Nonlinear perturbations of Friedmann-Lemaitre cosmologies with dust and a positive cosmological constant have recently attracted considerable attention. In this paper our first goal is to compare the evolution of the first and second order perturbations by determining their asymptotic behaviour at late times in ever-expanding models. We show that in the presence of spatial curvature K or a positive cosmological constant, the density perturbation approaches a finite limit both to first and second order, but the rate of approach depends on the model, being power law in the scale factor if the cosmological constant is positive but logarithmic if it is zero and and K<0. Scalar perturbations in general contain a growing and a decaying mode. We find, somewhat surprisingly, that if the cosmological constant is positive the decaying mode does not die away, i.e. it contributes on an equal footing as the growing mode to the asymptotic expression for the density perturbation. On the other hand, the future asymptotic regime of the Einstein-de Sitter universe (for which the cosmological constant and the spatial curvature are both zero) is completely different, as exemplified by the density perturbation which diverges; moreover, the second order perturbation diverges faster than the first order perturbation, which suggests that the Einstein-de Sitter universe is unstable to perturbations, and that the perturbation series do not converge towards the future. We conclude that the presence of spatial curvature or a cosmological constant stabilizes the perturbations. Our second goal is to derive an explicit expression for the second order density perturbation that can be used to study the effects of including a cosmological constant and spatial curvature.
In this thesis we first apply the 1+3 covariant description of general relativity to analyze n-fluid Friedmann-Lemaitre (FL) cosmologies; that is, homogeneous and isotropic cosmologies whose matter-energy content consists of n non-interacting fluids. We are motivated to study FL models of this type as observations suggest the physical universe is closely described by a FL model with a matter content consisting of radiation, dust and a cosmological constant. Secondly, we use the 1+3 covariant description to analyse scalar, vector and tensor perturbations of FL cosmologies containing a perfect f…
An infinite number of perturbed k=0 Friedmann cosmologies filled with dust and radiation is found. As we go up the sequence, the solutions contain an increasing number of integration functions. With the coordinate gauge adopted to co-move with the perturbed matter, the solution of a pair of coupled equations for the trace h of the metric perturbations and for the radiation density perturbations δρ_r is the key to the problem. An estimate is given of the temperature variation of the cosmic microwave background radiation due to the Sachs-Wolfe effect. It is found that the temperature fluctuation…
Primordial Black Hole Formation in Dust-Radiation Bouncing Cosmologies
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；University of Science and Technology of China（中国科学技术大学）；Universidade Estadual de Londrina（朗德里纳州立大学）；Université de Savoie, CNRS, IN2P3, LAPP（萨瓦省大学、法国国家科学研究中心、法国国家核子和粒子物理研究所、阿讷西粒子物理实验室）；Chengdu University of Technology（成都理工大学）；The University of Electronic Science and Technology of China（电子科技大学）；COSMO– Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）
In this paper, we develop in detail a fully geometrical method for deriving perturbation equations about a spatially homogeneous background. This method relies on the 3+1 splitting of the background space-time and does not use any particular set of coordinates: it is implemented in terms of geometrical quantities only, using the tensor algebra package xTensor in the xAct distribution along with the extension for perturbations xPert. Our algorithm allows one to obtain the perturbation equations for all types of homogeneous cosmologies, up to any order and in all possible gauges. As applications…
For general relativistic spacetimes filled with irrotational `dust' a generalized form of Friedmann's equations for an `effective' expansion factor $a_D (t)$ of inhomogeneous cosmologies is derived. Contrary to the standard Friedmann equations, which hold for homogeneous-isotropic cosmologies, the new equations include the `backreaction effect' of inhomogeneities on the average expansion of the model. A universal relation between `backreaction' and average scalar curvature is also given. For cosmologies whose averaged spatial scalar curvature is proportional to $a_D^{-2}$, the expansion law go…
We apply the causal interpretation of quantum mechanics to homogeneous and isotropic quantum cosmology where the sources of the gravitational field are either dust or radiation perfect fluids. We find non-singular quantum trajectories which tends to the classical one when the scale factor becomes much larger then the Planck length. In this situation, the quantum potential becomes negligible. There are no horizons. As radiation is a good approximation for the matter content of the early universe, this result suggests that the universe can be eternal due to quantum effects.
