A cosmological model with a specific form of the Hubble parameter is constructed in a flat homogeneous, and isotropic background in the framework of f (R, T ) gravity, where R is the scalar curvature and T is the trace of the stress-energy-momentum tensor. The proposed functional form of the Hubble parameter is taken in such a way that it fulfills the successful bouncing criteria to find the solution of the gravitational field equations provided the Universe is free from initial singularity. The various constraints on the parameters are involved in the functional form of the Hubble parameter which is analyzed in detail. In addition, we explore physical and geometrical consequences of the model based on the imposed constraints. Furthermore, we demonstrate the bouncing scenario which are realized in our model with some particular values of the model parameters. As a result, we find that all of the necessary conditions are satisfied for a successful bouncing model.

In this paper, we have studied flat Friedmann-Lemaître-Robertson-Walker (FLRW) model with modified Chaplygin gas (MCG) having equation of state p m = Aρ − B ρ γ , where 0 ≤ A ≤ 1, 0 ≤ γ ≤ 1 and B is any positive constant in f (R, T ) gravity with particle creation. We have considered a simple parametrization of the Hubble parameter H in order to solve the field equations and discussed the time evolution of different cosmological parameters for some obtained models showing unique behavior of scale factor. We have also discussed the statefinder diagnostic pair {r, s} that characterizes the evolution of obtained models and explore their stability. The physical consequences of the models and their kinematic behaviors have also been scrutinized here in some detail.

This article deals with a cosmological scenario in f (R, T ) gravity for a flat FLRW model of the universe. We consider the f (R, T ) function as f (R) + f (T ) which starts with a quadratic correction of the geometric term f (R) having structure f (R) = R + αR 2 , and a linear matter term f (T ) = 2λT . To achieve the solution of the gravitational field equations in the f (R, T ) formalism, we take the form of a geometrical parameter, i.e. scale factor a(t) = sinh 1 n (βt) [31], where β and n are model parameters. An eternal acceleration can be predicted by the model for 0 < n < 1, while the cosmic transition from the early decelerated phase to the present accelerated epoch can be anticipated for n ≥ 1. The obtained model facilitate the formation of structure in the Universe according to the Jeans instability condition as our model transits from radiation dominated era to matter dominated era. We study the varying role of the equation of state parameter ω. We analyze our model by studying the behavior of the scalar field and discuss the energy conditions on our achieved solution. We examine the validity of our model via Jerk parameter, Om diagnostic, Velocity of sound and Statefinder diagnostic tools. We investigate the constraints on the model parameter n and H0 (Hubble constant) using some observational datasets: SN eIa dataset, H(z) (Hubble parameter) dataset, BAO (Baryon Acoustic Oscillation data) and their combinations as joint observational datasets H(z) + SN eIa and H(z) + SN eIa + BAO. It is testified that the present study is well consistent with these observations. We also perform some cosmological tests and a detailed discussion of the model. PACS number: 98.80 cqIn the above equation, R ij is the Ricci tensor, R the Ricci scalar, g ij the covariant metric tensor of order 2, Λ the cosmological constant, G the gravitational constant, c indicates the speed of the light, and T ij the energymomentum-tensor (EMT). Despite the fact that general relativity (GR) is extremely well tested, alternatives are always present. According to observations, 95% of the matter content of the Universe is unexplored. GR has several problems, as the problem of initial big-bang spacetime singularity [1-3] and it is not yet quantised. GR has to be reconciled with quantum physics to discuss quantum effects. GR together with quantum physics forms the backbone of modern physics. The ΛCDM model of the cosmology is quite successful, but there remain several unresolved issues such as the fine tuning problem [4]. Hence it is worthwhile to examine alternative theories of gravity.Amongst large range of modified theories of gravity, f (R) gravity [5] is considered as an interesting alternative. A more general function of R i.e. f (R) is considered in the Einstein-Hilbert action . An intensively study on f (R) gravity seems to indicate that it is an improvement over GR [6][7][8]. It can also explain both phases of cosmic acceleration even in the absence of Λ (early and late times) [9]. f (R) gravity behaves extremely well on large scales...