We show that the radial geodesic motion of a particle inside a black hole in isotropic coordinates (the Einstein-Rosen bridge) is physically different from the radial motion inside a Schwarzschild black hole. A particle enters the interior region of an Einstein-Rosen black hole which is regular and physically equivalent to the asymptotically flat exterior of a white hole, and the particle's proper time extends to infinity. Because the motion across the Einstein-Rosen bridge is unidirectional, and the surface of a black hole is the event horizon for distant observers, an Einstein-Rosen black hole is indistinguishable from a Schwarzschild black hole for such observers. Observers inside an Einstein-Rosen black hole perceive its interior as a closed universe that began when the black hole formed, with an initial radius equal to the Schwarzschild radius of the black hole $r_g$, and with an initial accelerated expansion. Therefore the model of a universe as a black hole in isotropic coordinates explains the origin of cosmic inflation. We show that this kind of inflation corresponds to the effective cosmological constant $Λ=3/r_g^2$, which, for the smallest astrophysical black holes, is $~10^{-8}m^{-2}$. If we assume that our Universe is the interior of an Einstein-Rosen black hole, astronomical observations give the time of inflation $~10^{-3}s$ and the size of the Universe at the end of the inflationary epoch $~10^{32}m$.
The question of whether the Universe is spatially homogeneous and isotropic on the largest scales is of fundamental importance to cosmology, but has not yet been answered decisively. Surprisingly, neither an isotropic primary CMB nor combined observations of luminosity distances and galaxy number counts are sufficient to establish such a result. The inclusion of the Sunyaev-Zel'dovich effect in CMB observations, however, dramatically improves this situation. We show that even a solitary observer who sees an isotropic blackbody CMB can conclude that the universe is homogeneous and isotropic in …
Usually, we assume that there is no inhomogeneity isotropic in terms of our location in our uni- verse. This assumption has not been observationally confirmed yet in sufficient accuracy, and we need to consider the possibility that there are non-negligible large-scale isotropic inhomogeneities in our universe. The existence of large-scale isotropic inhomogeneities affects the determination of the cosmological parameters. In particular, from only the distance-redshift relation, we can not dis- tinguish the inhomogeneous isotropic universe model from the homogeneous isotropic one, because of the…
The near-isotropy of the cosmic microwave background (CMB) is considered to be the strongest indication for the homogeneity and isotropy of the universe, a cornerstone of most cosmological analysis. We derive new theorems which extend the Ehlers-Geren-Sachs result that an isotropic CMB implies that the universe is either stationary or homogeneous and isotropic, and its generalisation to the almost isotropic case. We discuss why the theorems do not apply to the real universe, and why the CMB observations do not imply that the universe would be nearly homogeneous and isotropic.
We explore the symmetry group of the pressure isotropy condition in isotropic coordinates finding a rich structure. We work out some specific examples.
We derive the relationship of the redshift and the angular diameter distance to the average expansion rate for universes which are statistically homogeneous and isotropic and where the distribution evolves slowly, but which have otherwise arbitrary geometry and matter content. The relevant average expansion rate is selected by the observable redshift and the assumed symmetry properties of the spacetime. We show why light deflection and shear remain small. We write down the evolution equations for the average expansion rate and discuss the validity of the dust approximation.
