Friedmann Robertson Walker Spacetime Research Articles

Noether symmetries of F(T,X,ϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(T,X,\\phi )$$\\end{document} cosmology

This article explores an analysis via the Noether symmetry approach to investigate an extended teleparallel F(T,X,ϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(T,X,\\phi )$$\\end{document} gravity model in the context of a Friedmann–Robertson–Walker spacetime. The model incorporates the torsion scalar T, scalar field ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} and the kinetic term X of the scalar field. This approach allows us to select physically interesting models by restricting arbitrariness in the F(T,X,ϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(T,X,\\phi )$$\\end{document} function. Thus we focus on two types of the function F(T,X,ϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(T,X,\\phi )$$\\end{document}, namely models involving the generalized teleparallel dark energy and the nonlinear function of the kinetic term and analyze the Noether symmetry properties and demonstrate the presence of non-vanishing Noether vectors. In the first model, by specifically considering the X4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbf{X_{4}}$$\\end{document} Noether symmetry, representing a scaling symmetry, we simplify the field equations and introduce a cyclic variable to enable a more workable formulation. Furthermore, we present a comprehensive graphical analysis, showcasing the time evolution of the scale factor and the scalar field by using the solutions obtained through these new variables. Additionally, we examine some fundamental cosmological parameters. For the second model, which includes the nonlinear form of the kinetic term, Noether symmetry results in obtaining simple power-law solutions for the dynamic variables. Our findings clearly show that the considered models represent an accelerating expansion of the Universe, which is consistent with observations. This study highlights the efficacy of the Noether symmetry approach in defining the functional form of F(T,X,ϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(T,X,\\phi )$$\\end{document} and obtaining precise cosmological solutions. The analytical solutions and graphical analysis offer valuable insights into the dynamic behavior of the models, contributing to understanding the evolving nature of the Universe.

Comparison of energy conditions in general relativity and modified theories of gravity

To make a comparison of energy conditions in the theory of general relativity and in the modified theories, we have considered [Formula: see text], [Formula: see text] and [Formula: see text] theories (where [Formula: see text] and [Formula: see text] are the Ricci scalar and trace of the energy–momentum tensor, respectively, while [Formula: see text]) to test the validity of all the four energy conditions. These energy conditions had been derived to check the viability of cosmological as well as astrophysical models. In this paper, we consider the standard Friedmann–Robertson–Walker spacetime representing the homogeneous and isotropic universe, and investigate the available literature on testing energy conditions as well as calculate these conditions ourselves. In order to provide the comparative results, we test these conditions analytically as well as graphically and present how energy bounds in modified theories depend on the values of the involved parameters and its validity within certain limits. We discuss here, that which of the modified theories comply with certain energy conditions, and hence provide a supporting argument on the existence of modified theories.

Unruh DeWitt probe of late time revival of quantum correlations in Friedmann spacetimes

Unruh DeWitt (UDW) detectors are important constructs in studying the dynamics of quantum fields in any geometric background. Curvature also plays an important role in setting up the correlations of a quantum field in a given spacetime. For instance, massless fields are known to have large correlations in de Sitter space as well as in certain class of Friedmann-Robertson-Walker (FRW) universes. However, some of the correlations are secular in nature while some are dynamic and spacetime dependent. An Unruh DeWitt detector responds to such divergences differently in different spacetimes. In this work, we study the response rate of Unruh DeWitt detectors which interact with quantum fields in FRW spacetimes. We consider both conventionally as well as derivatively coupled Unruh DeWitt detectors. Particularly, we consider their interaction with massless scalar fields in FRW spacetimes and nearly massless scalar fields in de Sitter spacetime. We discuss how the term which gives rise to the infrared divergence in the massless limit in de Sitter spacetime manifests itself at the level of the response rate of these Unruh DeWitt detectors in a wide class of Friedmann spacetimes. In order to carry out this study, we make use of an equivalence that exists between massless scalar fields in FRW spacetimes with massive scalar fields in de Sitter spacetime. Further, we show that while the derivative coupling regulates the divergence appearing in de Sitter spacetime, it does not completely remove them in matter dominated universe. This gives rise to large transitions in the detector which can be used as a probe of setting up of large correlations in late time era of the universe as well. We also apply the results of these otherwise formal analyses to the coupling of hydrogen atoms with gravitational waves. We show that the coupling of hydrogen atoms with gravitational waves takes a form that is similar to derivatively coupled UDW detectors and hence has significant observational implications as a probe of late time revival of quantum correlators.

