Locally Rotationally Symmetric Research Articles

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.

Cold dark matter and holographic dark energy in f(R,T) theory of gravity

In this study, we have examined the cosmological model of the locally rotationally symmetric (LRS) Bianchi Type-I universe within the framework of the [Formula: see text] theory of gravity. The [Formula: see text] theory incorporates the Ricci scalar (R) and the trace of the energy–momentum tensor (T) in its formulation. Our investigation focuses on the cold dark matter (CDM) and holographic dark energy (DE) cosmological models, particularly in relation to the occurrence of a big rip singularity. To solve the field equation, we have assumed a specific relationship between the parameters, [Formula: see text] and [Formula: see text], where [Formula: see text] is proportional to [Formula: see text] and m is held constant. We have examined the existence of both the Big Bang and Big Rip singularities within this cosmological model. Additionally, we have analysed the state-finder parameter, which provides insights into the dynamics and evolution of the universe. Furthermore, we have discussed the physical and geometrical parameters of the universe in this context. These parameters help characterize and describe the behavior of the universe, shedding light on its underlying properties and dynamics. Through our investigation, we aim to deepen our understanding of the LRS Bianchi Type-I cosmological model within the [Formula: see text] theory of gravity, exploring the interplay between CDM, holographic DE, singularities, and the various parameters that contribute to the understanding of the universe.

A study of Bianchi type I spacetime according to their Ricci collineations

Rici collineations (RCs) have been used in this research to study the locally rotationally symmetric (LRS) Bianchi type I spacetimes. To accomplish our objectives, the RC equations are typically integrated for both situations of the Ricci tensor, degenerate and non-degenerate. Throughout this work, a number of situations occur that provide various finite and infinite dimensional Lie algebras of RCs.

Constraining Rastall parameter for baryon asymmetry factor using isotropic and anisotropic universe models

This paper investigates the mystery of baryogenesis for isotropic and anisotropic universe models in the context of Rastall’s theory of gravity (RTG). In the first part, we utilize the Rastall field equations (FEs) for the flat Friedmann Robertson Walker (FRW) metric to find the solutions of density [Formula: see text] and Hubble parameter [Formula: see text]. Additionally, Rastall parameter plays a crucial role to discuss baryogenesis and fulfilling its criteria on the observational ground. It is found that very large positive/negative values of Rastall parameter like [Formula: see text] (for [Formula: see text]) and [Formula: see text] (for [Formula: see text]) are required to satisfy the observational bounds on baryon asymmetry factor (BAF), see Fig. 1. In the second part, we develop the FEs for RTG using the Locally Rotationally Symmetric (LRS) Bianchi type-1 line-element. Then we find the solutions of the FEs and use them to find the BAF using Rastall parameter as [Formula: see text] and anisotropic parameter [Formula: see text] to meet the consistency with the experimental limit, see Fig. 3. For [Formula: see text], the anisotropic model reduces to the isotropic FRW model, where we have a zero BAF. Finally, we conclude that RTG with both universe models is a good candidate to study baryogenesis in the early universe and the variable [Formula: see text] has a considerable impact on the BAF.

Modified [formula omitted]-gravity string cosmological models with observational constraints

In the current study, we have investigated a modified f(Q)-gravity theory in an anisotropic, locally rotationally symmetric (LRS) Bianchi type-I spacetime universe model. The arbitrary function f(Q)=Q+Λ, where Λ is the “cosmological constant,” and Q is the non-metricity scalar, has been taken into consideration. To obtain the exact solution of the modified field equations, we considered a dusty string fluid matter source and the shear scalar (σ) is proportional to the expansion scalar (θ). The resultant Hubble function has been fitted with observational datasets H(z) and SNe Ia datasets of apparent magnitude m(z) in order to obtain the best fit values for the cosmological parameters. And utilizing these best fit values throughout the investigation, the many cosmic phenomena are examined. We have investigated the cosmographic coefficients like H,q,j,s to see if an accelerated dual mode expanding dark energy (DE) model of the universe exists. Our Om diagnostic study shows that our universe model is a quintessence example of a dark energy model. We have also calculated the universe’s present age.

