Anisotropic Spacetime Research Articles

Cosmic evolution in the anisotropic space–time from modified f(R, T) gravity

Cosmic evolution in the anisotropic space–time from modified f(R, T) gravity

ACCELERATING COSMOLOGICAL MODELS WITH VARIABLE G AND Λ-TERM IN GENERAL RELATIVITY

In this paper, we have presented a new class of accelerating universe models with variable cosmological term Λ(t) and gravitational constant G(t) in the framework of general relativity. To get exact solution of Einstein’s field equations for homogeneous and anisotropic Bianchi type-V space-time, a time varying de- celeration parameters is considered as q = 1 + nα , where n, α are constants. The present model shows a point type singularity at origin. The results establish the quintessence like behavior of model initially, and approaches to ΛCDM model ultimately. Some geometrical and physical properties of the models have been evidenced, and conferred to derive the validity of models with respect to recent astrophysical observations. Stability of the model has been discussed through the means of Om(z) diagnostic and state-finder analysis.

Statefinder diagnosis of Tsallis holographic dark energy model in f(R, T) Theory

In this study, Tsallis Holographic Dark Energy (THDE) was studied in the framework of f(R, T) gravitational theory by taking into consideration the homogeneous and anisotropic Bianchi-I spacetime. The Hubble horizon was chosen as IR cutoff of the system. To obtain solutions of field equations, THDE density and a form of Hubble parameter were used. Additionally, various physical parameters such as energy of state parameter, deceleration parameter and scale factor have been discussed. The characteristics and parameters of the model have been also examined by plotting their evolution graphics for redshift z. Furthermore, statefinder parameters, which are effective tools for separating dark energy models, have been explored. By the illustration of trajectory in r − s plane, it is found that this model behaves like Chaplygin gas at initial stage, then ranging in quintessence region it finally approaches to Λ Cold Dark Matter. Lastly, from the evolutions of r − q and s − q planes it is seen that the model evolves to the De Sitter expansion point.

Some Bianchi Type Viscous Holographic Dark Energy Cosmological Models in the Brans–Dicke Theory

In this article, we analyze Bianchi type–II, VIII, and IX spatially homogeneous and anisotropic space-times in the background of the Brans–Dicke theory of gravity within the framework of viscous holographic dark energy. To solve the field equations, we have used the relation between the metric potentials as R = S n and the relation between the scalar field ϕ and the scale factor a as ϕ = a m . Also, we have discussed some of the dynamical parameters of the obtained models, such as the deceleration parameter q , the jerk parameter j , the EoS parameter ω v h d e , the density parameter Ω vhde , Om-diagnostic, squared speed of sound v s 2 , EoS plane ω v h d e − ω v h d e ′ , and statefinder plane r − s through graphical representation, which are significant in the discussion of cosmology. Furthermore, all the models obtained and graphically presented shown an expanding and accelerating Universe, which is in better agreement with the latest experimental data. The viscous holographic dark energy models are compatible with explaining the present cosmic accelerated expansion.

Tests of standard cosmology in Hořava gravity, Bayesian evidence for a closed universe, and the Hubble tension

We consider some background tests of standard cosmology in the context of Hořava gravity with different scaling dimensions for space and time, which has been proposed as a renormalizable, higher-derivative, Lorentz-violating quantum gravity model without ghost problems. We obtain the “very strong” and “strong” Bayesian evidences for our two cosmology models A and B, respectively, depending on the choice of parametrization based on Hořava gravity, against the standard, spatially-flat, LCDM cosmology model based on general relativity. An MCMC analysis with the observational data, including BAO, shows (a) preference of a closed universe with the curvature density parameter Omega _k=-0.005pm 0.001, -0.004^{+0.003}_{-0.001}, (b) reduction of the Hubble tension with the Hubble constant H_0=71.4^{+1.2}_{-0.9}, 69.5^{+1.6}_{-0.9}~ mathrm{km}, mathrm{s}^{-1}, mathrm{Mpc}^{-1} for the models A, B, respectively, and also (c) a positive result on the discordance problem. We comment on some possible further improvements for the “cosmic-tension problem” by considering the more complete early-universe physics, based on the Lorentz-violating standard model with anisotropic space-time scaling, consistently with Hořava gravity, as well as the observational data which are properly adopted for the closed universe.

Accelerating Universe scenario in anisotropic f(Q) cosmology

In this paper, we investigate the exact solution of an anisotropic space-time in the context of $f(Q)$ gravity, where $f\left( Q\right) $ is the arbitrary function of the non-metricity scalar $Q$. Here, we consider a specific power-law form as $f\left( Q\right) =\alpha Q^{n+1}+\beta $, where $\alpha $, $\beta $, and $n$ are free model parameters. Using power-law cosmology ($a\left( t\right) \propto t^{m}$), we analyze the physical behavior of cosmological parameters such as the energy density, pressure, EoS parameter, skewness parameter. Further, we validated the model with energy conditions and found that our $f\left( Q\right) $\ cosmological model behaves like the quintessence model in the present and $% \Lambda $CDM in the future.

