Bianchi Type Research Articles

Accelerating universe with wet dark fluid in modified theory of gravity

In the present work we have focused on the investigation of LRS Bianchi type –I metric within the framework of f(R) theory of gravity filled with wet dark fluid as the candidate of dark energy. The solution of the metric is an accelerating universe, derived by assuming the negative constant deceleration parameter and utilizing a power law relation. Additionally, we have visually analyzed the metric's dynamical and geometrical properties through graphical representations.

Constraints on Bianchi-I type universe with SH0ES anchored Pantheon+ SNIa data

We study the Bianchi-I cosmological model motivated by signals of statistical isotropy violation seen in cosmic microwave background (CMB) observations and others. To that end, we consider various kinds of anisotropic matter that source anisotropy in our model, specifically Cosmic strings, Magnetic fields, Domain walls and Lorentz violation generated magnetic fields. These anisotropic matter sources, taking one at a time, are studied for their co-evolution with standard model (isotropic) sources viz., dust-like (dark/normal) matter, and dark energy modelled as cosmological constant. We constrain the Hubble parameter, density fractions of anisotropic matter, cold dark matter (CDM), and dark energy (Λ) in a Bianchi-I universe with planar symmetry i.e., which has a global ellipsoidal geometry, and try to find signatures of a cosmic preferred axis if any.The latest compilation of Type Ia Supernova (SNIa) data from Pantheon+SH0ES collaboration is used in our analysis to obtain constraints on cosmological parameters and any preferred axis for our universe.In our analysis, we found mild evidence for a cosmic preferred axis. It is interesting to note that this preferred axis lies broadly in the vicinity of other prominent cosmic anisotropy axes reported in the literature from diverse data sets.Also we find some evidence for non-zero (negative) cosmic shear and eccentricity that characterize different expansion rates in different directions and deviation from an isotropic scale factor respectively.The energy density fractions of two of the sources considered are found to be non-zero at a2σ confidence level.To be more conclusive, we require more SNIa host galaxy data for tighter constraints on distance and absolute magnitude calibration which are expected to be available from the future JWST observations and others.

Cosmological first-order vacuum phase transitions in an expanding anisotropic universe

We examine the anisotropy originated from a first-order vacuum phase transitions through three-dimensional numerical simulations. We apply Bianchi Type-I metric to our model that has one scalar field minimally coupled to the gravity. We calculate the time evolution of the energy density for the shear scalar and the directional Hubble parameters as well as the power spectra for the scalar field and the gravitational radiation although there are a number of caveats for the tensor perturbations in Bianchi Type-I universe. We run simulations with different mass scales of the scalar field, therefore, in addition to investigation of anisotropy via the shear scalar, we also determine at which mass scale the phase transition completes successfully, hence, neglecting the expansion of the Universe does not significantly affect the results. Finally, we showed that such an event may contribute to the total anisotropy depending on the mass scale of the scalar field and the initial population of nucleated bubbles.

Anisotropic Generalization of the ΛCDM Universe Model with Application to the Hubble Tension

Anisotropic Generalization of the ΛCDM Universe Model with Application to the Hubble Tension

Killing vector fields of locally rotationally symmetric Bianchi type V spacetime

The classification of locally rotationally symmetric Bianchi type V spacetime based on its killing vector fields is presented in this paper using an algebraic method. In this approach, a Maple algorithm is employed to transform the Killing’s equations into a reduced evolutive form. Subsequently, the integration of the Killing’s equations is carried out subject to the constraints provided by the algorithm. The algorithm demonstrates that there exist fifteen distinct metrics that could potentially possess Killing vector fields. Upon solving the Killing equations for all fifteen metrics, it is observed that seven out of the fifteen metrics exclusively exhibit the minimum number of Killing vector fields. The remaining eight metrics admit a varying number of Killing vector fields, specifically 6, 7, or 10. The Kretschmann scalar has been computed for each of the obtained metrics, revealing that all of them possess a finite Kretschmann scalar and thus exhibit regular behavior.