Dynamical systems analysis of an interacting scalar field model in an anisotropic universe

In this paper, we investigate a non-canonical scalar field model in the background dynamics of anisotropic Locally Rotationally Symmetric (LRS) Bianchi type I universe where gravity is coupled minimally to scalar field which is taken as dark energy and pressureless dust as dark matter are the main matter content of the universe. We perform dynamical system analysis to characterize the cosmological evolution of the model with and without interaction in the dark sector separately. First, we convert the evolution equation into an autonomous system of ordinary differential equations by using a suitable choice of dimensionless variables, which are normalized over the Hubble scale. We choose scalar field coupling and potential in such a way that the autonomous system converted to a 2D system. Linear stability theory is employed to the extracted critical points to find the nature. From the analysis, we find some interesting cosmological scenarios, such as late-time scalar-field dominated solutions, which evolve in the quintessence era, cannot solve the coincidence problem. Accelerated scaling attractors are also obtained that correspond to the late phase evolution in agreement with present observational data, and these solutions also provide possible mechanisms to alleviate the coincidence problem. A complete cosmic evolution is obtained from early inflation to a late-time dark energy-dominated phase, connecting through a matter-dominated transient phase of the universe. Furthermore, we find that for different values of the interaction parameter α, the evolutionary trajectories of the Hubble parameter, and the distance modulus forecasted by the model are in quite well agreement with observational datasets.

An Investigation into LRS Bianchi I Universe in Brans-Dicke Theory

In this study, the homogenous and anisotropic locally rotationally symmetric (LRS) Bianchi type-I universe filled with the bulk viscous and the string cloud matter has been investigated in the Brans-Dicke (BD) scalar-tensor theory. The modified Einstein field equations of the constructed model have been solved by using the relation of the scale factors $A=B^m$ and considering the deceleration parameter to be $q=m-1$. It is found that the string does not survive for the model due to the obtained zero string energy density ($\rho_s=0$) and agrees with some studies in recent years. Moreover, it is possible to say that string matter may be turned into phantom energy over time, depending on the obtained negative rest energy density of the matter. When BD scalar field $\Phi$ is assumed constant, the attained solutions are reduced to General Relativity (GR) solutions for the static vacuum. Thus, the constructed model has not allowed the reduction of the BD solutions to GR solutions, including the matter distributions. In addition, some expansion models for choosing a value of constant $m$ have been obtained and provided. All the results have been analyzed in detail.

Anisotropic dark energy universe in f(Q, T) gravity with observational constraints

Aim of this paper is to investigate an anisotropic locally rotationally symmetric (LRS) Bianchi type-I space–time in the context of the recently proposed f( Q, T) gravity, where Q is the non-metricity scalar and T is energy–momentum tensor. We have considered f( Q, T) = α Q + β T a linear form, where α and β are model parameters. We have analyzed the exact solution of LRS Bianchi type-I space–time by assuming relation between metric potential A = B n , where n is arbitrary non-zero real number. To study the anisotropic nature of the dynamical dark energy, we assume that the skewness parameters are time dependent and n ≠ 1. We have constrained to our model by using observational Hubble dataset. Onwards, discussed the physical behavior of cosmological parameters such as energy density, pressure, EoS parameter, deceleration parameter and, Energy conditions.

Dynamical system analysis of interacting dark energy in LRS Bianchi type I cosmology

This paper deals with an interacting dark energy (DE) model in Locally rotationally symmetric (LRS) Bianchi type I cosmological model with scalar field in the form of an exponential potential. We reduce the transformation equations to an independent system of ordinary differential equations by appropriate alteration of the variables to setup the complementary dynamical system and after that we also calculate the critical points of the system. We get six critical points when our coupling parameter is positive. And we get two critical points when our coupling parameter is negative. And dark energy behaves like a perfect fluid for all the critical points. And after that we analyzed all the critical points by calculating the eigenvalues of the Jacobian matrix and we find out that out of these eight critical points, six critical points are stable, which shows that our Universe is accelerating. And two (2) critical points are unstable. We also present the phase plot analysis.

Magnetized Strange Quark Models in Lyra Theory

In this study, the behavior of magnetized strange quark matter (MSQM) distribution in Lyra theory was investigated for homogeneous anisotropic Bianchi III, locally rotationally symmetric (LRS) Bianchi I, and Kantowski-Sachs universe models. We have used the equations of state, anisotropy, and linearly varying deceleration parameters to obtain the exact solutions of field equations in Lyra theory. When switching from the anisotropic universe model to the isotropic universe model, the magnetic field was not observed in the LRS Bianchi I universe. Besides, the graphs of the dynamic quantities obtained for each universe model were analyzed in detail. Finally, we inquire whether further research should be conducted.