We consider flat Friedmann-Lema\^ıtre-Robertson-Walker cosmological models in the framework of general scalar-tensor theories of gravity with arbitrary coupling functions, set in the Jordan frame, in the cosmological epoch when the energy density of the ordinary dust matter dominates over the energy density of the scalar potential. Motivated by cosmological observations, we apply an approximation scheme in the regime close to the so-called limit of general relativity. The ensuing nonlinear approximate equations for the scalar field and the Hubble parameter can be solved analytically in cosmolo…
We study linear perturbations about a dust filled Bianchi Type I model with the vorticity set to zero. In comparison to linear perturbations about FLRW models, modes of perturbations about Bianchi type I models are coupled. We find that the tensor that represents the background shear needs to be degenerate in order for the scalar-mode perturbations to decouple from the rest of the flow.
The generalized Swiss - cheese model, consisting of a Lemaître - Tolman (inhomogeneous dust) region matched, by way of a comoving boundary surface, onto a Robertson-Walker background of homogeneous dust, has become a standard construction in modern cosmology. Here we ask if this construction can be made more realistic by introducing some evolution of the boundary surface. The answer we find is no. To maintain a boundary surface using the Darmois - Israel junction conditions, as opposed to the introduction of a surface layer, the boundary must remain exactly comoving. The options are to drop th…
Cosmological models typically neglect the complicated nature of the spacetime manifold at small scales in order to hypothesize idealized general relativistic solutions for describing the average dynamics of the Universe. Although these solutions are remarkably successful in accounting for data, they introduce a number of puzzles in cosmology, and their foundational assumptions are therefore important to test. In this paper, we go beyond the usual assumptions in cosmology and propose a formalism for averaging the local general relativistic spacetime on an observer's past null cone: we formulate…
Exact dynamical equations for a generic dust matter source field in a cosmological context are formulated with respect to a non-comoving Newtonian-like timelike reference congruence and investigated for internal consistency. On the basis of a lapse function $N$ (the relativistic acceleration scalar potential) which evolves along the reference congruence according to $\dot{N} = αΘN$ ($α= {const}$), we find that consistency of the quasi-Newtonian dynamical equations is not attained at the first derivative level. We then proceed to show that a self-consistent set can be obtained by linearising th…
We study the dynamical behaviour of gauge-invariant linear perturbations in spherically symmetric dust cosmologies including a cosmological constant. In contrast to spatially homogeneous FLRW models, the reduced degree of spatial symmetry causes a non-trivial dynamical coupling of gauge-invariant quantities already at first order perturbation theory and the strength and influence of this coupling on the spacetime evolution is investigated here. We present results on the underlying dynamical equations augmented by a cosmological constant and integrate them numerically. We also present a method …
The quantum theory of the Friedmann cosmological model with dust and cosmological constant ($Λ$) is not exactly solvable analytically. We apply Path Integral Monte Carlo (PIMC) techniques to study its quantum dynamics using the physical Hamiltonian corresponding to the dust field as a clock. We study (i) quantum fluctuations around classical paths and (ii) formulate the analogues of the no-boundary and tunnelling proposals and simulate the ground state wave functions. For $Λ< 0$ a unique ground state wave function exists. For $Λ> 0$ the physical Hamiltonian is not bounded below, but the path i…
Cosmological N-body simulations are now being performed using Newtonian gravity on scales larger than the Hubble radius. It is well known that a uniformly expanding, homogeneous ball of dust in Newtonian gravity satisfies the same equations as arise in relativistic FLRW cosmology, and it also is known that a correspondence between Newtonian and relativistic dust cosmologies continues to hold in linearized perturbation theory in the marginally bound/spatially flat case. Nevertheless, it is far from obvious that Newtonian gravity can provide a good global description of an inhomogeneous cosmolog…
Using the framework for solving the spherically symmetric field equations in observational coordinates given in Araujo and Stoeger (1999), their formulation and solution in the perturbed FLRW sperically symmetric case with observational data representing galaxy redshifts, number counts and observer area distances, both as functions of redshift on our past light cone, are presented. The importance of the central conditions, those which must hold on our world line C, is emphasized. In detailing the solution for these perturbations, we discuss the gauge problem and its resolution in this context,…
In this paper, we explore classes of irrotational-fluid cosmological models in the context of f(R)-gravity in an attempt to put some theoretical and mathematical restrictions on the form of the f(R) gravitational Lagrangian. In particular, we investigate the consistency of linearised dust models for shear-free cases as well as in the limiting cases when either the gravito-magnetic or gravito-elecric components of the Weyl tensor vanish. We also discuss the existence and consistency of classes of non-expanding irrotational spacetimes in f(R)-gravity.
