Bianchi Type Research Articles

Odd parity gravitational waves in modified Bianchi I cosmology

Abstract In this study, we primarily examine the behavior of axial (odd parity) gravitational waves (GWs) in an initially Bianchi Type-I Universe, with a particular focus on the influence of a scalar field within the framework of f ( R , T ψ ) theory. To this end, we employ the Regge–Wheeler perturbation framework, with a particular emphasis on the axial mode. Using these axial perturbations, we derive the perturbed field equations after formulating the field equations for the unperturbed cosmological model. Our results indicate that the scalar field primarily influences the temporal components of the perturbations, whereas the spatial components exhibit sinusoidal wave-like behavior. These findings provide new insights into the interplay between scalar fields and GWs, with potential implications for understanding the dynamics of the early Universe and testing modified gravity theories.

Even wave fluctuations in extended Bianchi I cosmology

In this study, we delve into the propagation characteristics of the even modes of the primordial gravity waves (GWs) represented by the Regge–Wheeler perturbation scheme within a locally rotationally symmetric Bianchi type-I universe from the perspective of the [Formula: see text] gravity to incorporate the effects of a scalar field. Initially, we consider the cosmological background without wave fluctuations and derive the corresponding field equations. Subsequently, by utilizing the even Regge–Wheeler perturbation scheme, we explore polar wave dynamics by deriving the pertinent field equations. Analytical solutions of the perturbed metric potentials are obtained under certain assumptions and the study observes the impact of the scalar field, examining its effects through the model parameter. The graphical analysis sheds light on the implications of the scalar field on the propagation of the polar modes of GWs. It is concluded that the presence of a scalar field influences the temporal perturbations however, the spatial part remains unaffected and is characterized by a combination of exponential functions.

Islands in Bianchi type I universe

We study the conditions for finding an island in an anisotropic universe—Bianchi type I universe filled with radiation. We verify that the existence of islands does not depend on their shape. We then find that islands may form at certain times, near the turnaround point—where the universe turns from contraction to expansion in one of the directions. This is in line with previous analyses regarding cosmological space-times where islands form if one has two energy scales in the problem, such as the typical temperature of the universe and, on top of that, cosmological constant, curvature, anisotropy, or some other mass scale. Published by the American Physical Society 2025

LRS Bianchi Type-I Cosmological Model in Modified f(R, T) Gravitation Theory filled with Perfect Fluid

This study explores LRS Bianchi Type-I space time filled with a perfect fluid within the framework of f(R,T) gravity, where R represents the Ricci scalar and T denotes the trace of the stress-energy momentum tensor. We analyze the simplest form of cosmic evolution in the context of general non-minimally coupled gravity models. Two specific models of f(R,T) gravity are considered. A time-dependent deceleration parameter is introduced, leading to an accelerated universe with an exact field solution. Additionally, we examine the kinematical and physical properties of the proposed models.

Topological defects in f(T) theory of gravity

Abstract In this paper, we investigate the behaviour of domain walls and one-dimensional cosmic string with locally rotationally symmetric (LRS) Bianchi type-I metric in the context of f(T) gravity. Three different types of deceleration parameter (DP) forms, such as (i) $$q=-kt+l-1$$ q = - k t + l - 1 , (ii) $$q=b(t)$$ q = b ( t ) , and (iii) $$q=-1+\frac{\gamma }{1+a^\gamma }$$ q = - 1 + γ 1 + a γ , are used to determine the exact solution of the field equation. We observe the profound effect of the torsion scalar T on physical parameters. Also, the universe was dominated by string at an early stage of evaluation.

Tsallis holographic dark energy model in an anisotropic universe with linearly varying deceleration parameter and its correspondence with phantom

Tsallis holographic dark energy model in an anisotropic universe with linearly varying deceleration parameter and its correspondence with phantom

Spatially homogeneous solutions of vacuum Einstein equations in general dimensions

We study time-dependent compactification of extra dimensions. We assume that the spacetime is spatially homogeneous, and solve the vacuum Einstein equations without cosmological constant in more than three dimensions. We consider globally hyperbolic spacetimes in which almost Abelian Lie groups act on the spaces isometrically and simply transitively. We give left-invariant metrics on the spaces and solve Ricci-flat conditions of the spacetimes. In the four-dimensional case, our solutions correspond to the Bianchi type II solution. By our results and previous studies, all spatially homogeneous solutions whose spaces have zero-dimensional moduli spaces of left-invariant metrics are found. For the simplest solution, we show that each of the spatial dimensions cannot expand or contract simultaneously in the late-time limit.