A Bianchi IX Mixmaster spacetime is the most general spatially homogeneous solution of Einstein's equations and it can represent the space-averaged Universe. We introduce two novel mechanisms resulting in a Mixmaster Universe with non-singular bounces which are quasi-isotropic. A fluid with a non-linear equation of state allows non-singular bounces. Using negative anisotropic stresses successfully isotropises this Universe and mitigates the well known Mixmaster chaotic behaviour. Thus the Universe can be an eternal Mixmaster, going through an infinite series of different cycles separated by bo…
The Kottler spacetime in isotropic coordinates is known where the metric is time-dependent. In this paper, the Kottler spacetime is given in isotropic static coordinates (i.e., the metric components are time-independent). The metric is found in terms of the Jacobian elliptic functions through coordinate transformations from the Schwarzschild-(anti-)de Sitter metric. In canonical coordinates, it is known that the unparameterized spatially projected null geodesics of the Kottler and Schwarzschild spacetimes coincide. We show that in isotropic static coordinates, the refractive indices of Kottler…
The success of the moving puncture method for the numerical simulation of black hole systems can be partially explained by the properties of stationary solutions of the 1+log coordinate condition. We compute stationary 1+log slices of the Schwarzschild spacetime in isotropic coordinates in order to investigate the coordinate singularity that the numerical methods have to handle at the puncture. We present an alternative integration method to obtain isotropic coordinates that simplifies numerical integration and that gives direct access to a local expansion in the isotropic radius near the punc…
It is shown that the RTG predicts an opportunity of the intensive production of gravitons at the early stage of evolution of the homogeneous isotropic Universe. A hypothesis is suggested that the produced gas of gravitons could be just the ``dark matter'' which presently manifests itself as a ``missing mass'' in our Universe.
We investigate the turbulence effect in dark fluid universe with linear inhomogeneous equation of state. Attention is attached to two physical situations. First, we perform the perturbative analysis of turbulence and check its effects around the Big Rip. Later, treating the turbulence energy density as a part of total dark fluid, we study the stability of the system. The result shows that the stability is achieving as the energy density of turbulence decreases, changing into heat (the radiation), in perfect agreement with the avoidance of the Big Rip.
We show the existence of spatially homogeneous but anisotropic cosmological models whose cosmic microwave background temperature is exactly isotropic at one instant of time but whose rate of expansion is highly anisotropic. The existence of these models shows that the observation of a highly isotropic cosmic microwave background temperature cannot alone be used to infer that the universe is close to a Friedmann-Lemaitre model.
We study spherically symmetric spacetimes for matter distributions with isotropic pressures. We generate new exact solutions to the Einstein field equations which also contains isotropic pressures. We develop an algorithm that produces a new solution if a particular solution is known. The algorithm leads to a nonlinear Bernoulli equation which can be integrated in terms of arbitrary functions. We use a conformally flat metric to show that the integrals may be expressed in terms of elementary functions. It is important to note that we utilise isotropic coordinates unlike other treatments.
The main objective of this work, is to show two inequivalent methods to obtain new spherical symmetric solutions of Einstein's Equations with anisotropy in the pressures in isotropic coordinates. This was done inspired by the MGD method, which is known to be valid for line elements in Schwarzschild coordinates. As example, we obtained four analytical solutions using Gold III as seed solution. Two solutions, out of four, (one for each algorithm), satisfy the physical acceptability conditions.
A fundamental assumption in the standard model of cosmology is that the Universe is isotropic on large scales. Breaking this assumption leads to a set of solutions to Einstein's field equations, known as Bianchi cosmologies, only a subset of which have ever been tested against data. For the first time, we consider all degrees of freedom in these solutions to conduct a general test of isotropy using cosmic microwave background temperature and polarization data from Planck. For the vector mode (associated with vorticity), we obtain a limit on the anisotropic expansion of $(σ_V/H)_0 < 4.7 \times …
We argue that all homogeneous and isotropic solutions in nonlinear massive gravity are unstable. For this purpose, we study the propagating modes on a Bianchi type--I manifold. We analyze their kinetic terms and dispersion relations as the background manifold approaches the homogeneous and isotropic limit. We show that in this limit, at least one ghost always exists and that its frequency tends to vanish for large scales, meaning that it cannot be integrated out from the low energy effective theory. This ghost mode is interpreted as a leading nonlinear perturbation around a homogeneous and iso…
We find various asymptotic limits of universes containing two interacting fluids which interact and exchange energy. We study the finite-time singularities that may develop in these cosmologies and obtain the asymptotic behaviours of the solutions near such blow up regimes.