In standard perturbation approaches and N-body simulations, inhomogeneities are described to evolve on a predefined background cosmology, commonly taken as the homogeneous-isotropic solutions of Einstein's field equations (Friedmann-Lemaître-Robertson-Walker (FLRW) cosmologies). In order to make physical sense, this background cosmology must provide a reasonable description of the effective, i.e. spatially averaged, evolution of structure inhomogeneities also in the nonlinear regime. Guided by the insights that (i) the average over an inhomogeneous distribution of matter and geometry is in gen…
We present a novel approach to construct cosmological models endowed with a particular scalar field, the stealth. The model is constructed by studying a scalar field no-minimally coupled to the gravitational field with sources; as sources, we used a perfect fluid and analyzed the simplest case of dust and the power-law cosmology. Surprisingly, we find that these stealth fields, which have no back-reaction to background space-time, have a contribution to cosmological dynamics. Furthermore, we provide analytic expressions of the stealth's contributions to the energy density in both cases, and fo…
A cosmology is considered driven by a stress-energy tensor consisting of a perfect fluid, an inhomogeneous pressure term (which we call a ``tachyonic dust'' for reasons which will become apparent) and a cosmological constant. The inflationary, radiation dominated and matter dominated eras are investigated in detail. In all three eras, the tachyonic pressure decreases with increasing radius of the universe and is thus minimal in the matter dominated era. The gravitational effects of the dust, however, may still strongly affect the universe at present time. In case the tachyonic pressure is posi…
We develop further our extension of the Ellis-Bruni covariant and gauge-invariant formalism to the general relativistic treatment of density perturbations in the presence of cosmological magnetic fields. We present detailed analysis of the kinematical and dynamical behaviour of perturbed magnetized FRW cosmologies containing fluid with non-zero pressure. We study the magnetohydrodynamical effects on the growth of density irregularities during the radiation era. Solutions are found for the evolution of density inhomogeneities on small and large scales in the presence of pressure, and some new p…
A first-order perturbation approach to $k=0$ Friedmann cosmologies filled with dust and radiation is developed. Adopting the coordinate gauge comoving with the perturbed matter, and neglecting the vorticity of the radiation, a pair of coupled equations is obtained for the trace $h$ of the metric perturbations and for the velocity potential $v$. A power series solution with upwards cutoff exists such that the leading terms for large values of the dimensionless time $ξ$ agree with the relatively growing terms of the dust solution of Sachs and Wolfe.
Nonsingular cosmologies are investigated in the framework of f(R) gravity within the first order formalism. General conditions for bounces in isotropic and homogeneous cosmology are presented. It is shown that only a quadratic curvature correction is needed to predict a bounce in a flat or to describe cyclic evolution in a curved dust-filled universe. Formalism for perturbations in these models is set up. In the simplest cases, the perturbations diverge at the turnover. Conditions to obtain smooth evolution are derived.
