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In this communication, we have explored spatially homogeneous, anisotropic Bianchi-II space-time in f(R, T) theory of gravity. Here, we have obtained an explicit solution of the field equations of f(R, T) theory with time dependent fractional linear varying deceleration parameter (FLVDP) i.e. q(t) . The accelerating expanding nature of the cosmos has been also discussed under the suitable assumption q ( t ) = α ( 1 − t ) 1 + t , here α > 0. It is observed that the universe was originated from a singularity in the past and is expanding at an accelerating rate. The FLVDP depicts a transitional phase i.e., early deceleration to the current accelerating phase.

In Saez–Ballester gravitational theory, we studied the role of particle creation and bulk viscosity in the evolution of a spatially homogeneous and anisotropic Bianchi type I universe. We treated particle creation and bulk viscosity as two distinct irreversible processes, and we modified the energy momentum tensor to account for viscous and particle creation pressures. We employed constant and variable deceleration parameters to obtain average scale factor solutions for the Bianchi type I model. The use of constant deceleration parameter resulted in two unique scale factor solutions that led to singular and non-singular natures of the universe with power-law and exponential laws, respectively. Furthermore, the variable deceleration parameter yielded a de Sitter like solution representing a non-singular universe. We also explored the temporal evolution of the bulk viscosity coefficient in Eckart’s theory, truncated theory, and full causal theory for all three models.

The present paper compares two LRS Bianchi type-I bulk viscous models of the universe constructed in f ( R ,  T ) theory of gravity. A parameterization of deceleration parameter (DP) is considered to find solutions of the models. This parameterization of DP reduces to both linear-varying deceleration parameter (LVDP) (Akarsu and Dereli in Int J Theor Phys 51:612–621, 2011) and bilinear-varying deceleration parameter (BVDP) (Mishra and Dua in Astrophys Space Sci 364:1–12, 2019) for specific values of model parameters. The cosmic evolution is discussed with the help of LVDP in model I and BVDP in model II. Both the models exhibit phase transition from early cosmic decelerated phase to the present accelerated phase. We discuss physical and geometrical properties of the models graphically and compare them in detail. In addition, best-fit values of model parameters are obtained using 51 values of observational Hubble parameter.

In this paper, we have studied plane symmetric cosmological model with the isotropic matter distribution. This is done under the framework of f R , L m gravity theory. This modified gravity theory, represented by f R , L m = R 2 + L m α + β , which is a combination of both the Ricci scalar (R) and matter Lagrangian density ( L m ) , we consider L m = ρ . Our goal was to analyse the behaviour of the expansion rate of the universe over time. We solved the field equation by assuming (i) the constant deceleration parameter (DP) proposed by Berman, i.e. q = constant. (ii) a time varying deceleration parameter q t = - 1 + n ζ ζ + t 2 , which yields a t = t ζ e t 1 n .We discussed the physical properties of the models. Additionally, we use the equation of state (EoS) parameter, the jerk parameter and the statefinder parameters as analytical tools to understand the evolution of the Universe in this modified gravity framework. This research offers significant insights into the anisotropic behaviour of the Universe within the framework of f R , L m gravity, enhancing our comprehension of the fundamental dynamics of cosmic evolution.

The spatially homogeneous and anisotropic Bianchi type-V universe filled with interacting Dark matter and Holographic dark energy has been studied. The exact solutions of Einstein’s field equations are obtained by (i) applying the special law of variation of Hubble parameter that yields constant values of the deceleration parameter and (ii) using a special form of deceleration parameter. It has been observed that for suitable choice of interaction between dark matter and holographic dark energy there is no coincidence problem (unlike Λ CDM). Also, in all the resulting models the anisotropy of expansion dies out very quickly and attains isotropy after some finite time. The physical and geometrical aspects of the models are also discussed.