We study the particular case in which Extended Geometric Deformation does consists of consecutive deformations of temporal and spatial components of the metric, in Schwarzschild-like and isotropic coordinates. In the latter, we present two inequivalent ways to perform this 2-steps GD. This was done in such a way that the method may be applied to different seed solutions. As an example, we use Tolman IV as seed solution, in order to obtain two inequivalent physical solutions with anisotropy in the pressures in Schwarzschild-like coordinates. In the isotropic sector, we obtained four different s…
We study the cosmological evolutions of the equation of state (EoS) for the universe in the homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) space-time. In particular, we reconstruct the cyclic universes by using the Weierstrass and Jacobian elliptic functions. It is explicitly illustrated that in several models the universe always stays in the non-phantom (quintessence) phase, whereas there also exist models in which the crossing of the phantom divide can be realized in the reconstructed cyclic universes.
In this work, an exact solution of Einstein's field equations in isotropic coordinates for anisotropic matter distribution is obtained by considering a particular metric choice of metric potential $g_{rr}$. To check the feasibility of the model, we have investigated all the physical characteristics of a realistic star. It is found that the model is potentially stable, and the adiabatic index is greater than $\frac{4}{3}$. The model have been analysed for Compact star \textbf{4U 1538-52}.
We introduce the redshift spherical shell energy (RSSE), which can be used to test in the redshift space the radial inhomogeneity of an isotropic universe, providing additional constraints for LTB models, and a more general test of cosmic homogeneity.
A solution of the linearized Einstein's equations for a spherically symmetric perturbation of the ultrarelativistic fluid in the homogeneous and isotropic universe is obtained. Conditions on the boundary of the perturbation are discussed. The examples of particle-like and wave-like solutions are given.
We demonstrate how one should transform correctly quasi-isotropic coordinates to Weyl-Papapetrou coordinates in order to compare the metric around a rotating star that has been constructed numerically in the former coordinates with an axially symmetric stationary metric that is given through an analytical form in the latter coordinates. Since a stationary metric associated with an isolated object that is built numerically partly refers to a non-vacuum solution (interior of the star) the transformation of its coordinates to Weyl-Papapetrou coordinates, which are usually used to describe vacuum …
We construct a model of a universe filled with a perfect fluid with isotropic particle pressure. The anisotropic plane symmetric Kasner spacetime is used as a seed metric and through a conformal mapping a perfect fluid is generated. The model is inhomogeneous, irrotational, shearing and accelerating. For negative time, the universe is expanding while for positive time it is collapsing. With the aid of graphical three dimensional plots it is established that the density and pressure hypersurfaces are smooth and singularity free. Additionally the sound-speed index is computed and the fluid obeys…
In this letter we will show that, contrary to what is widely believed, an almost isotropic cosmic microwave background (CMB) temperature does not imply that the universe is ``close to a Friedmann-Lemaitre universe''. There are two important manifestations of anisotropy in the geometry of the universe, (i) the anisotropy in the overall expansion, and (ii) the intrinsic anisotropy of the gravitational field, described by the Weyl curvature tensor, although the former usually receives more attention than the latter in the astrophysical literature. Here we consider a class of spatially homogeneous…
The relation between angular diameter distance and redshift in a spherically symmetric dust-shell universe is studied. This model has large inhomogeneities of matter distribution on small scales. We have discovered that the relation agrees with that of an appropriate Friedmann-Lemaitre(FL) model if we set a ``homogeneous'' expansion law and a ``homogeneous'' averaged density field. This will support the averaging hypothesis that a universe looks like a FL model in spite of small-scale fluctuations of density field, if its averaged density field is homogeneous on large scales.
We investigate the time evolution of a homogeneous isotropic universe which consists of a perfect gas governed by the Einstein-Euler-de Sitter equations. Under suitable assumptions on the equation of state and assumptions on the present states, we give a mathematically rigorous proof of the existence of the Big Bang at the finite past and expanding of the universe in the course to the infinite future.
We investigate the dynamical nature of the collapse process of a spherically symmetric star in quasi-static hydrodynamical equilibrium. The star collapses from an initial static configuration by dissipating energy in the form of a radial heat flux. The dissipation ensures that the singularity is never formed and the stellar mass completely evaporates over a finite time.