It is a common assumption amongst astronomers that, in the determination of the distances of remote sources from their apparent brightness, the cumulative gravitational lensing due to the matter in all the galaxies is the same, on average, as if the matter were uniformly distributed throughout the cosmos. The validity of this assumption is considered here by way of general Newtonian perturbations of Friedman-Robertson-Walker (FRW) cosmologies. The analysis is carried out in synchronous gauge, with particular attention to an additional gauge condition that must be imposed. The mean correction t…
Within the theory of the ghost-free bigravity, we present the most general cosmological solution for which the physical metric is homogeneous and isotropic, while the second metric is inhomogeneous. The solution includes a matter source and exists for any values of the theory parameters. The physical metric describes a universe with the late time acceleration due to the effective cosmological term mimicked by the graviton mass. When perturbed, this universe should rest approximately homogeneous and isotropic in space regions small compared to the graviton Compton length. In the limit where the…
We examine the dynamics of scalar perturbations in closed Friedmann-Lemaître-Robertson- Walker (FLRW) universes in the framework of Brane World theory with a timelike extra dimension. In this scenario, the unperturbed Friedmann equations contain additional terms arising from the bulk-brane interaction that implement non-singular bounces in the models with a cosmological constant and non-interacting perfect fluids. The structure of the phase-space of the models allows for two basic configurations, namely, one bounce solutions or eternal universes. Assuming that the matter content of the model i…
It has been argued that the spacetime of our universe can be accurately described by a perturbed conformal Newtonian metric, and hence even large density inhomogeneities in a dust universe can not change the observables predicted by the homogeneous dust model. In this paper we study a spherically symmetric dust model and illustrate conditions under which large spatial variations in the expansion rate can invalidate the argument.
In this paper, we first show that the Einstein field equations for all perfect-fluid FLRW cosmologies can be written as a planar dynamical system with the equation of state parameter $w$ and cosmological constant $Λ$ as parameters. An important equilibrium point of this dynamical system is the origin which represents Minkowski spacetime. It is shown that the Einstein field equations in a neigbourhood of this point are equivalent to a degenerate Bogdanov-Takens normal form. This normal form admits a set of equilibrium points that describes a set of solutions to the Einstein field equations that…
We apply a generic formalism of light propagation to linearly perturbed spherically symmetric dust models including a cosmological constant. For a comoving observer on the central worldline, we derive the equation of geodesic deviation and perform a suitable spherical harmonic decomposition. This allows to map the abstract gauge-invariant perturbation variables to well-known quantities from weak gravitational lensing like convergence or cosmic shear. The resulting set of differential equations can effectively be solved by a Green's function approach leading to line-of-sight integrals sourced b…
We investigate the Universe at the late stage of its evolution and inside the cell of uniformity 150-370 Mpc. We consider the Universe to be filled at these scales with dust like matter, a minimally coupled Galileon field and radiation. We use the mechanical approach. Therefore, the peculiar velocities of the inhomogeneities as well as the fluctuations of the other perfect fluids can be considered nonrelativistic. Such fluids are said to be coupled because they are concentrated around the inhomogeneities. We investigate the conditions under which the physical Galileon field, i.e. compatible wi…
The applications of numerical relativity to cosmology are on the rise, contributing insight into such cosmological problems as structure formation, primordial phase transitions, gravitational-wave generation, and inflation. In this paper, I present the infrastructure for the computation of inhomogeneous dust cosmologies which was used recently to measure the effect of nonlinear inhomogeneity on the cosmic expansion rate. I illustrate the code's architecture, provide evidence for its correctness in a number of familiar cosmological settings, and evaluate its parallel performance for grids of up…
