Anisotropic Spacetime Research Articles

Constraints on anisotropic properties of the universe in f(Q,T) gravity theory

Motivated by anomalies in cosmic microwave background observations, we investigate the implications of f(Q,T) gravity in Bianchi type-I spacetime, aiming to characterize the universe's spatially homogeneous and anisotropic properties. By using a linear combination of non-metricity Q and the energy-momentum tensor trace T, we parametrize the deceleration parameter and derive the Hubble solution, which we then impose in the Friedmann equations of f(Q,T) gravity. Bayesian analysis is employed to find the best-fit values of model parameters, with 1−σ and 2−σ contour plots illustrating the constraints from observational data, including H(z) data and the Pantheon+ sample. Our analysis reveals a transition from a decelerated to an accelerated expansion phase, with the present deceleration parameter indicating an accelerating universe. The energy density gradually decreases over time, approaching zero for the present and future, indicating continuous expansion. The anisotropic pressure, initially notably negative, transitions to slightly negative values, suggesting the presence of dark energy. The evolving equation of state parameter ω exhibits behavior akin to phantom energy, influenced by spacetime anisotropy. Violations of the null energy condition and the strong energy condition imply phantom-like behavior and accelerated expansion.

Isotropization of the magnetic universe in Horndeski theory with G 3(X,ϕ) and G 5(X)

We study the isotropization process of Bianchi-I space-times in Horndeski theory with and . A global unidirectional electromagnetic field interacts with a scalar field according to the law . In Horndeski theory, the anisotropy can develop in different ways. The proposed reconstruction method allows us to build models with acceptable anisotropy behavior. To analyze space-time anisotropy, we use the relations ( ), where are metric functions, and .

Barrow’s holographic dark energy model in axially symmetric spacetime

The Barrow’s Holographic Dark Energy (BHDE) Model is proposed in an axially symmetric anisotropic spacetime which is employing Hubble horizon as an infrared cutoff (IR cutoff). The transition of the universe from a matter dominated era to a dark energy dominated era is investigated in this model. Furthermore, the Equation of State (EoS) parameter explains how the universe evolves with non-extensive term or Barrow parameter [Formula: see text] for both phase (i) phantom era ([Formula: see text]) and (ii) quintessence era ([Formula: see text]). In order to reconcile the dark energy, the reconstruction of scalar field potential is considered. Some of the physical properties of the model are also described.

Nonneutral Weibel model plasma in the non-minimal CPT-odd coupling

Inspired by the extension of the Standard Model, we investigate the effects of the space-time anisotropy caused by Lorentz symmetry violation (LSV) on a plasma column confinement configuration. The model of Plasma taken into account is the z-pinch model that was in the earliest efforts in fusion power research. This model comprises particles in a nonequilibrium cylindrical distribution, which remains stationary in the absence of collisions. We propose a disturbance in the distribution by a Lorentz violation environment. As proposed by Carroll, Field, and Jackiw, in a scenario of (LSV), a background field vector could couple with the electromagnetic field, modifying the classical behavior of the electromagnetic field. As reported here, considering the presence of a background field vector, the intensities of the fields and particle densities would be disturbed by the influence of the LSV. For different values of the background field vector coupling constant, the contribution of the background vector field could modify the intensity of the electromagnetic fields, and concentrate even more the electrons densities in the edge of the plasma column, evidencing a behavior similar to a skin effect in this plasma column.

Cosmic Aspects of Sharma-Mittal Holographic Dark Energy Model in Brans-Dicke Theory of Gravity

We investigate the cosmological scenario involving spatially homogeneous and anisotropic Bianchi type-V I0 space-time in the context of the Sharma-Mittal holographic dark energy model within the framework of Brans-Dicke’s theory of gravitation. In order to achieve this objective, the Hubble, deceleration, equation-of-state parameters have been discussed. The deceleration parameter (q) is used to measure the pace at which the expansion of the universe is accelerating. The equation-of-state parameter (ωsmhde) characterizes the quintessence and vacuum areas of the universe. All the parameters demonstrate consistent behaviour following the Planck 2018 data. We assess the dynamical stability by defining the squared speed of sound and examining its behaviour. In addition, the energy conditions and the variation of ωsmhde and ω′smhde in the model indicate the present accelerating expansion of the universe.