Anisotropy Bianchi Type-III Cosmological Model in Brans-Dicke Theory of Gravitation

Objectives: To derive the multi-fluid anisotropic Bianchi type-III cosmological model filled with radiation and matter in the presence of Brans-Dicke scalar-tensor theory. Method: In this paper, we have calculated Brans-Dicke field equations in anisotropic Bianchi type -III space times in the presence of matter and radiation which are minimally interacting fields. To obtain the determinate solution of the model, we considered i) the state of the equation , ii) the shear scalar is directly proportional to the expansion scalar i.e., . Also, consider the deceleration parameter, , where with which yields models with constant deceleration parameter. Findings: This solution shows an anisotropic radiation model in Brans-Dicke's theory. Also, it shows accelerated expansion of the universe and transition of the universe from the deceleration phase to the accelerated phase. Novelty: The derived model's many parameters support recent cosmological findings, indicating the model's good discovery. Thus, within the framework of our established model, we are able to comprehend the cosmic development. Keywords: Bianchi type-III, Brans-Dicke theory, Multifluid, Deceleration parameter, Λ CDM

Perfect fluid locally rotationally symmetric Bianchi Type-I spacetimes admitting concircular vector fields in f(T) gravity

We obtained the solutions of Einstein’s Field Equations (EFEs) for locally rotationally symmetric (LRS) Bianchi type-I perfect fluid spacetimes through the concircular vector fields (CCVFs) in [Formula: see text] gravity. It is shown that such metrics admit CCVFs of 4, 5, 6, 7, 8 and 15 dimensions. We also calculated the energy density, fluid pressure, torsion scalar [Formula: see text] and the form of the function [Formula: see text]. We did not specify the form of [Formula: see text] for the solution of EFEs but found a particular form of [Formula: see text] during the process of finding the CCVFs. It is observed that energy density and fluid pressure of some solutions are related as [Formula: see text], which means that the universe represented by these spacetime metrics behaves like dark energy models. For other solutions, it is observed that the fluid pressure and energy density can remain positive for particular choices of the constants involved. Thus, in these cases the rate of expansion can slow down due to positive attractive effect. We also calculated the Hubble’s parameter ([Formula: see text]), scalar expansion ([Formula: see text]), shear scalar ([Formula: see text]), anisotropy parameter ([Formula: see text]) and the deceleration parameter ([Formula: see text]) associated with each of the obtained exact LRS Bianchi type-I solutions. It is observed that the physical behavior of the spacetime changes with the number of admitting CCVFs. A constant anisotropic behavior for 15-dimensional CCVFs is observed to change to isotropic nature for seven-dimensional CCVFs.

Creation Field Cosmological Model with Variable Cosmological Term (Λ) in Bianchi Type III Space-Time

The paper is devoted to the study of cosmological models with time-varying cosmological term (Λ) in the presence of creation field in the framework of Bianchi type III space-time. To obtain deterministic model of the universe, we have assumed Λ∝1/R3, where R is the scale factor, for steady state cosmology and creation field, and shear (σ) is proportion to expansion (θ) which leads to B=Cn, where B and C are the metric potentials to explain small anisotropic behaviour of the universe and its isotropy. To obtain the results in terms of cosmic time t, we have assumed n=2. The model satisfies conservation equations, and creation field increases with time. The present model is free from singularity, has particle horizon, and provides a natural explanation for inflationary scenario and isotropization. Creation field and Einstein field equations are derived using principle of least action and Lagrangian formulation of variable cosmological term. For illustrative purposes, evolutionary behaviour of some cosmological parameters are shown graphically. The other physical aspects like accelerating behaviour of the model are also discussed. Thus, the model represents not only expanding universe but also accelerating which matches with the results of present-day observations.

Anisotropic Bianchi Type-1 Cosmological Model Containing Dark Energy

Considering the LRS Bianchi type I metric here we studied the spatial homogeneous and anisotropic dark energy cosmological models in the frame work of B-D scalar tensor theory of gravity along with variable equation of parameter and deceleration parameter. Exact solutions of field equations are obtained with certain physical assumptions in different cases. The physical behavior of the model is also discussed in details.