LRS Bianchi Type-I String Cosmological Models in f Q Gravity

In the current study, we studied a f Q -gravitational, anisotropic, locally rotationally symmetric (LRS), Bianchi type-I spacetime universe. We have adopted the freely chosen function f Q = Q + α Q , where α is a model-free parameter. We assumed that the universe is filled with dusty string fluid and that the shear scalar ( σ ) and the expansion scalar ( θ ) are proportional to each other in order to solve field equations for the average Hubble parameter ( H ). The resultant Hubble function has been fitted with observational datasets H z and SNe Ia datasets of apparent magnitude m z in order to obtain the best fit values for the cosmological parameters. Utilizing these best fit values throughout the analysis, many cosmic phenomena are examined. We have investigated cosmographic coefficients such as H , q , j , a n d s to see if an accelerated transit phase dark energy model of the cosmos exists. Also, we have classified the dark energy models that are explored using Om diagnostic analysis; our universe model is a quintessential dark energy model. The age of the universe as it exists right now has been roughly calculated by the model.

Dynamics of cosmological model with domain walls and massive scalar fields in f(R,T) gravity

A spatially homogenous and anisotropic locally rotationally symmetric (LRS) Bianchi type-I space-time is considered in the presence of a massive scalar field containing domain walls in the framework of the [Formula: see text] gravity proposed by Harko et al. [Phys. Rev. D 84, 024020, (2011)]. Solving the field equations of the model using a relation between metric potentials and power law between the scalar field and average scale factor of the model, an anisotropic cosmological model with massive scalar fields and domain walls in [Formula: see text] theory is presented. These conditions result in a model solution that provides a dynamic deceleration parameter. The model’s geometrical and physical properties are also examined. The universe exhibits a smooth transition from its early decelerated phase to its current accelerated phase, as shown by the study of the deceleration parameter. The statefinder plane corresponds to the Chaplygin gas era and the model finally approaches [Formula: see text]CDM model.

Hyperbolic Scenario of Accelerating Universe in Modified Gravity

Throughout this study, locally rotationally symmetric (LRS) Bianchi type-V space-time is pondered with Tsallis holographic dark energy (THDE) with the Granda–Oliveros (GO) cut-off in the Sáez–Ballester (SB) theory of gravity. A parameterization of the deceleration parameter (q) has been suggested: q=α−βH2. The proposed deceleration parameterization demonstrates the Universe’s phase transition from early deceleration to current acceleration. Markov chain Monte Carlo (MCMC) was utilized to have the best-fit value for our model parameter and confirm that the model satisfies the recent observational data. Additional parameters such as deceleration parameter q with cosmographic parameters jerk, snap, and lerk have also been observed physically and graphically. The constructed model is differentiated from other dark energy models using statefinder pair analysis. Some important features of the model are discussed physically and geometrically.

Anisotropic solutions in f(Q) gravity with hybrid expansion

Abstract Despite having a reasonably successful account of accelerated cosmology, understanding of the early evolution of Universe has always been difficult for mankind. Our promising strategy is based on a novel class of symmetric teleparallel theories of gravity called f(Q), in which the gravitational interaction is caused by the non-metricity scalar Q, which may help to solve some problems. We consider the locally rotationally symmetric (LRS) Bianchi type-I spacetime cosmological models and derive the motion of equations to study the early evolution of the cosmos. By assuming the hybrid expansion law (HEL) for the average scale factor, we are able to determine the solutions to the field equations of Bianchi type-I spacetime. We discuss the energy density profile, the equation of state, and the skewness parameter and conclude that our models preserve anisotropic spatial geometry during the early stages of the Universe with the possibility of an anisotropic fluid present. However, as time goes on, even in the presence of an anisotropic fluid, the Universe may move towards isotropy due to inflation while the anisotropy of the fluid dims away at the same time. It is seen from the squared speed of sound that Universe shows phantom nature at the beginning then approaches to dark energy at present epoch. We analyze both geometrical and physical behaviours of the derived model.