We show that any accelerating Friedmann-Robertson-Walker (FRW) cosmology with equation of state w < -1/3 (and therefore not only a de Sitter stage with w =-1) exhibits three-dimensional conformal symmetry on future constant-time hypersurfaces. We also offer an alternative derivation of this result in terms of conformal Killing vectors and show that long wavelength comoving curvature perturbations of the perturbed FRW metric are just conformal Killing motions of the FRW background. We then extend theb boundary conformal symmetry to the bulk for accelerating cosmologies. Our findings indicate th…
We determine the behaviour of a time-varying fine structure 'constant' $α(t)$ during the early and late phases of universes dominated by the kinetic energy of changing $α(t)$, radiation, dust, curvature, and lambda, respectively. We show that after leaving an initial vacuum-dominated phase during which $α$ increases, $α$ remains constant in universes like our own during the radiation era, and then increases slowly, proportional to a logarithm of cosmic time, during the dust era. If the universe becomes dominated by negative curvature or a positive cosmological constant then $α$ tends rapidly t…
In this work we consider perturbations of homogeneous and hypersurface orthogonal cosmological backgrounds with local rotational symmetry (LRS), using a method based on the 1 + 1 + 2 covariant split of spacetime. The backgrounds, of LRS class II, are characterised by that the vorticity, the twist of the 2-sheets, and the magnetic part of the Weyl tensor all vanish. They include the flat Friedmann universe as a special case. The matter contents of the perturbed spacetimes are given by vorticity-free perfect fluids, but otherwise the perturbations are arbitrary and describe gravitational, shear,…
In a class of non-singular cosmologies derived from higher-order corrections to the low-energy bosonic string action, we derive evolution equations for the most general cosmological scalar, vector and tensor perturbations. In the large scale limit, the evolutions of both scalar and tensor perturbations are characterised by conserved quantities, the usual curvature perturbation in the uniform-field gauge and the tensor-type perturbed metric. The vector perturbation is not affected, being described by the conservation of the angular momentum of the fluid component in the absence of any additiona…
We investigate the integrability conditions of a class of shear-free perfect-fluid cosmological models within the framework of anisotropic fluid sources, applying our results to f(R) dark energy models. Generalising earlier general relativistic results for time-like geodesics, we extend the potential and acceleration terms of the quasi-Newtonian formulation of integrable dust cosmological models about a linearized Friedmann-Lemaitre-Robertson-Walker background and derive the equations that describe their dynamical evolutions. We show that in general, models with an anisotropic fluid source are…
The explicit form of perturbation equation for the $Ψ_4$ Weyl scalar, containing the matter source terms, is derived for general type D spacetimes. It is described in detail the particular case of the Schwarzschild spacetime using in-going penetrating coordinates. As a practical application, we focused on the emission of gravitational waves when a black hole is perturbed by a surrounding dust-like fluid matter. The symmetries of the spacetime and the simplicity of the matter source allow, by means of a spherical harmonic decomposition, to study the problem by means of a one dimensional numeric…
The density perturbations generated when the inflaton decay rate is perturbed by a light scalar field $χ$ are studied. By explicitly solving the perturbation equations for the system of two scalar fields and radiation, we show that even in low energy-scale inflation nearly scale-invariant spectra of scalar perturbations with an amplitude set by observations are obtained through the conversion of $χ$ fluctuations into adiabatic density perturbations. We demonstrate that the spectra depend on the average decay rate of the inflaton & on the inflaton fluctuations. We then apply this new mechanism …
In the framework of spatially averaged inhomogeneous cosmologies in classical General Relativity, effective Einstein equations govern the regional and the global dynamics of averaged scalar variables of cosmological models. A particular solution may be characterized by a cosmic equation of state. In this paper it is pointed out that a globally static averaged dust model is conceivable without employing a compensating cosmological constant. Much in the spirit of Einstein's original model we discuss consequences for the global, but also for the regional properties of this cosmology. We then cons…
