it lies in range of the estimated value of EoS parameter from the Planck+SNe+BAO observational data. Different aspects of this bouncing model including behavior of geometrical and physical quantities along with energy conditions have been discussed in detail.

We investigate the effect of particle creation in flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime under the higher derivative theory composition. The exact solution of the field equation in higher derivative theory is obtained by considering the quadratic equation of state, p = ωρ2 − ρ and different forms of deceleration parameter. The physical acceptance and stability of the models are explored by discussing energy conditions and squared sound speed. In addition to that, the statefinder diagnostic pair {r,s} is also scrutinized to measure the deviation of considered models from Λ cold dark matter (ΛCDM) model.

The present article deals with the study of interacting and non-interacting dark energy (DE) and dark matter (DM) in the spatially homogeneous and anisotropic Bianchi I space–time within the framework of Brans–Dicke (BD) scalar–tensor theory of gravitation. As the set of field equations is not closed, exact solutions are obtained using power-law relation and assuming a linearly varying deceleration parameter. The physical acceptability and stability of the obtained model are scrutinised using energy conditions and squared speed of sound. The statefinder diagnostic method is adopted to discuss and measure the deviation of the considered model from the $$\Lambda $$ cold dark matter ( $$\Lambda $$ CDM) model.