LRS (Locally Rotationally symmetric) Bianchi type-I magnetized strange quark matter cosmological model have been studied based on f (R, T ) gravity. The exact solutions of the field equations are derived with linearly time varying deceleration parameter which is consistent with observational data (from SNIa, BAO and CMB) of standard cosmology. It is observed that the model begins with big bang and ends with a Big Rip. The transition of deceleration parameter from decelerating phase to accelerating phase with respect to redshift obtained in our model fits with the recent observational data obtained by Farook et al. in 2017. 1 The well known Hubble parameter H(z) and distance modulus µ(z) are discussed with redshift.

Considering the Einstein, Møller, Bergmann-Thomson, Landau-Lifshitz (LL), Papapetrou, Qadir-Sharif and Weinberg's definitions in general relativity, we find the momentum four-vector of the closed Universe based on Marder space-time. The momentum four-vector (due to matter plus field) is found to be zero. These results support the viewpoints of Banerjee-Sen, Xulu and Aydoġdu-Saltı. Another point is that our study agrees with the previous works of Cooperstock-Israelit, Rosen, Johri et al.

In this paper, we have studied homogeneous and anisotropic locally rotationally symmetric (LRS) Bianchi type-I model with magnetized strange quark matter (MSQM) distribution and cosmological constant Λ in f (R, T ) gravity where R is the Ricci scalar and T the trace of matter source. The exact solutions of the field equations are obtained under bilinear and special form of time varying deceleration parameter (DP). Firstly, we have considered two specific forms of bilinear DP with a single parameter of the form: q = α(1−t) 1+t and q = − αt 1+t , which leads to the constant or linear nature of the function based on the constant α. Second one is the special form of the DP as q = −1 + β 1+a β . From the results obtained here, one can observe that in the early universe magnetic flux has more effects and it reduces gradually in the later stage. For t → ∞, we get p → −Bc and ρ → Bc. The behaviour of strange quark matter along with magnetic epoch gives an idea of accelerated expansion of the universe as per the observations of the type Ia Supernovae.The theoretical arguments for the late-time cosmic acceleration are being a major issue among cosmologist of the twentieth century. The idea of this accelerated expansion of universe was discovered nearly 20 years ago by observations through Supernovae Ia [1-5], CMB [6,7], baryon acoustic oscillation (BAO) in galaxy clustering [8][9][10] and WMAP [11] etc. To investigate the nature of the universe, modern cosmology continues to test the above predictions, which leads to the refinement of cosmological models. The nature and behaviour of some unknown mechanism of the universe are responsible for this accelerated expansion, commonly referred as dark energy and contains more energy budget of the universe along with negative pressure. It triggers one of the important issue to study the current acceleration of the universe.Instead of resorting the mysterious concept of dark energy, there is an alternative way to reproduce the dynamics of the expanding universe through modified theories of gravity which is an extension of general relativity. These modifications can occur in several ways such as: one can use a base as the torsional formulation of general relativity called the teleparallel gravity equivalent to general relativity [12] e.g. f (T ) gravity, where T is the torsion scalar. On the other hand one can start the curvature formulation of general relativity in Einstein-Hilbert action by replacing the Ricci scalar with its arbitrary functions or even more complicated curvature invariants such as: f (R), f (R, G) gravity, and the latest f (R, T ) gravity proposed by Harko et al. [13]. The matter Lagrangian of f (R, T ) gravity coupled with Ricci scalar R and trace of energy-momentum tensor T . Such Lagrangian with matter content will differ from the Einstein's one. It has much significance to study late-time cosmic acceleration as well as dark energy and dark matter problem [14][15][16][17]. Hypothetically matter plays more fundamental role in the description of gravitational eff...

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