F(R) gravity in an ellipsoidal universe

We propose a new model of cosmology based on an anisotropic background and a specific f(R) theory of gravity. It is shown that field equations of f(R) gravity in a Bianchi type I background give rise to a modified Friedmann equation. This model contains two important parameters: γ and δ. We, thus, simply call our model γδCDM. It is distinguished in two important aspects from the ΛCDM model: firstly, the contribution of different energy densities to the Hubble parameter are weighted with different weights, and then, dependence of energy densities to redshift is modified as well. This unorthodox relation of energy content to Hubble parameter brings forth a new way of interpreting the cosmological history. This solution does not allow the existence of a cosmological constant component, however, a dark energy contribution with dependence on redshift is possible. We tested observational relevance of the new solution by best fitting to different data sets. We found that our model could accommodate the idea of cosmological coupling of black holes.

Anisotropic f(Q) gravity model with bulk viscosity

This study investigates the dynamics of a spatially homogeneous and anisotropic LRS Bianchi type-I Universe with viscous fluid in the framework of [Formula: see text] symmetric teleparallel gravity. We assume a linear form for [Formula: see text] and introduce hypotheses regarding the relationship between the expansion and shear scalars, as well as the Hubble parameter and bulk viscous coefficient. The model is constrained using three observational datasets: the Hubble dataset (31 data points), the Pantheon SN dataset (1048 data points), and the BAO dataset (6 data points). The calculated cosmological parameters indicate expected behavior for matter-energy density and bulk viscous pressure, supporting the universe’s accelerating expansion. Diagnostic tests suggest that the model aligns with a [Formula: see text]CDM model in the far future and resides in the quintessence region. These findings are consistent with recent observational data and contribute to our understanding of cosmic evolution within the context of modified gravity and bulk viscosity.

An anisotropic cosmological model with Bianchi type III universe in f(G) gravity

The paper is devoted to exploring the exact solution of the modified Einstein's field in the setting of spatially homogeneous and anisotropic Bianchi type III spacetime in modified f(G) gravity, where G is Gauss-Bonnet invariant. Here, by employing the hyperbolic hybrid scale factor a = emt (sinh(t))n in which m,n are positive constants, with the power-law f (G)=βGm+1 model where β,m are arbitrary constants, we computed the physical and geometrical properties of the cosmological parameters of the model. The results of the model parameters are well satisfied with recent cosmological observational data. To get the exact solution of the field equation of the Bianchi type III model in the presence of an anisotropic dark fluid, we consider the relation in which the shear scalar (σ) is proportional to the expansion scalar (θ), resulting in C = An. Furthermore, the energy conditions for the power-law f(G) model are graphically examined, and it turns out that the null energy condition (NEC), weak energy condition (WEC), and dominant energy condition (DEC) are well satisfied except for the strong energy condition (SEC). The violation of the strong energy conditions (SEC) indicates the f(G) model supports the universe's current expansion with negative pressure, having a quintessence model in the present and Λ cold dark matter (CDM) model in the future.

Perfect Fluid with Heat Flow in f(T) Theory of Gravity

Bianchi Type-I cosmological models have been a subject of extensive research in cosmology due to their simplicity and relevance in understanding the dynamics of the early Universe. In this study, we investigate the dynamics of such models within the framework of f(T) gravity, an alternative theory of gravity that extends teleparallel gravity by introducing a general function of the torsion scalar, T. We focus on the presence of a perfect fluid with heat flow in the cosmic medium. By solving the field equations of f(T) gravity, we obtain exact solutions for the Bianchi Type-I cosmological models. These solutions provide valuable insights into the evolution of the Universe and how it is influenced by the modified gravity theory. Furthermore, we derive cosmological parameters in terms of redshift, offering a convenient way to interpret observational data and connect theoretical predictions to empirical measurements. Our findings not only contribute to a deeper understanding of the dynamics of Bianchi Type-I cosmological models but also provide a foundation for comparing f(T) gravity with standard general relativity in the context of observational cosmology. This research paves the way for further exploration of alternative gravity theories and their implications for the early Universe’s evolution and structure.