Qualitative study of Lyra cosmologies with spatial curvature

We investigate the spatially curved Friedmann–Robertson–Walker space–time with Lyra geometry model. The cosmological solutions are studied by using dynamical system methodology to explore the universe evolution in the model. The constructed autonomous system has been explored to extract the physically viable cosmological solutions by studying the behavior of eigenvalues at the fixed points of the system. Late-time attractor solution corresponding to the accelerated expansion exist in the model and thus, the model may explain the late-time accelerating expansion of universe. The model is also composed of deceleration to acceleration transition with Λ cold dark matter evolution at late-times. The evolution of cosmological parameters like deceleration parameter , effective equation of state parameter, total matter density and role of energy conditions with scale factor have been studied along with statefinder diagnostic to explain the universe evolution in the model. By dynamical system analysis, it has been observed that the displacement field plays a dominant role during the early times and, the universe is dominated by stiff matter like component. Implications of bouncing behavior in the model with role of energy conditions and continuity equation have been discussed in detail along with their physical consequences. • Lyra geometry model with FRW metric having spatial curvature is investigated. • Dynamical system method has been used to extract the cosmic dynamics of model. • The model explains late-time accelerating evolution of universe. • Cosmological parameters are studied by integrating the dynamical variables. • We illustrate that the fixed point corresponding to radiation phase is absent.

Dynamics of tachyonic dark matter

Usually considered highly speculative, tachyons can be treated via straightforward Einsteinian dynamics. Kinetic theory and thermodynamics for a gas of “dark” tachyons are readily constructed. Such a gas exhibits density and pressure which, for the dominant constituent of a suitable Friedmann–Robertson–Walker space–time, can drive cosmic evolution with features both similar to and distinct from those of a standard dark-energy/dark-matter model. Hence, tachyons might bear further consideration as a cosmic dark-matter candidate.

A new way to study on generalized Friedmann–Robertson–Walker spacetime

A new way to study on generalized Friedmann–Robertson–Walker spacetime

Complex structures for Klein–Gordon theory on globally hyperbolic spacetimes

We develop a rigorous method to parametrize complex structures for Klein–Gordon theory in globally hyperbolic spacetimes that satisfy a completeness condition. The complex structures are conserved under time-evolution and implement unitary quantizations. They can be interpreted as corresponding to global choices of vacuum. The main ingredient in our construction is a system of operator differential equations. We provide a number of theorems ensuring that all ingredients and steps in the construction are well-defined. We apply the method to exhibit natural quantizations for certain classes of globally hyperbolic spacetimes. In particular, we consider static, expanding and Friedmann–Robertson–Walker spacetimes. Moreover, for a huge class of spacetimes we prove that the differential equation for the complex structure is given by the Gelfand–Dikki equation.

FRW universe in f(R,T) gravity

In this study, Friedmann–Robertson–Walker space-time filled with a perfect fluid in [Formula: see text] modified theory, where [Formula: see text] is the Ricci scalar and [Formula: see text] is the trace of the energy–momentum tensor of matter, has been considered. The investigation of the phase transition of the universe from the decelerating expansion phase to the accelerating one has been made by adopting a special form of the varying deceleration parameter that is inversely proportional to the Hubble parameter. The exact solution of the field equations has been derived. The kinematic and dynamical quantities of the model have been obtained and their evolutions have been discussed by means of their graphs. The statefinder diagnostic has been used and the age of the universe has been computed for testing the validity of the model. It has been shown that the dominant energy of the model is ordinary matter which behaves as the SCDM model at the beginning and it is a quintessence like fluid which behaves as the [Formula: see text]CDM model at late times.