We investigated the behavior of an open isotropic universe generated by a scalar field which couples with background curvature nonminimally with the coupling constant $ξ$. In particular we focus on the situation where the initial value for the scalar field $ϕ_{\rm in}$ is greater than the critical value ${\hat ϕ}_c$=${m_p}/{\sqrt{8πξ(1-6ξ)}}$. The behavior is similar to an open de Sitter universe with $k=-1$ with a negative cosmological constant $Λ<0$. It is found that the universe will collapse eventually to a singularity and thus has a finite extent in time in the future. Furthermore, there …
McVittie's solution of Einstein's field equations, representing a point mass embedded into an isotropic universe, possesses a scalar curvature singularity at proper radius $R=2m$. The singularity is space-like and precedes, in the expanding case, all other events in the space-time. It is shown here that this singularity is gravitationally weak, and the possible structure of the region $R\leq 2m$ is investigated. A characterization of this solution which does not involve asymptotics is given.
We study the evolution of linear density perturbations in a large spherical void universe which accounts for the acceleration of the cosmic volume expansion without introducing dark energy. The density contrast of this void is not large within the light cone of an observer at the center of the void. Therefore, we describe the void structure as a perturbation with a dimensionless small parameter $κ$ in a homogeneous and isotropic universe within the region observable for the observer. We introduce additional anisotropic perturbations with a dimensionless small parameter $ε$, whose evolution is …
Some basic theorems on Killing vector fields are reviewed. In particular, the topic of a constant-curvature space is examined. A detailed proof is given for a theorem describing the most general form of the metric of a homogeneous isotropic space-time. Although this theorem can be considered to be commonly known, its complete proof is difficult to find in the literature. An example metric is presented such that all its spatial cross sections correspond to constant-curvature spaces, but it is not homogeneous and isotropic as a whole. An equivalent definition of a homogeneous and isotropic space…
We study the homogeneous and anisotropic dynamics of pseudoscalar inflation coupled to an SU($N$) gauge field. To see how the initially anisotropic universe is isotropized in such an inflation model, we derive the equations to obtain axisymmetric SU($N$) gauge field configurations in Bianchi type-I geometry and discuss a method to identify their isotropic subsets which are the candidates of their late-time attractor. Each isotropic solution is characterized by the corresponding SU(2) subalgebra of the SU($N$) algebra. It is shown numerically that the isotropic universe is a universal late-time…
The relation between the angular diameter distance and redshift in a spherically symmetric dust-shell universe is studied. We have discovered that the relation agrees with that of an appropriate Friedmann-Lemaitre (FL) model if we set a ``homogeneous'' expansion law and a ``homogeneous'' averaged density field. This will support the averaging hypothesis that a universe looks like a FL model in spite of small-scale fluctuations of density field, if its averaged density field is homogeneous on large scales. We also study the connection of the proper mass of a shell with the mass of gravitational…
As an alternative to dark energy it has been suggested that we may be at the center of an inhomogeneous isotropic universe described by a Lemaitre-Tolman-Bondi (LTB) solution of Einstein's field equations. In order to test this hypothesis we calculate the general analytical formula to fifth order for the redshift spherical shell mass. Using the same analytical method we write the metric in the light-cone by introducing a gauge invariant quantity $G(z)$ which together with the luminosity distance $D_L(z)$ completely determine the light-cone geometry of a LTB model.
We study a broad class of isotropic vacuum cosmologies in fourth-order gravity under the condition that the gravitational Lagrangian be scale-invariant or almost scale-invariant. The gravitational Lagrangians considered will be of the form L = f(R) + k(G) where R and G are the Ricci and Gauss-Bonnet scalars respectively. Specifically we take f(R) = R^2n and k(G) = G^n or k(G) = G ln G. We find solutions in closed form for a spatially flat Friedmann space-time and interpret their asymptotic early-time and late-time behaviour as well as their inflationary stages. One unique example which we disc…
We present a matrix method for obtaining new classes of exact solutions for Einstein's equations representing static perfect fluid spheres. By means of a matrix transformation, we reduce Einstein's equations to two independent Riccati type differential equations for which three classes of solutions are obtained. One class of the solutions corresponding to the linear barotropic type fluid with an equation of state $p=γρ$ is discussed in detail.