Numerical study of the use of residual- and non-residual-based stabilized VMS formulations for incompressible power-law fluids

In this study, two stabilized, variational-multiscale-type finite element methods were assessed for the numerical approximation of incompressible fluids using anisotropic space–time discretizations. The first method has a classical residual structure, whereas the second has a non-residual term-by-term structure. In both cases, the computational benefits of using dynamic sub-scales are evaluated. A comparison between the two methods is made concerning (i) a numerical study of the influence of solvers (direct and iterative) in the approximation of power-law fluid flows using anisotropic space–time discretizations, (ii) their ability and performance to approximate dynamic and convective flows, and (iii) a sensitivity analysis of the formulations for the use of Lumped or L2 projections to define the orthogonal structure of the sub-scales. The problem employed to perform the numerical tests is the two-dimensional flow over an unconfined cylinder using Lagrangian P1 and P2 finite elements. The analyzed flows are characterized by Reynolds’ numbers 100 and 1,000 for power-law fluids. In addition, the study is extended to a three-dimensional problem using tetrahedral linear elements.

Anisotropic spacetimes in f(T, B) theory I: Bianchi I universe

That is the first part of a series of studies on analyzing the higher-order teleparallel theory of gravity known as the f(T, B)-theory. This work attempts to understand how the anisotropic spacetimes are involved in the f(T, B)-theory. In this work, we review the previous analysis of f(T, B)-gravity, and we investigate the global dynamics in the case of a locally rotational Bianchi I background geometry. We focus in the case of \(f\left( T,B\right) =T+F\left( B\right) \) theory and we determine the criteria where \(f\left( T,B\right) \)-theory solves the homogeneity problem. Finally, the integrability properties for the field equations are investigated by applying the Painlevé analysis. The analytic solution is expressed by a right Painlevé expansion.

A simple application of quantum metrology to isotropic and anisotropic spacetimes

In this work, we study quantum metrology protocol in the context of relativistic quantum fields in curved spacetimes. In particular, we restrict our attention to the isotropic and anisotropic models. We investigate how the oscillatory anisotropy affects a quantum metrology protocol. Here, the oscillatory anisotropy is incorporated as a small gravitational disturbance. We calculate the Fisher information for both cosmological parameters [Formula: see text] (expansion volume) and [Formula: see text] (expansion rate). We find that, unlike the isotropic case, the Fisher information of both the parameters [Formula: see text] and [Formula: see text] are oscillating functions of the momentum [Formula: see text]. The oscillatory spectra of Fisher information can theoretically be understood as results of the dependence of the Bogoliubov coefficients on the anisotropic oscillations. In principle, this framework can be used to infer about the underlying spacetime structure and examine the effects of the universe scale factor oscillations.

On Finslerian extension of special relativity

In this paper, we demonstrate that Robb-Geroch’s definition of a relativistic interval admits a simple and fairly natural generalization leading to a Finsler extension of special relativity. Another justification for such an extension goes back to the works of Lalan and Alway and, finally, was put on a solid basis and systematically investigated by Bogoslovsky under the name “Special-relativistic theory of locally anisotropic spacetime”. The isometry group of this spacetime, DISIM[Formula: see text], is a deformation of the Cohen and Glashow’s very special relativity symmetry group ISIM(2). Thus, the deformation parameter [Formula: see text] can be regarded as an analog of the cosmological constant characterizing the deformation of the Poincaré group into the de Sitter (anti-de Sitter) group. The simplicity and naturalness of Finslerian extension in the context of this paper adds weight to the argument that the possibility of a nonzero value of [Formula: see text] should be carefully considered.

Study of axially symmetric viscous Ricci dark energy model in Brans–Dicke theory

In this paper, we have investigated axially symmetric and anisotropic space–time filled with viscous Ricci dark energy and pressure-less dark matter in the frame-work of Brans–Dicke(BD) theory of gravitation. To solve the field equations, we use the following conditions: (i) the relationship between metric potentials which is obtained from the condition that shear scalar of the model is directly proportional to the expansion scalar, (ii) the average scale factor varies with time as a(t)=[sinh(αt)]1k, and (iii) the bulk viscous coefficient (ξ) as ξ=ξ0+ξ1h+ξ2h′′, where ξ0, ξ1 and ξ2 are constants and h=HH0. We have studied the cosmological parameters, like bulk viscosity coefficient (ξ), effective equation of state (ωeft), deceleration (q), Om diagnostic and cosmological planes like state-finder diagnostics {r,s} and {r,q} planes. And also, we have analyzed the physical behavior of these parameters through pictorial representation. The deceleration and effective equation of state parameters are very close to recent observational data in our model.