Inflation Driven by Nonlinear Electrodynamics in Anisotropic Spacetime

The well-known Big Bang theory has explained how the universe came into being. This extraordinary event caused the later universe to be accelerated by a scale factor a(t). However, standard Big Bang theory has had some problems that can’t be explained, such as monopoles, horizons, and flatness. To solve this problem, a model of inflation in the early universe is required. Recent studies show that nonlinear electrodynamics coupled with general relativity can describe the inflation of the universe. In this work, we consider a model of nonlinear electrodynamics in anisotropic spacetime. We derive the dynamical equation from Einstein’s field equation and the law of conservation of energy-momentum tensor. Then, we use the perturbation method to solve the dynamical equation of the universe and obtain the evolution of the non-singular scale factor with anisotropy parameter ϵ. Using a phase-space analysis of the inflationary model, we obtain a phase portrait in the presence of fixed points. Our result shows that in the model of nonlinear electrodynamics coupled to gravity in anisotropic spacetime, the universe can undergo an inflationary mechanism if ϵ < 1. We also show the absence of singularity in density and pressure using this model.

On the consequences of Raychaudhuri equation in Kantowski-Sachs space-time

The paper aims to study the geometry and physics of the Raychaudhuri equation (RE) in the background of a homogeneous and anisotropic space–time described by Kantowski–Sachs (KS) metric. Role of anisotropy/shear in the context of convergence and possible avoidance of singularity has been analyzed subject to a physically motivated constraint. Moreover, using a suitable transformation the first order RE has been converted to a second order differential equation analogous to a Harmonic Oscillator and criterion for convergence has been shown to be associated with the time varying frequency of the Oscillator. Finally, the paper points out a geometric and physical notion of anisotropy along with their corresponding behavior towards convergence.

Cosmological model in f(R, T) theory with time-varying FLVDP

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 , 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.

Ricci solitons on anisotropic fluid spacetime in f(R, T)-gravity

In this paper we study the behaviour of anisotropic fluid spacetimes in f(R, T)-gravity for admitting Ricci Soliton. We obtain the form of tangential pressure of the fluid for steady, shrinking and expanding Ricci soliton when Ricci soliton vector field becomes a Killing vector field. Modified Poisson and Liouville equations are derived from the Ricci soliton equation in f(R, T)-gravity having anisotropic fluid. Also harmonic significance of Ricci soliton on anisotropic fluid spacetime in f(R, T)-gravity with a harmonic potential function is derived. We derive field equations for perfect fluid plane symmetric static spacetime and obtain their solutions. For each solution we then obtain Ricci soliton vector fields. We observe that such spacetimes admit expanding, shrinking or steady Ricci solitons. All the obtained solitons are trivial in nature. When these Ricci soliton vector fields become Killing vector fields then our results are in full agreement with the theorems deduced from our study.

Anisotropic inflation in dipolar Bose–Einstein condensates

Early during the era of cosmic inflation, rotational invariance may have been broken, only later emerging as a feature of low-energy physics. This motivates ongoing searches for residual signatures of anisotropic space-time, for example in the power spectrum of the cosmic microwave background. We propose that dipolar Bose–Einstein condensates (BECs) furnish a laboratory quantum simulation platform for the anisotropy evolution of fluctuation spectra during inflation, exploiting the fact that the speed of dipolar condensate sound waves depends on direction. We construct the anisotropic analogue space-time metric governing sound, by linking the time-varying strength of dipolar and contact interactions in the BEC to the scale factors in different coordinate directions. Based on these, we calculate the dynamics of phonon power spectra during an inflation that renders the initially anisotropic Universe isotropic. We find that the expansion speed provides an experimental handle to control and study the degree of final residual anisotropy. Gravity analogues using dipolar condensates can thus provide tuneable experiments for a field of cosmology that was until now confined to a single experiment, our Universe.

