Scalar Expansion Research Articles

Cold dark matter and holographic dark energy cosmological model with big rip singularity

In this paper, we have explored cold dark matter and holographic dark energy cosmological model with big rip singularity. To obtain the solution of the field equation, we supposed that scalar expansion [Formula: see text] is proportional to shear scalar [Formula: see text], which leads to [Formula: see text], where [Formula: see text], [Formula: see text] are metric potentials and [Formula: see text] is constant. Big bang and big rip singularity are investigated. The state-finder parameter is analyzed. The physical and geometrical parameters of the universe are explained.

Kaluza–Klein cosmological model with strange-quark-matter in f(R,T) theory of gravity

This work deals with the Kaluza–Klein cosmological model with strange-quark-matter in [Formula: see text] theory of gravity, where R is the Ricci scalar and T is the trace of the energy–momentum tensor. To determine the solution of the field equation, we have assumed that scalar expansion [Formula: see text] is proportional to shear scalar [Formula: see text] which leads to [Formula: see text], where R and A are metric potentials and m is constant. The cosmological parameters are investigated with the help of the equation of state strange-quark-matter (SQM) is [Formula: see text], where [Formula: see text] is Bag constant. We have concentrated on the distances of cosmology such as the look-back time, proper distance, luminosity distance, angular-diameter distance and distance modulus which are presented graphically by using suitable data of [Formula: see text]. The physical and geometrical properties of models are also discussed.

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.

Kinematic parameters and Raychaudhuri equation in the Kantowski-Sachs model

In this work we present a review of the calculations of homogeneous and anisotropic cosmological models, particularly the Kantowski-Sachs cosmological model. As an innovative contribution, we calculate an exact solution to the field equations with a general expression for the material content of the Universe. We obtain the expressions for energy density in this general case. We also study the case involving a scalar field. We investigate the evolution dynamics of the model, encompassing the Hubble, density, and deceleration parameters. We calculate the kinematic parameters associated with the model, namely: the scalar expansion Θ, the shear scalar σ, the rotation parameter ω and the parameter R α β U α U β , also known as Raychaudhuri scalar or convergence condition, all these parameters expressed in the Raychaudhuri equation.

A Study on Cosmological Model of Anisotropic Universe with Electromagnetic Field and Cloud Strings in the Frame Work of General Relativity

In this study, we have investigated the Bianchi type-III anisotropic cosmological model in the presence of cloud strings with the electromagnetic field in the general theory of relativity. Exact solutions of field equations are obtained using the fact that shear scalar is proportional to scalar expansion and constant decelerating parameter, which is derived from the variation law of Hubble parameter proposed by Berman(Nuovo Cimento B 74, 182 (1983))and linearly varying decelerating parameter proposed by Akarsu and Dereli(International Journal of Theoretical Physics, 51,612(2012)). The dynamics and significance of the physical parameters of the model are discussed using a graphical representation of these parameters. The dynamics and significance of the physical parameters of the models are discussed.

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 Isotropic Cosmological Model with Aetherically Active Axionic Dark Matter

Within the framework of the extended Einstein–aether–axion theory, we studied the model of a two-level aetheric control over the evolution of a spatially isotropic homogeneous Universe filled with axionic dark matter. Two guiding functions are introduced, which depend on the expansion scalar of the aether flow being equal to the tripled Hubble function. The guiding function of the first type enters the aetheric effective metric, which modifies the kinetic term of the axionic system; the guiding function of the second type predetermines the structure of the potential axion field. We obtained new exact solutions to the total set of master equations in the model (with and without cosmological constant), and studied four analytically solvable submodels in detail, for which both guiding functions are reconstructed and illustrations of their behavior are presented.

Dynamic Aether as a Trigger for Spontaneous Spinorization in Early Universe

In the framework of the Einstein–Dirac-aether theory we consider a phenomenological model of the spontaneous growth of the fermion number, which is triggered by the dynamic aether. The trigger version of spinorization of the early Universe is associated with two mechanisms: the first one is the aetheric regulation of behavior of the spinor field; the second mechanism can be related to a self-similarity of internal interactions in the spinor field. The dynamic aether is designed to switch on and switch off the self-similar mechanism of the spinor field evolution; from the mathematical point of view, the key of such a guidance is made of the scalar of expansion of the aether flow, proportional to the Hubble function in the isotropic cosmological model. Two phenomenological parameters of the presented model are shown to be considered as factors predetermining the total number of fermions born in the early Universe.

Cloud String Cosmological Models Using Different Decelerating Parameters with Electromagnetic Field in General Theory of Relativity

In this study, we have investigated the Bianchi type-III anisotropic cosmological model in the presence of cloud strings with electro- magnetic field in general theory of relativity. Exact solutions of field equations are obtained using the fact that shear scalar is proportional to scalar expansion and constant decelerating parameter which is derived from variation law of Hubble parameter proposed by Berman[1] and linearly varying decelerating parameter proposed by Akarsu and Dereli [2]. The dynamics and significance of physical parameters of the model are discussed using a graphical representation of these parameters.The dynamics and significance of physical parameters of the models are discussed.

