[Formula: see text] gravity is a recently proposed modified theory of gravity due to Xu et al. ([Formula: see text]). It is an extension of the symmetric teleparallel gravity, in which the gravitational action is given by an arbitrary function [Formula: see text] of the non-metricity tensor [Formula: see text] and the trace of energy-momentum tensor [Formula: see text]. In this paper also, we have investigated the cosmological model with Friedmann–Lemaitre–Robertson–walker (FLRW) Universe in [Formula: see text] theory with [Formula: see text]. Applying the energy conservation condition [Formula: see text], we have obtained the various cosmological parameters viz. Hubble parameter [Formula: see text], deceleration parameter [Formula: see text], etc. in terms of redshift [Formula: see text]. Using the available observational Hubble datasets [Formula: see text], the best fit values of the model parameters are determined by the [Formula: see text]-test formula. For these obtained values of model parameters, our model represents a transit cosmological model with past decelerating to present accelerating expansion phase of the Universe with the present value [Formula: see text]. The point of signature-flipping (transition) is calculated as [Formula: see text]. We have analyzed the variations of physical parameters viz. matter energy density [Formula: see text], isotropic pressure [Formula: see text], equation of state [Formula: see text] with respect to redshift [Formula: see text] and coupling parameter [Formula: see text]. For checking the viability of our derived model, we have tested energy conditions and also performed statefinder diagnosis. The age of the Universe is also calculated.
This paper examines the stability of the transition from the early decelerating stage of the Universe to the recent accelerating stage for the perfect fluid cosmological {locally rotationally symmetric (LRS) Bianchi-I model in f(R, T) theory. To determine the solution of field equations, the idea of a time-varying deceleration parameter (DP) which yields a scale factor, for which the Universe attains a phase transition scenario and is consistent with recent cosmological observations, is used. The time-dependent DP yields a scale factor , where β and k are respectively arbitrary and integration constants. By using the recent constraints (H0 = 73.8, and q0 = −0.54) from Type Ia Supernova (SN Ia) data in combination with Baryonic Acoustic Oscillations (BAO) and Cosmic Microwave Background (CMB) observations (Giostri et al.), we obtain the values of β = 0.0062 and k = 0.000016 for which we have derived a cosmological model from the early decelerated phase to the present accelerating phase. By applying other recent constraints (H0 = 73.8, q0 = −0.73) from SNe Ia Union data (Cunha), we obtain the values of β = 0.0036 and k = 0.000084 for which we have derived a cosmological model in the accelerating phase only. We have compared both models with experimental data. The stability of the background solution has been examined also for the metric perturbations alongside the properties of future singularities in a Universe ruled by dark energy with phantom type fluid. We demonstrate the presence of a stable fixed point with a condition of state ω < − 1 and numerically affirm this is really a late-time attractor in the ghost overwhelmed Universe. Some physical and geometric properties of the model are found and examined.
In this paper, spatially homogeneous and anisotropic Bianchi type-[Formula: see text] dark energy (DE) cosmological transit models with string fluid source in [Formula: see text] gravity [T. Harko et al., Phys. Rev. D 84 (2011) 024020], where [Formula: see text] is the Ricci scalar and [Formula: see text] the trace of the stress energy–momentum tensor, have been studied in the context of early time decelerating and late-time accelerating expansion of the Universe as suggested by the recent observations. The exact solutions of the field equations are obtained first by using generalized hybrid expansion law (HEL) [Formula: see text] which yields a time-dependent deceleration parameter [Formula: see text] and second by considering the metric coefficient [Formula: see text]. By using recent constraints from supernovae type-Ia union data [Cunha, arXiv:0811.2379[astro-ph]], we obtain [Formula: see text] and [Formula: see text] for transit model [Formula: see text]. The Universe has an initial singularity and is anisotropic closed and it tends to be flat at the late time, i.e. our Universe is in accelerating expansion. Our model shows a phase transition property from decelerating to accelerating. It is remarkable to mention here that our Universe is homogeneous and anisotropic in the early phase whereas it becomes homogeneous and isotropic for [Formula: see text]. We have also discussed the stability of the background solution with respect to perturbations of the metric along with the properties of future singularities in the Universe dominated by DE including the phantom-type fluid. Various physical and dynamical parameters are also calculated and investigated in terms of time and redshift both.
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