Anisotropic solutions in symmetric teleparallel fleft( Qright) -theory: Kantowski–Sachs and Bianchi III LRS cosmologies

We investigate the existence of anisotropic self-similar exact solutions in symmetric teleparallel fleft( Qright) -theory. For the background geometry we consider the Kantowski–Sachs and the Locally Rotationally Symmetric Bianchi type III geometries. These two anisotropic spacetimes are of special interest because in the limit of isotropy they are related to the closed and open Friedmann–Lemaître–Robertson–Walker cosmologies respectively. For each spacetime there exist two distinct families of flat, symmetric connections, which share the symmetries of the spacetime. We present the field equations, and from them, we determine the functional form of the fleft( Qright) Lagrangian which yields self-similar solutions. We initially consider the vacuum case and subsequently we introduce a matter source in terms of a perfect fluid. Last but not least, we report some self-similar solutions corresponding to static spherically symmetric spacetimes.

Is the Universe Anisotropic Right Now? Comparing the Real Universe with the Kasner’s Space-Time

We investigate possible astronomical manifestations of space-time anisotropy. The homogeneous vacuum Kasner solution was chosen as a reference anisotropic cosmological model because there are no effects caused by inhomogeneity in this simple model with a constant degree of anisotropy. This anisotropy cannot become weak. The study of its geodesic structure made it possible to clarify the properties of this space-time. It showed that the degree of manifestation of anisotropy varies significantly depending on the travel time of the light from the observed object. For nearby objects, for which it does not exceed half the age of the universe, the manifestations of anisotropy are very small. Distant objects show more pronounced manifestations; for example, in the distribution of objects over the sky and over photometric distances. These effects for each of the individual objects decrease with time but, in general, the manifestations of anisotropy in the Kasner space-time remain constant due to the fact that new sources come from beyond the cosmological horizon. We analyze observable signatures of the Kasner-type anisotropy and compare it to observations. These effects were not found in astronomical observations, including the study of the CMB. We can assume that the Universe has always been isotropic or almost isotropic since the recombination era. This does not exclude the possibility of its significant anisotropy at the moment of the Big Bang followed by rapid isotropization during the inflationary epoch.

Anisotropic Cosmological Model in f (R,T) Theory of Gravity with a Quadratic Function of T

In this paper, we study spatially homogeneous and anisotropic Bianchi type-I space-time filled with perfect fluid within the framework of f(R,T) theory of gravity for the functional form f(R,T)=R+2f(T) with f(T)=αT+βT2, where α and β are constants. Exact solutions of the gravitational field equations are obtained by assuming the average scale factor to obey a hybrid expansion law and some cosmological parameters of the model are derived. Two special cases, leading to the power-law expansion and the exponential expansion, are also considered. We investigate the physical and geometrical properties of the models by studying the evolution graphs of some relevant cosmological parameters such as the Hubble parameter (H), the deceleration parameter ( q) etc.

Rip behaviour in Brans–Dicke theory

In this work, we present little rip and pseudo rip scenarios in the framework of the generalised Brans–Dicke (GBD) theory where an evolving BD parameter along with a self-interacting potential is considered. The GBD field equations are derived for an anisotropic space time to provide a more general approach to the cosmic expansion. The evolutionary behaviour of the Brans–Dicke (BD) scalar field, dynamical Brans–Dicke parameter and the self interacting potential are studied. It is not possible to separate out the dynamical Brans–Dicke parameter into distinct evolving and non-evolving part for the rip scenarios as is obtained for constant deceleration parameter. While the little rip behaviour requires a positive value for the GBD parameter, a small negative value around −1.33 favours a pseudo rip behaviour.

On the anisotropic bouncing universe with viscosity

We investigate the role of bulk and shear viscosity in the spatially homogeneous anisotropic spacetime, in particular, the Kantowski–Sachs (KS) spacetime. General conditions for the bouncing evolution of universe in anisotropic background have been obtained by using the derived propagation equations of expansion scalar, shear scalar and spatial 3-curvature. We show that the presence of shear viscosity in the model prohibits the energy density to attain its extremum in the bouncing model. We explore the qualitative behavior of KS cosmologies by formulating the Einstein’s field equations into a plane-autonomous system of equations by taking dimensionless equation of state. The stability of the system has been investigated by evaluating and analyzing the eigenvalues at the critical points. The stable solutions exist for the system composed of bulk and shear viscosity. The present analysis through dynamical system method illustrates that the universe does not exhibit synchronous bounce with perfect fluid and/or viscous fluids in the KS spacetime.