Visualization of flat and curved spacetimes with simple cartography tools

Well-developed tools from cartography are adapted and used to visualize curved and flat spacetime to further understanding of relativistic effects, while interpretation of these tools is aided through their application to the familiar world map. First spacetime is cut into two-dimensional subspaces that are mapped to the Minkowski or Euclidean plane using map projections. Then, exploiting the cartographic technique of map interruptions, the two-dimensional subspaces are further cut into ‘wedges’ to minimize the distortion. The mental exercise of sewing the wedges back together aids in visualizing and interpreting the geometry of the spacetime slice. Map distortion indicators alert the reader to the inevitable effects of distortion. This wedge diagram provides a simple yet powerful tool to visualize both flat and curved spacetime geometry. It is more general than the familiar embedding diagram and avoids the pitfall of confusing the space in question with the embedding space. The wedge diagram is applied first to Minkowski spacetime with the cartographers’ azimuthal equidistant map projection and, when combined with the wedge technique, provides a simple visualization of the twin paradox. The wedge diagram is then applied to the exterior Schwarzschild spacetime to visualize the physical significance of spacetime curvature. In particular it is shown how gravitational time dilation results from intrinsic curvature of a radial-time slice of spacetime. Then this diagram is applied to the Friedmann–Robertson–Walker (FRW) spacetime revealing how expansion of the Universe results from a qualitatively similar curvature of a radial-time slice, but with the roles of space and time reversed. The analogy between the two spacetimes suggests novel interpretations of the two spacetimes. We interpret the Schwarzschild spacetime as time expanding with increasing distance from the horizon. And we interpret the FRW spacetime as the Universe expanding as the influence of the big bang peters out.

Bouncing scenario of general relativistic hydrodynamics in extended gravity

In this paper, we have framed bouncing cosmological model of the Universe in the presence of general relativistic hydrodynamics in an extended theory of gravity. The metric assumed here is the flat Friedmann–Robertson–Walker space–time and the stress energy tensor is of perfect fluid. Since general relativity (GR) has certain issues with late time cosmic speed up phenomena, here we have introduced an additional matter geometry coupling that described the extended gravity to GR. The dynamical parameters are derived and analyzed. The dynamical behavior of the equation of state parameter has been analyzed. We have observed that the bouncing behavior is mostly controlled by the coupling parameter.

Analysis of observational parameters and stability in extended teleparallel gravity

In this paper, we have investigated the stability of General Relativistic Hydrodynamics (GRHD) model in a Friedmann–Robertson–Walker space-time with the volumetric power law in teleparallel gravity. The basic equations are derived along with its thermodynamical aspects. Thermodynamic temperature and entropy density of the model are also obtained. The state finder diagnostic pair and jerk parameter are analyzed to characterize different phases of the universe and the well-known astrophysical phenomena such as look-back time, the luminosity distance with redshift are derived. The model shows an accelerated expansion with inflationary era in the early and the very late time of the cosmic evolution. The GRHD model is stable at the early phases of the universe and is unstable at late times.

Dynamical wormholes in Einstein\u2013Gauss\u2013Bonnet gravity

In the present work, we investigate evolving wormhole configurations in higher-dimensions, by adding a Gauss–Bonnet term to the standard Einstein–Hilbert action. Using a generalized Friedmann–Robertson–Walker spacetime, we derive evolving wormhole geometries by considering a constraint on Ricci scalar. In standard cosmological models, the Ricci scalar is independent of radial coordinate r and is only a function of time. We use this property to introduce a particular class of wormhole solutions for which microscopic wormholes may have been enlarged to macroscopic sizes in an expanding inflationary cosmological background. We find, for the first time, specific solutions that satisfy the weak energy condition (WEC) throughout the entire spacetime in four dimensions. In addition to this, we also present other wormhole solutions that satisfy the WEC throughout their respective evolution.

Dynamics of classes of barotropic fluids in spatially curved FRW spacetimes

In this article we perform dynamical analysis of a broad class of barotropic fluids in the spatially curved Friedmann-Robertson-Walker (FRW) spacetime background without considering the cosmological constant. The first part of our study concerns the dynamics of a fluid with an unspecified barotropic equation of state (EoS) having as the only assumption the non-negativity of the fluid's energy density. After defining a new set of dimensionless variables and a new evolution parameter, we introduce the function $\Gamma$ that encodes the EoS. In this general setup several features of the system are identified: critical points, invariant subsets and the characteristics of the function $\Gamma$, along with their cosmological interpretations. The second part of our work provides two examples with specific $\Gamma$ functions. In the first example we provide a $\Gamma$ function and then we exhibit how it can be trimmed down to a specific class of EoS through physical arguments, while in the second example we discuss the quadratic EoS studied in Phys.Rev. D {\bf 74}, 023523 (2006) by comparing our approach with their analysis.