Generic anisotropic Lifshitz scalar field theory: New massive minimal subtraction

We formulate the simplest minimal subtraction version for massive scalar fields with O(N) symmetry for generic anisotropic Lifshitz spacetimes. We introduce the simplest geometric concepts to define it as a special manifold. Then we restrict ourselves to flat Euclidean spaces. An appropriate partial-p operation is applied in the bare two-point vertex function diagrams, which separates the original diagram into a sum of two different integrals which are the coefficients of the corresponding polynomials in the mass and external momentum. Within the proposed method, the coefficient of the mass terms can be discarded and we obtain a minimal subtraction method almost identical to the same scheme in the massless theory in every external momentum/mass subspace. We restrict our demonstration of the method up to three-loop order in the two-point vertex part. We verify its consistency through a diagrammatic computation of static critical exponents, which validates the universality hypothesis.

Viscous fluid accelerating model in modified gravity

In the framework of extended theory of gravity, an accelerating cosmological model has been presented in this paper in an anisotropic space-time. The extended gravity is considered as [Formula: see text] gravity with the matter field as viscous fluid. The role of viscous coefficient has been discussed on the cosmic expansion issue. In the developed formalism, a variable Hubble parameter has been incorporated to express the dynamical parameter with respect to redshift. The model is observed to be compatible with recent observational data.

Conharmonic Curvature Inheritance in Spacetime of General Relativity

The motive of the current article is to study and characterize the geometrical and physical competency of the conharmonic curvature inheritance (Conh CI) symmetry in spacetime. We have established the condition for its relationship with both conformal motion and conharmonic motion in general and Einstein spacetime. From the investigation of the kinematical and dynamical properties of the conformal Killing vector (CKV) with the Conh CI vector admitted by spacetime, it is found that they are quite physically applicable in the theory of general relativity. We obtain results on the symmetry inheritance for physical quantities (μ,p,ui,σij,η,qi) of the stress-energy tensor in imperfect fluid, perfect fluid and anisotropic fluid spacetimes. Finally, we prove that the conharmonic curvature tensor of a perfect fluid spacetime will be divergence-free when a Conh CI vector is also a CKV.

Propagation of axial and polar gravitational waves in Kantowski–Sachs universe

We apply the Regge-Wheeler formalism to study axial and polar gravitational waves in Kantowski-Sachs universe. The background field equations and the linearised perturbation equations for the modes are derived in presence of matter. To find analytical solutions, we analyze the propagation of waves in vacuum spacetime. The background field equations in absence of matter are solved by assuming the expansion scalar to be proportional to the shear scalar. Using the method of separation of variables, the axial perturbation parameter $ h_0(t, r) $ is obtained from its wave equation. The other perturbation $ h_1(t, r) $ is then determined from $ h_0(t, r) $. The anisotropy of the background spacetime is responsible for the damping of the axial waves. The polar perturbation equations are much more involved compared to their FLRW counterparts, as well as to the axial perturbations in Kantowski-Sachs background. In both the axial and polar cases, the radial and temporal solutions separate out as products. The temporal part of the polar perturbation solutions are plotted against time to obtain an order of magnitude estimate of the frequency of the propagating GWs and lies in the range 1000-2000 Hz. Using standard observational data for the GW strain we have placed constraints on the parameters in the polar perturbation solutions. The perturbation equations in presence of matter show that the axial waves can cause perturbations only in the azimuthal velocity of the fluid without deforming the matter field. But the polar waves must perturb the energy density, the pressure and also the non-azimuthal components of the fluid velocity.

Weyl Curvature Hypothesis in Light of Quantum Backreaction at Cosmological Singularities or Bounces

The Weyl curvature constitutes the radiative sector of the Riemann curvature tensor and gives a measure of the anisotropy and inhomogeneities of spacetime. Penrose’s 1979 Weyl curvature hypothesis (WCH) assumes that the universe began at a very low gravitational entropy state, corresponding to zero Weyl curvature, namely, the Friedmann–Lemaître–Robertson–Walker (FLRW) universe. This is a simple assumption with far-reaching implications. In classical general relativity, Belinsky, Khalatnikov and Lifshitz (BKL) showed in the 70s that the most general cosmological solutions of the Einstein equation are that of the inhomogeneous Kasner types, with intermittent alteration of the one direction of contraction (in the cosmological expansion phase), according to the mixmaster dynamics of Misner (M). How could WCH and BKL-M co-exist? An answer was provided in the 80s with the consideration of quantum field processes such as vacuum particle creation, which was copious at the Planck time (10−43 s), and their backreaction effects were shown to be so powerful as to rapidly damp away the irregularities in the geometry. It was proposed that the vaccum viscosity due to particle creation can act as an efficient transducer of gravitational entropy (large for BKL-M) to matter entropy, keeping the universe at that very early time in a state commensurate with the WCH. In this essay I expand the scope of that inquiry to a broader range, asking how the WCH would fare with various cosmological theories, from classical to semiclassical to quantum, focusing on their predictions near the cosmological singularities (past and future) or avoidance thereof, allowing the Universe to encounter different scenarios, such as undergoing a phase transition or a bounce. WCH is of special importance to cyclic cosmologies, because any slight irregularity toward the end of one cycle will generate greater anisotropy and inhomogeneities in the next cycle. We point out that regardless of what other processes may be present near the beginning and the end states of the universe, the backreaction effects of quantum field processes probably serve as the best guarantor of WCH because these vacuum processes are ubiquitous, powerful and efficient in dissipating the irregularities to effectively nudge the Universe to a near-zero Weyl curvature condition.