This paper is devoted to study the cosmological behavior of homogeneous and isotropic universe model in the context of $f(R,T^φ)$ gravity where $φ$ is the scalar field. For this purpose, we follow the first order formalism defined by $H=W(φ)$. We evaluate Hubble parameter, effective equation of state parameter $(ω^{eff})$, deceleration parameter and potential of scalar field for three different values of $W(φ)$. We obtain phantom era in some cases for the early times. It is found that exponential expression of $W(φ)$ yields $ω^{eff}$ independent of time for flat universe and independent of mod…
We give a simple example of spacetime metric, illustrating that homogeneity and isotropy of space slices at all moments of time is not obligatory lifted to a full system of six Killing vector fields in spacetime, thus it cannot be interpreted as a symmetry of a four dimensional metric. The metric depends on two arbitrary and independent functions of time. One of these functions is the usual scale factor. The second function cannot be removed by coordinate transformations. We prove that it must be equal to zero, if the metric satisfies Einstein's equations and the matter energy momentum tensor …
We construct metric perturbations of two families of isotropic expanding universes describing gravitational waves propagating through these universes. The waves are non--planar and owe their wave front expansion solely to the expansion of the universes. The presence of this radiation leads to a small perturbation of the perfect fluid matter content of the universes by the appearance of an anisotropic stress. We then construct exact models of gravity waves in these universes. In this case the matter content of the models consists of the perfect fluid matter supplemented by anisotropic stress an…
We analyze some relevant semiclassical and quantum features of the implementation of Polymer Quantum Mechanics to the phenomenology of the flat isotropic Universe. We firstly investigate a parallelism between the semiclassical polymer dynamics of the flat isotropic Universe, as reduced to the effect of a modified simplectic structure, and the so-called Generalized Uncertainty Principle. We show how the difference in the sign of the fundamental Poisson bracket is reflected in a sign of the modified source term in the Friedmann equation, responsible for the removal of the initial singularity in …
The variant of quasiclassical (half-quantum) theory of gravity in strong gravitational field is presented. The exact solution of the problem of the renormalized energy-momentum tensor calculation is performed in terms of non-local operator-signed function. The procedure of quasilocalization is proposed, which leads to the equations of non-equilibrium thermodynamics for temperature and curvature. The effects of induced particle creation and media polarization are taking into account and used to solve the problem of non-Einstein's branches damping. The problem of Universe creation from "nothing"…
We explore the character of finite-time singularities that are possible to arise in FRW universes and in specific braneworld configurations. For FRW universes, we derive a first classification of singularities that is based on the behaviour of the Hubble rate. We further extend and complete this classification with the use of the Bel-Robinson energy. The braneworld models that we study consist of a three-brane embedded in a five-dimensional bulk space that is inhabited by a scalar field or a perfect fluid. Our analysis that is performed with the method of asymptotic splittings shows that these…
We present a spherically symmetric solution of the general relativistic field equations in isotropic coordinates for anisotropic neutral fluid, compatible with a super dense star modeling by considering a specific choice of anisotropy factor that includes a positive constant defined as anisotropy parameter, which varies the relation between the radial and tangential pressure. Further, we have constructed a super-dense star model with all degree of suitability. We have found that the maximum mass decreases with the increase of anisotropy parameter. The robustness of our result is that it matche…
A method for constructing statistically homogeneous and isotropic perfect fluid universe models with significant cosmic backreaction is proposed. The method is illustrated using a simplified model constructed as a Swiss-cheese model with Lemaitre-Tolman-Bondi structures. The model exhibits significant cosmic backreaction and is used to study methods proposed in the literature for relating volume averaged quantities with observations. The comparison shows a poor agreement between exact redshift-distance relations and the relations predicted by schemes based on volume averages. Most of these dev…
We derive the redshift and the angular diameter distance in rotationless dust universes which are statistically homogeneous and isotropic, but have otherwise arbitrary geometry. The calculation from first principles shows that the Dyer-Roeder approximation does not correctly describe the effect of clumping. Instead, the redshift and the distance are determined by the average expansion rate, the matter density today and the null geodesic shear. In particular, the position of the CMB peaks is consistent with significant spatial curvature provided the expansion history is sufficiently close to th…
This paper has been withdrawn by the authors due to an incorrect statement on the viability of the Robinson-Wilczek method when applied to the case when the metric determinant vanishes at the horizon. This paper has been replaced by arXiv:0803.1338 [hep-th].
