Anisotropic Bianchi type-III Space-time Research Articles

Transit two-fluid models in anisotropic Bianchi type-III space-time

In the present paper, we are seeking some new exact solutions of Einstein’s field equations under the purview of a spatially homogeneous and anisotropic Bianchi type-III space-time, with the assumption that, the universe is filled with two fluid, barotropic fluid, and dark energy. For obtaining new solutions, which are consistent with recent observations, we have considered an average scale factor a(t)=(tαeβt)1n, and obtains a variable deceleration parameter q(t)=−1+αn(α+βt)2. For appropriate values of α, β and n, the proposed work, represents a transit model, showing the transition from decelerating (q > 0) to the present accelerating universe (q < 0). We have analyzed our model in the two contexts. First, when the two fluids do not interact with each other and second when these fluid interact. We have found that, the equation of state (EoS) for Dark Energy(DE) ω(de), during the evolution of the universe, in both the cases, approaches to −1.196 (phantom model,ω(de)<−1) at late time, showing consistency with recent observations. Also, we have investigated the characteristics with respect to cosmic redshift z and found very close to recent observational data. Some other geometric and physical properties of cosmological models are also studied.

Scenario of two-fluid dark energy models in Bianchi type-III Universe

In this paper, we have analyzed the equation of state parameter for dark energy in the spatially homogeneous and anisotropic Bianchi type-III spacetime filled with a barotropic fluid and dark energy by considering a variable deceleration parameter. To solve the Einstein field equations, we assume that the expansion scalar is proportional to the shear scalar. We find that during the evolution of the Universe, the equation of state and the cosmological parameters are positive decreasing functions of cosmic time [Formula: see text]. Also, we discuss the physical parameters, as well as the jerk and cosmic span parameters, which predict that the Universe in this model approaches the [Formula: see text]CDM model at late times.

A dynamical system approach to Bianchi III cosmology for Hu–Sawicki type f(R) gravity

The cosmological dynamics of spatially homogeneous but anisotropic Bianchi type-III space-time is investigated in presence of a perfect fluid within the framework of Hu–Sawicki model. We use the dynamical system approach to perform a detailed analysis of the cosmological behaviour of this model for the model parameters \(n=1, c_1=1\), determining all the fixed points, their stability and corresponding cosmological evolution. We have found stable fixed points with de Sitter solution along with unstable radiation like fixed points. We have identified a matter like point which act like an unstable spiral and when the initial conditions of a trajectory are very close to this point, it stabilizes at a stable accelerating point. Thus, in this model, the universe can naturally approach to a phase of accelerated expansion following a radiation or a matter dominated phase. It is also found that the isotropisation of this model is affected by the spatial curvature and that all the isotropic fixed points are found to be spatially flat.

Bulk viscous string cosmological models in f(R) gravity

In this paper, we derive f(R) gravity field equations with the help of a spatially homogeneous and anisotropic Bianchi type-III space–time, in the presence of a bulk viscous fluid, containing one-dimensional cosmic strings. Here we obtained the solutions of the field equations, both in the presence and in the absence of cosmic strings, under some specific plausible physical conditions. In particular, cosmological models with bulk viscous strings in f(R) theory of gravity are obtained by using the special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cimento, B74, 182 (1983)). Various physical and kinematical properties of the models are also discussed.

Bianchi type-III dark energy models with constant deceleration parameter in self-creation cosmology

We have constructed dark energy cosmological models in an anisotropic Bianchi type-III space–time with a variable equation of state (EoS) parameter ω in Barber’s (Gen. Relativ. Gravitation, 14, 117, 1982) second self-creation theory of gravitation. The models are obtained using the special law of variation of Hubble’s parameter that yields a constant value of the deceleration parameter. In the two different models that we have obtained, the EoS parameter ω for dark energy is found to be time dependent. In one model the value of ω is in good agreement with the recent observations of type Ia supernovae (SNe Ia) data, SNe Ia data with cosmic microwave background radiation anisotropy and galaxy clustering statistics. Further we have discussed the well-known astrophysical phenomena, namely, the Hubble parameter H(z), luminosity distance dL, proper distance d(z), distance modulus μ(z), and look-back time with red shift. The expression for jerk parameter and statefinder parameters are also derived.