Anisotropic spacetimes in chiral scalar field cosmology

Study the behaviour and the evolution of the cosmological field equations in an homogeneous and anisotropic spacetime with two scalar fields coupled in the kinetic term. Specifically, the kinetic energy for the scalar field Lagrangian is that of the Chiral model and defines a two-dimensional maximally symmetric space with negative curvature. For the background space we assume the locally rotational spacetime which describes the Bianchi I, the Bianchi III and the Kantowski-Sachs anisotropic spaces. We work on the $H$% -normalization and we investigate the stationary points and their stability. For the exponential potential we find a new exact solution which describes an anisotropic inflationary solution. The anisotropic inflation is always unstable, while future attractors are the scaling inflationary solution or the hyperbolic inflation. For scalar field potential different from the exponential, the de Sitter universe exists.

Commutatively deformed general relativity: foundations, cosmology, and experimental tests

An integral kernel representation for the commutative star -product on curved classical spacetime is introduced. Its convergence conditions and relationship to a Drin’feld differential twist are established. A star -Einstein field equation can be obtained, provided the matter-based twist’s vector generators are fixed to self-consistent values during the variation in order to maintain star -associativity. Variations not of this type are non-viable as classical field theories. star -Gauge theory on such a spacetime can be developed using star -Ehresmann connections. While the theory preserves Lorentz invariance and background independence, the standard ADM 3+1 decomposition of 4-diffs in general relativity breaks down, leading to different star -constraints. No photon or graviton ghosts are found on star -Minkowski spacetime. star -Friedmann equations are derived and solved for star -FLRW cosmologies. Big Bang Nucleosynthesis restricts expressions for the twist generators. Allowed generators can be constructed which account for dark matter as arising from a twist producing non-standard model matter field. The theory also provides a robust qualitative explanation for the matter-antimatter asymmetry of the observable Universe. Particle exchange quantum statistics encounters thresholded modifications due to violations of the cluster decomposition principle on the nonlocality length scale sim 10^{3-5} ,L_P. Precision Hughes–Drever measurements of spacetime anisotropy appear as the most promising experimental route to test deformed general relativity.

Panorama behaviors of general relativistic hydrodynamics and holographic dark energy in [formula omitted] gravity

The main motive of this study is to investigate behaviors of general relativistic hydrodynamics in the form of perfect fluid and holographic dark energy for anisotropic and homogenous space-time in the framework of f(R,T) gravity. The field equations are solved using (i) the shear scalar of the metric is proportional to the expansion scalar which results a relationship between metric potentials and (ii) special law of variation of Hubble's parameter (Berman (1983)) that yields constant deceleration parameter. The cosmological parameters like energy density, EoS parameter, statefinder parameters, jerk parameter, thermodynamic temperatures and entropy densities of the models are obtained and discussed their physical significance in the light of the recent scenario of accelerated expansion of the universe and cosmological observations. The well-known astrophysical phenomena, namely the Hubble parameter H(z), luminosity distance (dL) and distance modulus μ(z)with redshift are studied.

Past extendibility and initial singularity in Friedmann-Lemaître-Robertson-Walker and Bianchi I spacetimes

We study past-directed extendibility of Friedmann-Lemaître-Robertson-Walker (FLRW) and Bianchi type I spacetimes with a scale factor vanishing in the past. We give criteria for determining whether a boundary for past-directed incomplete geodesics is a parallelly propagated curvature singularity, which cannot necessarily be read off from scalar curvature invariants. It is clarified that, for incomplete FLRW spacetime to avoid the singularity, the spacetime necessarily reduces to the Milne universe or flat de Sitter universe toward the boundary. For incomplete Bianchi type I spacetime to be free of singularity, it is necessary that the spacetime asymptotically fits into the product of the extendible isotropic geometry (Milne or flat de Sitter) and flat space, or, anisotropic spacetime with specific power law scale factors. Furthermore, we investigate in detail the time-dependence of the scale factor compatible with the extendibility in both spacetimes beyond the leading order.