Induced Brownian motion by the Friedmann–Robertson–Walker spacetime in the presence of a cosmic string

In this paper, we investigate the quantum Brownian motion of a massive scalar point particle induced by the FRW spacetime in the presence of a linear topological defect named cosmic string. In addition, we also consider a flat boundary orthogonal to the defect to analyze its effect on the particle’s motion. For both cases, we found exact expressions for the renormalized mean square deviation of the particle velocity, the quantity that measures the induced Brownian motion, and obtain asymptotic expressions when the point particle is near and far away from the cosmic string and the boundary. Furthermore, in both cases, there appear divergencies in the mean square deviation of the particle velocity coming from a time interval that correspond to a round trip of the massive point particle between its position and the cosmic string/flat boundary. The number of divergencies depends upon the radial position of the particle and the parameter associated with the cosmic string in the case without boundary, and upon this parameter and the radial and z positions of the particle in the case with boundary.

Dark energy model in higher-dimensional FRW universe with respect to generalized entropy of Sharma and Mittal of flat FRW space–time

In this study, we report the state parameter of dark energy in higher dimensional Friedmann–Robertson–Walker (FRW) space–time according to generalized entropy of Sharma and Mittal. In this case we analyze the state parameter of dark energy according to today’s observational evidence.

Compact Einstein multiply warped product space with nonpositive scalar curvature

In this paper, we characterize the Einstein multiply warped product space with nonpositive scalar curvature. As a result, it is shown that, if [Formula: see text] is Einstein multiple-warped product spaces with compact base and nonpositive scalar curvature, then [Formula: see text] is simply a Riemannian manifold. Next, we apply our result on Generalized Robertson–Walker space-time and Generalized Friedmann–Robertson–Walker space-time.

Viscous accelerating universe with nonlinear and logarithmic equation of state fluid

We describe the accelerated expansion of the late-time universe using a generalized equation of state (EoS) when account is taken of bulk viscosity. We assume a homogeneous and isotropic Friedmann–Robertson–Walker spacetime. Solutions of the gravitational equations for dark energy are obtained in implicit form. Characteristic properties of the universe evolution in the presence of the viscosity effects are discussed. Finally, the dynamics of the accelerated expansion of the viscous universe are discussed on the basis of a modified logarithmic-corrected EoS.

Investigating cosmology with equation of state

The aim of this paper is to investigate the field equations of modified [Formula: see text] theory of gravity, where R and [Formula: see text] represent the Ricci scalar and scalar potential, respectively. We consider the Friedmann–Robertson–Walker space–time for finding some exact solutions by using different values of equation of state parameter. In this regard, different possibilities of the exact solutions have been discussed for dust universe, radiation universe, ultra-relativistic universe, sub-relativistic universe, stiff universe, and dark energy universe. Mainly power law and exponential forms of the scale factor are chosen for the analysis.

Classes of nonminimally coupled scalar fields in spatially curved FRW spacetimes

In this work we perform a dynamical analysis of a broad class of non-minimally coupled real scalar fields in the Friedmann-Robertson-Walker (FRW) spacetime framework. The first part of our study concerns the dynamics of an unspecified positive potential in a spatially curved FRW spacetime, for which we define a new set of dimensionless variables and a new evolution parameter. In the framework of this general setup we have recognized several general features of the system, like symmetries, invariant subsets and critical points, and provide their cosmological interpretation. The second part of our work focuses on flat FRW cases for which the tracker parameter is constant, i.e. we examine specific classes of potentials. After analyzing these cases dynamically, we discuss their physical interpretation.

Scalar Casimir effect in a linearly expanding universe

We investigate quantum vacuum effects for a massive scalar field, induced by two planar boundaries in background of a linearly expanding spatially flat Friedmann–Robertson–Walker spacetime for an arbitrary number of spatial dimensions. For the Robin boundary conditions and for general curvature coupling parameter, a complete set of mode functions is presented and the related Hadamard function is evaluated. The results are specified for the most important special cases of the adiabatic and conformal vacuum states. The vacuum expectation values of the field squared and of the energy–momentum tensor are investigated for a massive conformally coupled field. The vacuum energy–momentum tensor, in addition to the diagonal components, has nonzero off-diagonal component describing energy flux along the direction perpendicular to the plates. The influence of the gravitational field on the local characteristics of the vacuum state is essential at distances from the boundaries larger than the curvature radius of the background spacetime. In contrast to the Minkowskian bulk, at large distances the boundary-induced expectation values follow as power law for both massless and massive fields. Another difference is that the Casimir forces acting on the separate plates do not coincide if the corresponding Robin coefficients are different. At large separations between the plates the decay of the forces is power law. We show that during the cosmological expansion the forces may change the sign.