Classification of Bianchi type I spacetime via its self-similar vector fields

The focus of this paper is the examination of self-similar vector fields (SSVFs) within Bianchi type I spacetime utilizing the Rif tree approach. The paper employs a computer algorithm to convert the equations into a reduced involutive form, dividing the integration problem into multiple cases represented in a tree structure. These cases are subject to specific constraints on the metric functions. By employing these constraints, the set of equations governing self-similar symmetries is solved, yielding explicit expressions for the metrics and their associated self-similar vector fields.

Noether symmetries of Bianchi type II universe in modified teleparallel f(T) gravity

The aim of this paper is to explore Noether symmetries of Bianchi type II universe in the modified teleparallel [Formula: see text] gravity, where [Formula: see text] is a function of the torsion scalar [Formula: see text]. In a physical context, the selection of Noether symmetries provides constraints that are helpful in building conservation laws. Some of the well-known examples of such laws are the conservation of energy and momentum. In this study, initially, we explore certain classes of Bianchi type II universe considering linear as well as nonlinear [Formula: see text] gravity models. In view of such models, equations of motion of the [Formula: see text] gravity have been solved in twelve cases. In each of the cases, we apply the definition of Noether symmetry which tends to a set of nineteen equations. Upon solving these equations, we reach the fact that the Bianchi type II universe in the background of [Formula: see text] gravity admits only four Noether vector fields (NVFs). As a result, the physical entities which we observe are the conservation of linear and generalized momentum.

Non-null homogeneous Petrov type VIII space-time by Bianchi classification

Non-null homogeneous Petrov type VIII space-time by Bianchi classification

Non-commutative classical and quantum fractionary cosmology: anisotropic Bianchi type I case

Non-commutative classical and quantum fractionary cosmology: anisotropic Bianchi type I case

Bianchi type- V Cosmological modelsin the presence of a bulk viscous fluid based on Lyra geometry in F(R, T) theory of gravity

In this paper an attempt is made to investigate the exact solution of Bianchi type- V Cosmological models in the framework of f(R,T) specifically considering the form F(R,T)=R+2f(T) and f(T) = ???? T where ???? is a constant . This modified theory of gravity introduces a coupling between the Ricci scalar R and the trace of the energy-momentum tensor T, potentially offering new insights into the dynamics of the early universe. We derive the field equations for the Bianchi Type V metric and explore exact solutions under specific assumptions. The physical and geometrical properties of the models, including the behavior of the scale factors, Hubble parameter, deceleration parameter, and energy conditions, are analyzed. We find that the models exhibit a variety of cosmological behaviors, including inflationary and decelerating phases, depending on the choice of initial conditions and model parameters. Our results demonstrate the potential of F(R,T) gravity to provide alternative explanations for the observed accelerated expansion of the universe. The physical and geometrical behaviors of such models have been discussed

Anisotropic Cosmic Expansion Inspired by Some Novel Holographic Dark Energy Models in f(Q)$f(Q)$ Theory

AbstractThe present work discusses the topic of cosmic evolution in an intriguing framework of theory of gravity (with as a non‐metricity (NM) scalar which controls the gravitational interaction) by using some recently proposed holographic dark energy (HDE) models. To achieve this goal, the dynamical equations for locally rotationally symmetric (LRS) Bianchi type‐I (BI) geometry are formulated with matter contents as a mixture of dust and anisotropic fluids. By assuming that the time‐redshift relation follows a Lambert function, the cosmological model is constructed by using Rényi HDE (RHDE), Sharma–Mittal HDE (SMHDE) and Generalized HDE (GHDE) as separate cases where Hubble horizon is taken as an infrared (IR) cutoff. Cosmological characteristics of these models are then examined through graphs of energy densities, skewness parameter , deceleration, and EoS parameters. The evolution of the EoS parameter is also studied, i.e., to discuss the dynamical characteristics of constructed DE models and assess the stability of models via the squared speed of sound parameter. It is found that the plane shows the freezing region for RHDE and GHDE models while the thawing region for the SMHDE case. Also, it is concluded that all constructed models exhibit cosmologically viable and stable behavior.