Kinematics in metric-affine geometry

In a given geometry, the kinematics of a congruence of curves is described by a set of three quantities called expansion, rotation, and shear. The equations governing the evolution of these quantities are referred to as kinematic equations. In this paper, the kinematics of congruence of curves in a metric-affine geometry are analysed. Without assuming an underlying theory of gravity, we derive a generalised form of the evolution equations for expansion, namely, Raychaudhuri equation (timelike congruences) and Sachs optical equation (null congruences). The evolution equations for rotation and shear of both timelike and null congruences are also derived. Generalising the deviation equation, we find that torsion and non-metricity contribute to a relative acceleration between neighbouring curves. We briefly discuss the interpretation of the expansion scalars and derive an equation governing angular diameter distances. The effects of torsion and non-metricity on the distances are found to be dependent on which curves are chosen as photon trajectories. We also show that the rotation of a hypersurface orthogonal congruence (timelike or null) is a purely non-Riemannian feature.

Anisotropic Magnetized String model with Constant Decelerating Parameter in General Theory of Relativity

Cosmological model in the presence of cloud strings with electro- magnetic field in general theory of relativity. Exact solutions of field equations are obtained using the fact that shear scalar is proportional to scalar expansion and constant decelerating parameter which is derived from variation law of Hubble parameter proposed by Berman [1]. The dynamics and significance of physical parameters of the model are discussed using a graphical representation of these parameters. The physical and kinematical properties found in this model exhibit an accelerating expansion of the universe, which are compatible with current cosmological observations.

Plane Symmetric Cosmological Model with Strange Quark Matter in f(R,T) Gravity

A plane symmetric Bianchi-I model filled with strange quark matter (SQM) was explored in f(R,T)=R+2λT gravity, where R is the Ricci scalar, T is the trace of the energy-momentum tensor, and λ is an arbitrary constant. Three different types of solutions were obtained. In each model, comparisons of the outcomes in f(R,T) gravity and bag constant were made to comprehend their roles. The first power-law solution was obtained by assuming that the expansion scalar is proportional to the shear scalar. This solution was compared with a similar one obtained earlier. The second solution was derived by assuming a constant deceleration parameter q. This led to two solutions: one power-law and the other exponential. Just as in the case of general relativity, we can obtain solutions for each of the different eras of the universe, but we cannot obtain a model which shows transitional behavior from deceleration to acceleration. However, the third solution is a hybrid solution, which shows the required transition. The models start off with anisotropy, but are shear free at late times. In general relativity, the effect of SQM is to accelerate the universe, so we expect the same in f(R,T) gravity.

Renyi Holographic Dark Energy Model in f(R) Gravity with Hubble's IR Cut-Off

In the present study, a homogeneous and anisotropic LRS Bianchi type-I universe model is considered with an interacting dark matter and Renyi holographic dark energy model (RHDE) in f(R) gravity. The deceleration parameter (DP) shows a signature flipping for a universe which was decelerating in past and accelerating at present epoch. Therefore, the DP is a most physically justified parameter to analyze the solution of cosmological model. In order to find an exact solution of the field equations of the model, the shear scalar is considered to be proportional to the expansion scalar. We have considered f(R) = b Rn, the depiction model of f(R) which is the function of Ricci scalar R. The physical and geometrical characteristics of the universe model have been studied.

Bianchi type-III holographic dark energy cosmological model in [formula omitted] theory of gravitation

In this paper, we have studied the spatially homogeneous and anisotropic Bianchi type-III cosmological model in the presence of pressureless matter and Holographic dark energy within the framework of f(R,T) gravity. We have constructed a cosmological model with an appropriate choice of function f(T). Field equations are solved using the relation between the metric potentials A=Cn and using a simple power-law form of a metric potential C=tn. The main objective behind this paper is to explore some physically significant discussions on the evolution of the universe. It is observed that the Hubble parameter H, scalar expansion θ and shear scalar σ diverge at the initial epoch while they approach zero for a large value of time and the anisotropic parameter Am is constant. The negative value of the deceleration parameter indicates the present acceleration of the universe.

LRS Bianchi Type-II Cosmological Model with New Holographic Dark Energy in General Relativity with Quintessence

Abstract: In this paper, we investigate the LRS Bianchi Type-II universe filled with pressureless cold dark matter and non-interacting new holographic dark energy in the framework of general relativity. To obtain the deterministic solution of Einstein’s field equations, we assume the scalar of expansion to be proportional to the eigenvalue of the shear tensor. The expressions for some parameters of cosmological importance are obtained and physical and geometrical properties of the model are discussed. The correspondence between the new holographic dark energy and quintessence scalar field model is also established by comparing their equations of state and densities. Our results are consistent with the recent cosmological observations. Keywords: Bianchi type-II, Holographic principle, Dark energy, Quintessence.

