Shear Scalar Research Articles

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

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.

Statefinder Diagnostic of Interacting Dark Fluid in Bianchi Type-IX Universe

In this paper, we deal with spatially homogeneous and anisotropic Bianchi types-IX and Universe filled with Holographic dark energy and cold dark matter. Assuming the condition that the shear scalar is proportional to expansion scalar, we have obtained solutions of Einstein field equations. The Statefinder diagnostic pair i.e. {r‚s} is adopted to distinguish our dark energy models from other dark energy models. Some important physical features of the models have been discussed.

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.

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.

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.

HIGHER DIMENSIONAL TOPOLOGICAL DEFECT SOLUTIONS WITH MASSIVE SCALAR FIELD IN GENERAL RELATIVITY

In this paper, we investigate a ve dimensional Locally Rotationally Symmetric (LRS) Bianchi type- V string cosmological model with massive scalar eld in general relativity. In order to obtain an exact solution of the field equations, we used the following conditions: (i) the shear scalar is proportional to the expansion scalar, resulting in a relationship between metric potentials, and (ii) the average scale factor is proportional to the massive scalar gield, resulting in a power law relationship. In addition, the physical and kinematical parameters are discussed in detail.

Bianchi type-III cosmic strings and domain walls in f(r, t) gravity

In this paper, we have considered Bianchi type-III space time in the presence of cosmic strings and domain walls within the framework of f(R, T) gravity formulated by Harko et al. (Phys. Rev. D, 84: 024020, 2011). To obtain the exact solution of the corresponding cosmological model, we assume the condition that the shear scalar is directly proportional to the scalar expansion of the space-time and special law of variation for Hubble’s parameter proposed by Berman (Nuovo Ciment B, 74:182, 1983). Some physical and kinematical properties of the models are also discussed.

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.

The study of Bianchi type-III, V, and VI0 models in modified theory

Bianchi type-III, V, and VI0 perfect fluid anisotropic cosmological models have been discussed in the theory of gravity suggested by [T. Harko, F. S. N. Lobo, S. Nojiri and S. D. Odintsov, f(R, T) gravity, Phys. Rev. D 84 (2011) 024020] with two well-known functional forms, namely, [Formula: see text] and [Formula: see text], here [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] are constants. To acquire the solutions of the field equations of the three models, the average scale factor and the proportionality of expansion scalar with shear scalar are used. The behavior of all the physical and geometrical properties of the three models is explained with their plots. For all the three models, the NEC is positive, which implies that the EoS parameter is in the quintessence region. For the Bianchi type-III model, the SEC is violated, which recommends that the present universe is accelerating and expanding. Also, we have observed that, if [Formula: see text], [Formula: see text], and [Formula: see text], then the two functional forms lead to the linear form and for [Formula: see text], the second form leads to the quadratic form, these two are interesting points in this paper. It can be observed that the stability analysis of the obtained models background solutions is discussed through perturbation techniques and observed that the background solutions are stable. The values of all the parameters in the three models match with the recent cosmological observations.

Study of Strange Quark Matter and Variable ∧ in Bianchi VI Universe

The present paper deals with strange quark matter i.e. ( 4 ) in the presence of variable cosmological term in Bianchi VI universe. Here we adopt the physical conditions (i)The shear scalar is proportional to expansion scalar and ( ii ) The time dependent cosmological term of the type 2 for the simplification of field equations. We observed some cosmological parameters such as deceleration parameter, quark density, quark pressure etc. Lastly we conclude with the discussion of cosmological perturbations of resultant universe. Also graphs are plotted for the detail study of the resultant model.

Anisotropic minimally interacting dark energy models with cosmic strings and a massive scalar field

This paper deals with the construction of locally rotationally symmetric (LRS) Bianchi type-II (B-II) cosmological models obtained by solving Einstein field equations coupled with an attractive massive scalar field (MSF) when the source of gravitation is the mixture of cosmic string cloud and anisotropic dark energy (DE) fluid which are minimally interacting. We have obtained exact cosmological models by using (i) shear scalar is proportional to the scalar expansion of the space–time and (ii) a power-law relation between the average scale factor of the universe and the scalar field. Our models represent string cosmological model and DE model in the presence of MSF. Using our model, we determine cosmological parameters such as energy densities, deceleration parameter, statefinders and equation of state parameter. We, also, present the tension density and energy density of the string. We discuss the physical aspects of these cosmological parameters. It is observed that our models represent accelerated expansion phenomenon of our universe as confirmed by Supernova Ia experiment.

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.

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.

Higher dimensional Bianchi type-III string cosmological models with dark energy in Brans-Dicke scalar-tensor theory of gravitation

The Five dimensional anisotropic Bianchi type-III cosmological model has been investigated within the framework of Brans-Dicke (Phys. Rev. 124:925, 1961) scalar-tensor theory of gravitation. Dark Energy fluid and cosmic strings are considered as a source of energy-matter field and minimal interacting. To determine the solutions of field equations we have used Berman’s special law of variation, power law relation between scalar field ϕ and average scale factor a and proportionality between scalar expansion and shear scalar. It gives two model of the universe i.e. power law model and exponential model. Physicals and kinematical parameters of the model are also discussed for both the scenarios.

Higher Dimensional LRS Bianchi Type-I String Cosmological Model with Bulk Viscosity in General Relativity

Objective: To present a new solution to the field equations obtained for higher dimensional LRS Bianchi type-I universe generated by means of a cloud of strings with particles connected to them with bulk viscosity in general relativity. Methods: To obtain the solutions of field equations of higher dimensional LRS Bianchi type-I universe we consider that the shear scalar of the model is proportional to the scalar expansion of the model (saq ), which leads to, c=b^n. The physical and geometrical behaviors of the model universe are studied by comparing with the present cosmological scenario and observations. Findings: It is observed that our model is anisotropic, expanding and decelerates at early stage and then accelerates in late universe giving the inflation model universe. Novelty: We obtained new solution to the field equations for higher dimensional LRS Bianchi type-I generated by means of a cloud of strings with bulk viscous fluid in general relativity. Keywords: LRS Bianchi TypeI Metric; Bulk Viscous Fluid; Strings

Role of structure scalars on the evolution of compact objects in Palatini [formula omitted] gravity

The utmost concern of this article is the construction of modified scalar functions (structure scalars) by taking Palatini f(R) gravitational theory into account. At first, a general formalism is established in which we assess gravitational stellar equations by putting into use the Palatini’s technique. Later, from the perspective of tilted observer, we Lorentz boosted the components of energy-momentum tensor using relative velocity ω. To examine the physical as well as mathematical aspects of the fluid source, we carry out a detailed analysis of kinematical variables by evaluating shear tensor and scalar, four-acceleration and expansion scalar. For the fluid content inside our spherical star, we inferred the mass function (geometric mass) and the active gravitational mass. Raychaudhuri equation, Bianchi identities in addition to few other equations are worked out to discern the structure formation and analyze the object’s evolutionary stages. The Riemann tensor is then broken up orthogonally to set up few scalar functions connected with fundamental physical characteristics of the fluid source like energy density, effects of tidal forces and anisotropic stresses etc.