Anisotropic LRS-BI Universe with f(Q) gravity theory

The possible anisotropic nature in the early phases of the Universe is one of the interesting aspects of study in cosmology. We investigate the evolution of the Universe in terms of few cosmological parameters considering an anisotropic locally rotationally symmetric (LRS) Bianchi type-I spacetime (LRS-BI) under the $f(Q)$ gravity of symmetric teleparallel theory equivalent to the GR (STEGR). In this study we consider two $f(Q)$ gravity models, viz., $f(Q) = -\,(Q+2\Lambda)$, a simple model with the cosmological constant $\Lambda$ and the power law model, $f(Q) = -\, \alpha Q^n$ with two constant parameters $\alpha$ and $n$. Considering a proportionality relation between the directional Hubble parameters with a proportionality constant parameter $\lambda$ we find a significant contribution of the anisotropic factor in the evolution of the early Universe for both models. The power law model shows the more dominating effect of anisotropy in comparison to the simple model depending on model parameters, especially on the parameter $n$. The power law model also shows some possible effects of anisotropy on the Universe's evolution in the near future. In addition, both models confirm that the anisotropy does not obtain any appreciable signature in the current stage of the Universe. From our analysis we also set rough constraints on our model parameters as $0.5 \le \lambda \le 1.25$, $0.75 \le \alpha \le 1.5$ and $0.95 \le n \le 1.05$.

Anisotropic Universe in [formula omitted] gravity, a novel study

f(Q,T) theory of gravity is very recently proposed to incorporate within the action Lagrangian, the trace T of the energy–momentum tensor along with the non-metricity scalar Q. The cosmological application of this theory in a spatially flat isotropic and homogeneous Universe is well-studied. However, our Universe is not isotropic since the Planck era and therefore to study a complete evolution of the Universe we must investigate the f(Q,T) theory in a model with a small anisotropy. This motivated us to presume a locally rotationally symmetric (LRS) Bianchi-I spacetime and derive the motion equations. We analyse the model candidate f(Q,T)=αQn+1+βT, and to constrain the parameter n, we employ the statistical Markov chain Monte Carlo (MCMC) method with the Bayesian approach using two independent observational datasets, namely, the Hubble datasets, and Type Ia supernovae (SNe Ia) datasets.

Hyperbolic behavior of anisotropic Bianchi type-I cosmological model

Locally Rotationally Symmetric (LRS) Bianchi type-I metric is examined in the presence of perfect fluid. Exact solutions of Einstein’s field equations (EFE) have been studied by taking into account a hyperbolic scale factor. We observed that the model has initial singularity. It is found that the Universe approaches isotropy at late times. Through state finder pair [Formula: see text], it is observed that at late cosmic time, the model behaves analogous to [Formula: see text]CDM model. Energy conditions of the model are studied and it is found that null energy condition (NEC), weak energy condition (WEC) and dominant energy conditions (DEC) are satisfied for our model while SEC is violated. We investigate some physically and geometrically realistic models in order to develop a viable cosmological model.

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.

Constraining anisotropic cosmological model in f(R,ℒm) Gravity

The observational evidence regarding the present cosmological aspects tells us about the presence of very little anisotropy in the universe on a large scale. Here, in this paper, we attempt to study locally rotationally symmetric (LRS) homogeneous Bianchi-I spacetime with the isotropic matter distribution. This is done within the framework of $f(\mathcal{R},\mathscr{L}_m)$ gravity. Particularly, we consider a non-linear $f(\mathcal{R},\mathscr{L}_m)$ model, $f(\mathcal{R},\mathscr{L}_m)=\dfrac{1}{2}\mathcal{R}+\mathscr{L}_m^{\,{\alpha}}$. Furthermore, $\omega$, the equation of state parameter, which is vital stuff in determining the present phase of the universe is constrained. To constrain the model parameters and the equation of state parameter, we use 57 Hubble data points and 1048 Pantheon supernovae type Ia data sample. And, for our statistical analysis, we use Markoc Chain Monte Carlo (MCMC) simulation. Moreover, with the help of obtained values of parameters, we measure the anisotropy parameter for our model.

Nonsingular Phantom Cosmology in Five-Dimensional f(R, T) Gravity

We obtain exact solutions to the field equations for five-dimensional locally rotationally symmetric (LRS) Bianchi type-I spacetime in the f(R,T) theory of gravity, where specifically, the following three cases are considered: (i) f(R,T)=μ(R+T), (ii) f(R,T)=Rμ+RTμ2, and (iii) f(R,T)=R+μR2+μT, where R and T, respectively, are the Ricci scalar and trace of the energy–momentum tensor. It is found that the equation of state (EOS) parameter w is governed by the parameter μ involved in the f(R,T) expressions. We fine-tune the parameter μ to obtain the effect of phantom energy in the model. However, we also restrict this parameter to obtain a stable model of the universe.