In this work, we explore the cosmological stability of f(Q, B) gravity using a dynamical system approach, where Q denotes the nonmetricity scalar and B represents the boundary term. We determine the model parameters of f(Q, B) through Bayesian statistical analysis, employing Markov Chain Monte Carlo techniques. This analysis incorporates numerical solutions and observational data from cosmic chronometers, the extended Pantheon+ data set, and baryonic acoustic oscillation measurements. Our findings reveal a stable critical point within the dynamical system of the model, corresponding to the de Sitter phase, which is consistent with current observations of the Universe dominated by dark energy and undergoing late-time accelerated expansion. Additionally, we utilize center manifold theory to examine the stability of this critical point, providing deeper insights into the behavior of the model. The cosmological implications of f(Q, B) gravity indicate a smooth transition in the deceleration parameters from deceleration to the acceleration phase, underscoring the potential of the model to describe the evolution of the Universe. Our results suggests that the f(Q, B) model presents a viable alternative to the standard ΛCDM model, effectively capturing the observed acceleration of the Universe and offering a robust framework for explaining the dynamics of cosmic expansion.

In this paper, we investigate the modified symmetric teleparallel gravity or f(Q) gravity, where Q is the nonmetricity, to study the evolutionary history of the universe by considering the functional form of f(Q)=αQn, where α and n are constants. Here, we consider the parametrization form of the deceleration parameter as q=q0+q1z/(1+z)2 (with the parameters q0(q at z=0), q1, and the redshift, z), which provides the desired property for a sign flip from a decelerating to an accelerating phase. We obtain the solution of the Hubble parameter by examining the mentioned parametric form of q, and then we impose the solution in Friedmann equations. Employing the Bayesian analysis for the Observational Hubble data (OHD), we estimated the constraints on the associated free parameters (H0,q0,q1) with H0 the current Hubble parameter to determine if this model may challenge the ΛCDM (Λ cold dark matter with the cosmological constant, Λ) limitations. Furthermore, the constrained current value of the deceleration parameter q0=−0.832−0.091+0.091 shows that the present universe is accelerating. We also investigate the evolutionary trajectory of the energy density, pressure, and EoS (equation-of-state) parameters to conclude the accelerating behavior of the universe. Finally, we try to demonstrate that the considered parametric form of the deceleration parameter is compatible with f(Q) gravity.

The present study deals with the investigation of the Friedmann-Lemaitre-Robertson-Walker models (often FLRW-models) with time varying G and ∧ in the framework of General theory of Relativity. The Einstein field equations have been solved by considering the time-varying deceleration parameter q(t) and Scale factor α ( t ) = e β t + ( sinh β t ) 1 m , where m and β are arbitrary constants. We have analysed the value of m , which will generate a transition for universe from early decelerating phase to recent acceleration phase. The physical and graphic behaviour have also been planned to study in this communication.

A generalized version for the Rastall theory is proposed showing the agreement with the cosmic accelerating expansion. In this regard, a coupling between geometry and the pressureless matter fields is derived which may play the role of dark energy, responsible for the current accelerating expansion phase. Moreover, our study also shows that the radiation field may not be coupled to the geometry in a non-minimal way which represents that the ordinary energy-momentum conservation law is respected by the radiation source. It is also shown that the primary inflationary era may be justified by the ability of the geometry to couple to the energy-momentum source in an empty flat FRW universe. In fact, this ability is independent of the existence of the energy-momentum source and may compel the empty flat FRW universe to expand exponentially. Finally, we consider a flat FRW universe field by a spatially homogeneous scalar field evolving in potential V ( ϕ ) , and study the results of applying the slow-roll approximation to the system which may lead to an inflationary phase for the universe expansion.

In this article, we present and analyze cosmological models with an anisotropic variable parameter. We have set up the field equations with the space time in the form of Bianchi I metric with an f(R, T) gravity. The functional form for the f(R, T) gravity has been assumed to be f(R,T)=R+2f(T) , where R and T are, respectively, the Ricci scalar and trace of the energy–momentum tensor. Two different models are constructed with respect to the scale factors, such as power law scale factor and hybrid scale factor. Moreover, the anisotropic parameter taken here in the form of hyperbolic function further gives clarity on the behavior of equation of state parameter. It is to note that when the values of the coefficient constant vanish, the model yields the isotropic universe. For both the cases, the deceleration parameter, state finder diagnostic pair and energy conditions have been obtained and analyzed which provide physical plausibility of the models.