As first part of this work, experimental information about the decay of isotropic turbulence in ordinary hydrodynamics, u^2(t) proportional to t^{-6/5}, is used as input in FRW equations in order to investigate how an initial fraction f of turbulent kinetic energy in the cosmic fluid influences the cosmological development in the late, quintessence/phantom, universe. First order perturbative theory to the first order in f is employed. It turns out that both in the Hubble factor, and in the energy density, the influence from the turbulence fades away at late times. The divergences in these quan…
We review the evolution of a spatially homogeneous and isotropic universe described by a Friedmann-Robertson-Walker spacetime filled with a collisionless, neutral, simple, massive gas. The gas is described by a one-particle distribution function which satisfies the Liouville equation and is assumed to be homogeneous and isotropic. Making use of the isometries of the spacetime, we define precisely the homogeneity and isotropicity property of the distribution function, and based on this definition we give a concise derivation of the most general family of such distribution functions. For this fa…
We investigate the dynamics of the spatially flat universes submitted to isotropic tidal forces and adiabatic expansion under Einstein's equations. Surprisingly, the tendency to a high Hubble anisotropy at late times starts to appear as far as we assume the strong energy condition, a characteristic which becomes dominant in the radiation era and even more stringent under a stiff matter regime. We introduce the parameter b which measures the relative change in the magnitudes of the Hubble anisotropy and the scale factor and use it to show that the anisotropies must be kept small as long as we a…
Lorentz gauge theory of gravity was recently introduced. We study the homogeneous and isotropic universe of this theory. It is shown that some time after the matter in the universe is diluted enough, at $z \sim 0.6$, the decelerating expansion shifts spontaneously to an accelerating one without a dark energy. We discuss that Lorentz gauge theory puts no constraint on the total energy content of the universe at present time and therefore the magnitude of vacuum energy predicted by field theory is not contradictory anymore. It is demonstrated that in this theory the limit on the number of relati…
Criteria which a space-time must satisfy to represent a point mass embedded in an open Robertson--Walker (RW) universe are given. It is shown that McVittie's solution in the case $k=0$ satisfies these criteria, but does not in the case $k=-1$. Existence of a solution for the case $k=-1$ is proven and its representation in terms of an elliptic integral is given. The following properties of this and McVittie's $k=0$ solution are studied; uniqueness, behaviour at future null infinity, recovery of the RW and Schwarzschild limits, compliance with energy conditions and the occurence of singularities…
We investigate the quantum dynamics of the quasi-isotropic inflationary solution. This is achieved by deriving the Lagrangian and Hamiltonian for both the FLRW background and the inhomogeneous correction, via an expansion of the Einstein-Hilbert action up to second order in the perturbation amplitudes. We do this in a gauge invariant fashion adopting the Mukhanov-Sasaki variable for the scalar degree of freedom. Then we construct the quantum dynamics in terms of a semiclassical WKB scenario for which the inhomogeneous component of the Universe is treated as a "small" quantum subsystem, evolvin…
We present a new class of spherically symmetric spacetimes for matter distributions with anisotropic pressures in the presence of an electric field. The equation of state for the matter distribution is linear. A class of new exact solutions is found to the Einstein-Maxwell system of equations with an isotropic form of the line element. We achieve this by specifying particular forms for one of the gravitational potentials and the electric field intensity. We regain the masses of the stars PSR J1614-2230, Vela X-1, PSR J1903+327, 4U 1820-30 and SAX J1808.4-3658 for particular parameter values. A…
The "dark energy" problem is investigated in the framework of the Poincare gauge theory of gravity in 4-dimensional Riemann-Cartan space-time. By using general expression for gravitational Lagrangian homogeneous isotropic cosmological models with pseudoscalar torsion function are built and investigated. It is shown that by certain restrictions on indefinite parameters of gravitational Lagrangian the cosmological equations at asymptotics contain effective cosmological constant and can lead to observable acceleration of cosmological expansion. This effect has geometrical nature and is connected …