Astrophysical implications of an eternal homogeneous gravitational collapse model with a parametrization of expansion scalar

In this study, we continue our previous work (Annu et al. 2023) by introducing a novel parametrization of the expansion scalar Theta as a rational function of time t. The paper provides a comprehensive analysis of a homogeneous gravitational collapsing system, wherein the exact solutions of the Einstein field equations (EFEs) are determined using a new parametrization of Theta in a model-independent way. The model is especially significant for the astrophysical applications because we have addressed the physical and geometrical quantities of the model in terms of Schwarzschild mass M. We have estimated the numerical value of the model parameter involved in the functional form of Theta -parametrization using the masses and radii data of some massive stars namely, Westerhout 49-2, BAT99-98, R136a1, R136a2, WR 24, Pismis 24-1, lambda Cephei, alpha Camelopardalis, beta Canis Majoris. We have presented theoretical investigations about such astrophysical stellar systems. The formation of an apparent horizon is also studied for the collapsing system, and it has been shown that our model produces a continuing collapsing scenario of star (an eternal collapsing object).

Kantowski–Sachs Barrow holographic dark energy model in Saez–Ballester theory of gravitation

In this paper, we have studied a spatially homogeneous and anisotropic Kantowski–Sachs universe in the presence of Barrow Holographic Dark Energy in the background of Saez–Ballester scalar–tensor theory of gravitation. To find the exact solution of the SB field equations, we have assumed that the shear scalar is directly proportional to expansion scalar. This assumption leads to relation between metric potentials of the models. We have discussed non-interacting and interacting cosmological models. Moreover, we have discussed several cosmological parameters such as energy densities of DM and DE (ρm &ρb), deceleration (q), equation of state (ωb) and skewness (α) parameters, squared sound speed (vs2), ωb−ωb′ plane statefinders and Om-diagnostics parameters through graphical representation for both the interacting models. Also, we have observed that the current values of deceleration and EoS parameters of our constructed models are coincide with the recent observational data.

Consideration on the Relationship of Theoretical Ultraviolet Cut-Off Energy with Experimental Data

We formulated a field theory in space-time elements, which are obtained by dividing the space-time continuum into arbitrary-shaped space-time elements, such as hyper-octahedra (orthoplexes), which are aligned locally periodically, without long-range order. Each field is expressed in terms of scalar expansion functions with rotationally covariant coefficients. The cosmological constant was related to the cut-off energy of the quadratic Higgs self-energy. From the literature, examinations find an experimental break in the cosmic ray energy spectrum called 'knee' at about 3 [PeV], which agrees with this theoretical ultraviolet cut-off energy. Moreover, the expansion functions are updated to plane waves using the Lorentz/Poincar\'e covariant/invariant inner product of vectors with each four-momentum within the cut-off energy. Due to the long-range disordered alignment of space-time elements, this study newly introduces an effective field, which is not in the standard model and lies within the Planck energy. Particles are then rarely excited to the energy region between the cut-off energy and the Planck energy via extremely weak interaction solely with the effective field. The theoretical ultraviolet cut-off energy is consistent with the experimental phenomena such as the stability of our Universe, inflation in the early Universe and no detection of neutrinos above PeV-order energy.

The Study of Kantowski-Sachs Perfect Fluid Cosmological Model in Modified Gravity

Kantowski-Sachs perfect fluid cosmological model is explored in modified gravity with functional form f (R, T) = f1(R) + f2 (T) where R is Ricci scalar and T is the trace of energymomentum tensor. With this functional form, three different cases have been formulated, namely negative and positive powers of curvature, logarithmic curvature and exponential curvature given by f1 (R) = R + γ R2 – μ4 / R, f1(R) = R+ v ln(τR) and f1(R) = R+ κe–ιR respectively, and for all these three cases, f2 (T) = λT, here γ,λ,μ,v,τ,κ and ι are constants. While solving the field equations, two constraints i) Expansion scalar is proportional to shear scalar ii) Hyperbolic scale factor are used. By using these conditions the required optimum solutions are obtained. The physical parameters are calculated and geometrical parameters of three cases are analysed against redshift z with the help of pictorial representation. In the context of f (R, T) gravity energy conditions are discussed with the help of pressure and energy density. If strong energy condition is positive the gravity should be attractive but in our model it is negative. It means that cosmic acceleration is due to antigravity, whereas NEC and DEC are fulfilled. The perturbation technique is used to test the stability of the background solutions of the obtained models. The inferences obtained from this paper are in persistent with the present cosmological observations and the model represents an accelerating universe.

The Raychaudhuri equation in inhomogeneous FLRW space-time: A f(R)-gravity model

In general description of the Raychaudhuri equation it is found that this first order non-linear differential equation can be written as a second order linear differential equation in the form of Harmonic Oscillator with varying frequency. Further, the integrability of the Raychaudhuri equation has been studied and also the expansion scalar is obtained in an explicit form. Subsequently, f(R) gravity theory has been studied in the background of inhomogeneous FLRW spacetime with an aim to formulate the Raychaudhuri equation. A congruence of time-like geodesics has been investigated using the Raychaudhuri equation to examine whether the geodesics converge or not and some possible conditions are determined to avoid singularity. Finally, a brief quantum description has been presented.