Exact Bianchi type-I inflationary model with non-minimally coupled scalar field

In the present work, we try to build up an inflationary model within the framework of Bianchi type-I spacetime using a non-minimally coupled, homogeneous, self-interacting canonical scalar field. Specifically, using the Lie symmetry method, we are able to find some novel exact solutions to the Einstein field equations by assuming a power-law relationship between the scalar field and average scale factor. These symmetry-based solutions have been used to derive the values of some important parameters of the anisotropic universe. In this anisotropic model, we find that the volume of space expands with time in an inflationary scenario, depicting the Universe’s accelerating phases. An important characteristic of this model is that it initially represents anisotropic spacetime and then isotropizes the spacetime as time goes on, which favors recent cosmological observations.

Noether Symmetries and Some Exact Solutions in f(R, T 2) Theory

The main objective of this article is to examine some physically viable solutions through the Noether symmetry technique in $f(R, T^{2})$ theory. For this purpose, we assume a generalized anisotropic and homogenous spacetime that yields distinct cosmic models. In order to investigate Noether equations, symmetry generators and conserved quantities, we use a specific model of this modified theory. We find exact solutions and examine the behavior of various cosmological quantities. It is found the behavior these quantities is consistent with current observations indicating that this theory describes the cosmic accelerated expansion. We conclude that generators of Noether symmetry and conserved quantities exist in this theory.

Flows into de Sitter space from anisotropic initial conditions: An effective field theory approach

For decades, physicists have analyzed various versions of a ``cosmic no-hair'' conjecture, to understand under what conditions a spacetime that is initially spatially anisotropic and/or inhomogeneous will flow into an isotropic and homogeneous state. Wald's theorem, in particular, established that homogeneous but anisotropic spacetimes, if filled with a positive cosmological constant plus additional matter sources that satisfy specific energy conditions, will necessarily flow toward an (isotropic) de Sitter state at late times. In this paper we study the flow of homogeneous but anisotropic spacetimes toward isotropic states under conditions more general than those to which Wald's theorem applies. We construct an effective field theory (EFT) treatment for generic ``single-clock'' systems in anisotropic spacetimes---which are not limited to realizations compatible with scalar-field constructions---and identify fixed points in the resulting phase space. We identify regions of this phase space that flow to isotropic fixed points---including a de Sitter fixed point---even in the absence of a bare cosmological constant, and for matter sources that do not obey the energy conditions required for Wald's theorem. Such flows into de Sitter reveal the emergence of an effective cosmological constant.

Anisotropic background for two fluids: Matter and holographic dark energy

We discuss a spatially homogeneous and anisotropic Bianchi type-I space-time with two fluids as the content of the Universe: Matter and holographic dark energy in the framework of general relativity. To get the exact solutions of Einstein’s field equations, we choose the scale factor as a hyperbolic function, specifically, \(a( t) =\sinh ^{{1}/{n}}(\gamma t) \), where \(\gamma \) and \(n>0\) are arbitrary constants, which gives us a time-dependent deceleration parameter. Then, we study our cosmological model under the conditions of parameters as: \(\gamma \) fixed and \(n>1\). Our cosmological solutions led to an early deceleration phase followed by the current observed acceleration phase. Further, the anisotropic parameter and some other physical parameters are discussed. We conclude that our cosmological model is consistent with the results of recent astronomical observations.

Classification of the Lie and Noether Symmetries for the Klein–Gordon Equation in Anisotropic Cosmology

We carried out a detailed group classification of the potential in Klein–Gordon equation in anisotropic Riemannian manifolds. Specifically, we consider the Klein–Gordon equations for the four-dimensional anisotropic and homogeneous spacetimes of Bianchi I, Bianchi III and Bianchi V. We derive all the closed-form expressions for the potential function where the equation admits Lie and Noether symmetries. We apply previous results which connect the Lie symmetries of the differential equation with the collineations of the Riemannian space which defines the Laplace operator, and we solve the classification problem in a systematic way.