Bianchi type-III bulk viscous string cosmological model in Brans-Dicke theory of gravitation

A spatially homogeneous and anisotropic Bianchi type-III space-time is considered in the framework of a scalar-tensor theory of gravitation proposed by Brans and Dicke (Phys. Rev. 124:925, 1961) in the presence of bulk viscous fluid containing one dimensional cosmic strings. We have found a determinate solution of the field equations using the plausible physical conditions (i) a barotropic equation state for the pressure and density, (ii) special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cimento B74:182, 1983), (iii) shear scalar is proportional to scalar expansion and (iv) the trace of the energy tensor of the fluid vanishes. We have also assumed that bulk viscous pressure is proportional to energy density. Some physical and kinematical properties of the model are, also, discussed.

Bianchi type-III bulk viscous cosmic string model in a scalar-tensor theory of gravitation

A spatially homogeneous and anisotropic Bianchi type-III space-time is considered in the presence of bulk viscous fluid containing one dimensional cosmic strings in the frame work of a scalar-tensor theory of gravity proposed by Saez and Ballester (in Phys. Lett. A 113:467, 1986). We have obtained a determinate solution of the field equations of this theory, using (i) a barotropic equation of state for the pressure and density and (ii) the bulk viscous pressure is proportional to the energy density. Some physical properties of the model are also discussed.

Anisotropic Bianchi type-III perfect fluid cosmological models in f(R, T) theory of gravity

Einstein’s field equations are considered for spatially homogeneous and anisotropic Bianchi type-III space–time in presence of a perfect fluid within the framework of f(R, T) theory of gravity. Algorithms are derived to generate new classes of solutions of field equations starting from known solutions to the same type. Starting with the solution of Reddy and coworkers, new classes of Bianchi type-III cosmological models in f(R, T) gravity theory are generated. Kinematical and physical behaviors of the cosmological models are discussed. These models may be physically significant for discussion on early stages of evolution of the universe.

Non-existence of Bianchi type-III bulk viscous string cosmological model in f(R,T) gravity

A spatially homogeneous and anisotropic Bianchi type-III space-time is considered in the presence of bulk viscous fluid containing one dimensional cosmic strings in the frame work of f(R,T) gravity proposed by Harko et al. (Phys. Rev. D 84:024020, 2011). To get a determinate solution of the field equations of this theory, we have used (i) a barotropic equation of state for the pressure and density and (ii) the bulk viscous pressure is proportional to the energy density. It is interesting to observe that, in this case, Bianchi type-III bulk viscous string cosmological model does not exist and degenerates into vacuum model of general relativity.

Two-Fluid Dark Energy Models in Bianchi Type-III Universe with Variable Deceleration Parameter

Some new exact solutions of Einstein's field equations have come forth within the scope of a spatially homogeneous and anisotropic Bianchi type-III space-time filled with barotropic fluid and dark energy by considering a variable deceleration parameter. We consider the case when the dark energy is minimally coupled to the perfect fluid as well as direct interaction with it. Under the suitable condition, the anisotropic models approach to isotropic scenario. We also find that during the evolution of the universe, the equation of state (EoS) for dark energy $\omega^{(de)}$, in both cases, tends to -1 (cosmological constant, $\omega^{(de)} = -1$), by displaying various patterns as time increases, which is consistent with recent observations. The cosmic jerk parameter in our derived models are in good agreement with the recent data of astrophysical observations under appropriate condition. It is observed that the universe starts from an asymptotic Einstein static era and reaches to the $\Lambda$CDM model. So from recently developed Statefinder parameters, the behavior of different stages of the universe has been studied. The physical and geometric properties of cosmological models are also discussed.

Dark energy model in anisotropic Bianchi type-III space-time with variable EoS parameter

A new dark energy model in anisotropic Bianchi type-III space-time with variable equation of state (EoS) parameter has been investigated in the present paper. To get the deterministic model, we consider that the expansion $\theta$ in the model is proportional to the eigen value $\sigma^{2}_{~2}$ of the shear tensor $\sigma^{j}_~i$. The EoS parameter $\omega$ is found to be time dependent and its existing range for this model is in good agreement with the recent observations of SNe Ia data (Knop et al. 2003) and SNe Ia data with CMBR anisotropy and galaxy clustering statistics (Tegmark et al. 2004). It has been suggested that the dark energy that explains the observed accelerating expansion of the universe may arise due to the contribution to the vacuum energy of the EoS in a time dependent background. Some physical aspects of dark energy model are also discussed.