Using a gauge-invariant formalism we derive and solve the perturbed cosmological equations for the BSBM theory of varying fine structure 'constant'. We calculate the time evolution of inhomogeneous perturbations of the fine structure constant, $\frac{δα}α$ on small and large scales with respect to the Hubble radius. In a radiation-dominated universe small inhomogeneities in $α$ will decrease on large scales but on scales smaller than the Hubble radius they will undergo stable oscillations. In a dust-dominated universe small inhomogeneous perturbations in $α$ will become constant on large scale…
Hamiltonian formalism, master functions and Darboux transformations for perturbed (interiors and exteriors of) nonrotating black holes
Université Libre de Bruxelles (ULB)（布鲁塞尔自由大学）；Instituto de Estructura de la Materia, IEM-CSIC（物质结构研究所）；Departamento de Física Teórica, Universidad Complutense de Madrid（马德里康普顿斯大学理论物理系）；Institut de Ciències de l’Espai (ICE, CSIC)（空间科学研究所）；Institut d’Estudis Espacials de Catalunya (IEEC)（加泰罗尼亚太空研究所）
We present an anisotropic cosmological model based on a new exact solution of Einstein equations. The matter content consists of an anisotropic scalar field minimally coupled to gravity and of two isotropic perfect fluids that represent dust matter and radiation. The spacetime is described by a spatially homogeneous, Bianchi type III metric with a conformal expansion. The model respects the evolution of the scale factor predicted by standard cosmology, as well as the isotropy of the cosmic microwave background. Remarkably, the introduction of the scalar field, apart from explaining the spaceti…
We use expansion-normalised variables to investigate the Bianchi type VII$_0$ model with a tilted $γ$-law perfect fluid. We emphasize the late-time asymptotic dynamical behaviour of the models and determine their asymptotic states. Unlike the other Bianchi models of solvable type, the type VII$_0$ state space is unbounded. Consequently we show that, for a general non-inflationary perfect fluid, one of the curvature variables diverges at late times, which implies that the type VII$_0$ model is not asymptotically self-similar to the future. Regarding the tilt velocity, we show that for fluids wi…
The behavior near the initial singular state of the anisotropy parameter of the arbitrary type, homogeneous and anisotropic Bianchi models is considered in the framework of the brane world cosmological models. The matter content on the brane is assumed to be an isotropic perfect cosmological fluid, obeying a barotropic equation of state. To obtain the value of the anisotropy parameter at an arbitrary moment an evolution equation is derived, describing the dynamics of the anisotropy as a function of the volume scale factor of the Universe. The general solution of this equation can be obtained i…
We undertake a rigorous study of the stability of the Cauchy horizon in the naked self-similar Lemaitre-Tolman-Bondi spacetimes under even parity linear perturbations. We use a combination of energy methods and results about L^p-spaces to determine the behaviour of the perturbations as they evolve through the spacetime. We first establish that an average of the perturbation generically diverges on the Cauchy horizon. We next introduce a rescaled version of the perturbation, and show that it is bounded and non-zero on the Cauchy horizon. This in turn shows that the perturbation itself diverges …
The problems of coarse-graining and averaging of inhomogeneous cosmologies, and their backreaction on average cosmic evolution, are reviewed from a physical viewpoint. A particular focus is placed on comparing different notions of average spatial homogeneity, and on the interpretation of observational results. Among the physical questions we consider are: the nature of an average Copernican principle, the role of Mach's principle, the issue of quasilocal gravitational energy and the different roles of spacetime, spatial and null cone averages. The observational interpretation of the timescape …
The cosmological backreaction arises when one directly averages the Einstein equations to recover an effective Robertson-Walker cosmology, rather than assuming a background a priori. While usually discussed in the context of dark energy, strictly speaking any cosmological model should be recovered from such a procedure. We apply the Buchert averaging formalism to linear Robertson-Walker universes containing matter, radiation and dark energy and evaluate numerically the discrepancies between the assumed and the averaged behaviour, finding the largest deviations for an Einstein-de Sitter univers…