Observation constraints on scalar field cosmological model in anisotropic universe

In this study, we have explored a scalar field cosmological model in the axially symmetric Bianchi type-I universe. In this study, our aim is to constrain the scalar field dark energy model in an anisotropic background. For this purpose, the explicit solution of the developed field equations for the model is determined and analyzed. Constraints on the cosmological model parameters are established utilizing Markov Chain Monte Carlo (MCMC) analysis and using the latest observational datasets of OHD, BAO, and Pantheon. For the combined dataset (OHD, BAO, and Pantheon), the best-fit values of Hubble and density parameters are estimated as [Formula: see text], [Formula: see text] [Formula: see text] and [Formula: see text]. The model shows a flipping nature and redshift transition occurs at [Formula: see text], and the present value of decelerated parameter is computed to be [Formula: see text] for the combined dataset. We have explored characteristics like the universe’s age, particle horizon, deceleration parameter, and jerk parameter. The dynamical properties, such as energy density [Formula: see text], scalar field pressure [Formula: see text], and equation of state parameter [Formula: see text], are analyzed and presented. We have also described the behavior of the scalar potential [Formula: see text] and scalar field. Furthermore, the authors also described the behavior of energy conditions in scalar-tensor cosmology. The scenario of the present accelerated expansion of the universe is described by the contribution of the scalar field.

Cold dark matter and holographic dark energy in f(R,T) theory of gravity

In this study, we have examined the cosmological model of the locally rotationally symmetric (LRS) Bianchi Type-I universe within the framework of the [Formula: see text] theory of gravity. The [Formula: see text] theory incorporates the Ricci scalar (R) and the trace of the energy–momentum tensor (T) in its formulation. Our investigation focuses on the cold dark matter (CDM) and holographic dark energy (DE) cosmological models, particularly in relation to the occurrence of a big rip singularity. To solve the field equation, we have assumed a specific relationship between the parameters, [Formula: see text] and [Formula: see text], where [Formula: see text] is proportional to [Formula: see text] and m is held constant. We have examined the existence of both the Big Bang and Big Rip singularities within this cosmological model. Additionally, we have analysed the state-finder parameter, which provides insights into the dynamics and evolution of the universe. Furthermore, we have discussed the physical and geometrical parameters of the universe in this context. These parameters help characterize and describe the behavior of the universe, shedding light on its underlying properties and dynamics. Through our investigation, we aim to deepen our understanding of the LRS Bianchi Type-I cosmological model within the [Formula: see text] theory of gravity, exploring the interplay between CDM, holographic DE, singularities, and the various parameters that contribute to the understanding of the universe.

Bianchi type $${VI}_{0}$$ cosmological model for expanding universe with flat potential in general relativity

Bianchi type $${VI}_{0}$$ cosmological model for expanding universe with flat potential in general relativity

A study of Bianchi type I spacetime according to their Ricci collineations

Rici collineations (RCs) have been used in this research to study the locally rotationally symmetric (LRS) Bianchi type I spacetimes. To accomplish our objectives, the RC equations are typically integrated for both situations of the Ricci tensor, degenerate and non-degenerate. Throughout this work, a number of situations occur that provide various finite and infinite dimensional Lie algebras of RCs.

Testing the effect of anisotropy on the parametrization of deceleration parameter from recent observational data

In this work, we investigate Bianchi type I universe in the presence of dark energy and dark matter by three parameterizations of deceleration parameter models, which are considered to find solutions of the models. In the framework of an anisotropic cosmology, we constrain the parameters of these models and compared the results with the [Formula: see text]CDM model, by using the datasets from different observational, namely, the Hubble data and type Ia Supernovae Pantheon data. Additionally, the evolution of kinematic cosmographic parameters is investigated. In particular, we analyze the effects of anisotropy on the physical behavior of our mentioned models and compare them with standard [Formula: see text]CDM model.

Stability aspects of an LRS Bianchi type-I cosmological model in f(Q) gravity

Stability aspects of an LRS Bianchi type-I cosmological model in f(Q) gravity

Stability analysis of anisotropic Bianchi type I cosmological model

Stability analysis of anisotropic Bianchi type I cosmological model