A Note on Lie Algebra of Killing Vector Fields of Locally Rotationally Symmetric Bianchi Type-I Spacetime in f(Q)-Gravity

A Note on Lie Algebra of Killing Vector Fields of Locally Rotationally Symmetric Bianchi Type-I Spacetime in f(Q)-Gravity

First Eigenvalues of Some Operators Under the Backward Ricci Flow on Bianchi Classes

Let λ(t) be the first eigenvalue of the operator −∆+aRb on locally three-dimensional homogeneous manifolds along the backward Ricci flow, where a,b are real constants and R is the scalar curvature. In this paper, we study the properties of λ(t) on Bianchi classes. We begin by deriving an evolution equation for the quantity λ(t) on three-dimensional homogeneous manifolds in the context of the backward Ricci flow. Utilizing this equation, we subsequently establish a monotonic quantity that is contingent upon λ(t). Additionally, we present both upper and lower bounds for λ(t) within the framework of Bianchi classes.

A study of self-similar vector fields in bianchi type III spacetime via Rif tree approach

Abstract In this study, we use the Rif tree approach to explore self-similar vector fields in Bianchi type III spacetime. This work adopt a computer-based method to transform symmetry equations into an involutive form that is simplified and divides the integration problem into multiple cases, each represented as a tree structure. In some cases, the metric functions are subject to particular constraints. These conditions allow one to solve the system of equations governing self-similar symmetries and provide explicit formulations for the metrics and their corresponding self-similar vector fields. This approach is novel in that it covers not only the analysis of the direct integration strategy but also some metrics that are practically relevant. For a detailed investigation of the created models, stability and physical importance are also considered.

Exact Model of Gravitational Waves and Pure Radiation

An exact non-perturbative model of a gravitational wave with pure radiation is constructed. It is shown that the presence of dust matter in this model contradicts Einstein’s field equations. The exact solution to Einstein’s equations for gravitational wave and pure radiation is obtained. The trajectories of propagation and the characteristics of radiation are found. For the considered exact model of a gravitational wave, a retarded time equation for radiation is obtained. The obtained results are used to construct an exact model of gravitational wave and pure radiation for the Bianchi type IV universe.

Quantum Cosmology in Bianchi-I model: A study of symmetry analysis

Quantum Cosmology in Bianchi-I model: A study of symmetry analysis

Maxwell–Dirac system in cosmology

Within the scope of a Bianchi type-I (BI) cosmological model, we study the interacting system of spinor and electromagnetic fields and its role in the evolution of the Universe. In some earlier studies, it was found that in the case of a pure spinor field, the presence of nontrivial nondiagonal components of energy–momentum tensor (EMT) leads to some severe restrictions both on the space–time geometry and/or spinor field itself, whereas in the case of electromagnetic field with induced nonlinearity, such components impose severe restrictions on metric functions and the components of the vector potential. It is shown that in the case of interacting spinor and electromagnetic fields, the restrictions are not as severe as in the other cases and in this case, a nonlinear and massive spinor field with different components of vector potential can survive in a general Bianchi type-I space–time.

The deceleration parameter in perturbed Bianchi universes with a peculiar-velocity “tilt”

Bianchi cosmologies are “natural” anisotropic extensions of the Friedmann universes and they have long been used to investigate the cosmological implications of anisotropy. The latter introduces new ingredients to the standard scenarios, although there are physical processes and effects that maintain their basic Friedmann features when extended to Bianchi universes. Here, we assume a perturbed Bianchi model and look into the implications of the observers’ peculiar flow for their measurement and their interpretation of the deceleration parameter. Our motivation is twofold. To begin with, relative motions have long been known to deceive the observers by “contaminating” the observations, which also still suffer from sample limitations that cloud the statistical significance of the findings. Further motivation comes from claims that observers in bulk flows that expand slightly slower than their surroundings can have the illusion of cosmic acceleration in a universe that is actually decelerating. The claim was originally based on studies of a perturbed tilted Einstein–de Sitter model, but persisted when the background cosmology was replaced by any of the three Friedmann universes. This raised the possibility that the peculiar-motion effect on the deceleration parameter may be generic and largely independent of the host spacetime. Here, we investigate this possibility by extending the earlier studies to perturbed Bianchi models. We find that the Friedmann picture remains unchanged, unless the Bianchi background has unrealistically high anisotropy. The bulk-flow observers can still be misled to the illusion of accelerated expansion by their own peculiar motion.