A detailed study of an inhomogeneous dust cosmology contained in a $γ$-law family of perfect-fluid metrics recently presented by Mars and Senovilla is performed. The metric is shown to be the most general orthogonally transitive, Abelian, $G_2$ on $S_2$ solution admitting an additional homothety such that the self-similar group $H_3$ is of Bianchi type VI and the fluid flow is tangent to its orbits. The analogous cases with Bianchi types I, II, III, V, VIII and IX are shown to be impossible thus making this metric privileged from a mathematical viewpoint. The differential equations determining…
This thesis concerns the compatibility of inhomogeneous cosmologies with our present understanding of the universe. It is a problem of some interest to find the class of all relativistic cosmological models which are capable of providing a reasonable `fit' to the universe. This thesis, in some respects, is part of this process. We consider Stephani models, which are a generalisation of the standard Friedmann-Lemaitre-Robertson-Walker (FLRW) models, which can be thought of as FLRW models with acceleration and pressure gradients. Thus these models generalise the `dust' assumption of standard cos…
The standard model of cosmology is based on homogeneous-isotropic solutions of Einstein's equations. These solutions are known to be gravitationally unstable to local inhomogeneous perturbations, commonly described as evolving on a background given by the same solutions. In this picture, the FLRW backgrounds are taken to describe the average over inhomogeneous perturbations for all times. We study in the present article the (in)stability of FLRW dust backgrounds within a class of averaged inhomogeneous cosmologies. We examine the phase portraits of the latter, discuss their fixed points and or…
We investigate a simple inhomogeneous anisotropic cosmology (plane symmetric $G_2$ model) filled with a tilted perfect fluid undergoing velocity diffusion on a scalar field. Considered are two types of fluid: dust and radiation. We solve the system of Einstein field equations and diffusion equations numerically and demonstrate how the universe evolves towards its future asymptotic state. Also, typical time scales of characteristic processes are determined. The obtained results for dust- and radiation-filled cosmologies are compared to each other and to those in the diffusionless case, giving a…
We derive the linearly perturbed matching conditions between a Schwarzschild spacetime region with stationary and axially symmetric perturbations and a FLRW spacetime with arbitrary perturbations. The matching hypersurface is also perturbed arbitrarily and, in all cases, the perturbations are decomposed into scalars using the Hodge operator on the sphere. This allows us to write down the matching conditions in a compact way. In particular, we find that the existence of a perturbed (rotating, stationary and vacuum) Schwarzschild cavity in a perturbed FLRW universe forces the cosmological pertur…
The Einstein vacuum equations on an (n+1)-dimensional toroidal manifold $\mathbb{M}^{n+1}=\mathbb{T}^{n}\times\mathbb{R}^{+}$ reduce to a system of n-dimensional nonlinear ODEs in terms of the set of toroidal radii $(a_{i})_{i=1}^{n}$ or the radial moduli fields $(ψ_{i})_{i=1}^{n}=(\log(a_{i}(t))_{i=1}^{n}$ of the n-torus $\mathbb{T}^{n}$. This geometry is also the basis of Kasner-Bianchi-type cosmologies. The equations are trivially satisfied for static solutions $ψ_{i}^{E}=ψ^{E}$ or radii $a_{i}^{E}=a^{E}$, describing an initially static toroidal 'micro-universe' or 'vacuum bubble'. It is Ly…
We examine the radial asymptotic behavior of spherically symmetric Lemaitre-Tolman-Bondi dust models by looking at their covariant scalars along radial rays, which are spacelike geodesics parametrized by proper length $\ell$, orthogonal to the 4-velocity and to the orbits of SO(3). By introducing quasi-local scalars defined as integral functions along the rays, we obtain a complete and covariant representation of the models, leading to an initial value parametrization in which all scalars can be given by scaling laws depending on two metric scale factors and two basic initial value functions. …
We consider a generalization of the Lemaitre-Tolman-Bondi (LTB) solutions by keeping the LTB metric but replacing its dust matter source by an imperfect fluid with anisotropic pressure $Π_{ab} $. Assuming that total matter-energy density $ρ$ is the sum of a rest mass term, $\rhom$, plus a radiation $\rhor=3p$ density where $p$ is the isotropic pressure, Einstein's equations are fully integrated without having to place any previous assumption on the form of $Π_{ab} $. Three particular cases of interest are contained: the usual LTB dust solutions (the dust limit), a class of FLRW cosmologies (th…
