We generalize the superposition principle for time-symmetric initial data of black hole spacetimes to (anti-)de Sitter cosmologies in terms of an eigenvalue problem $Δ_gϕ={1/8}(R_g-2Λ)ϕ$ for a conformal scale $ϕ$ applied to a metric $g_{ij}$ with constant three-curvature $R_g$. Here, $R_g=0,2$ in the Brill-Lindquist and, respectively, Misner construction of multihole solutions for $Λ=0$. For de Sitter and anti-de Sitter cosmologies, we express the result for $R_g=0$ in incomplete elliptic functions. The topology of a black hole in de Sitter space can be extended into an infinite tower of universes, across the turning points at the black hole and cosmological event horizons. Superposition introduces binary black holes for small separations and binary universes for separations large relative to the cosmological event horizon. The evolution of the metric can be described by a hyperbolic system of equations with curvature-driven lapse function, of alternating sign at successive cosmologies. The computational problem of interacting black hole-universes is conceivably of interest to early cosmology when $Λ$ was large and black holes were of mass $<{1/3}Λ^{-1/2}$, here facilitated by a metric which is singularity-free and smooth everywhere on real coordinate space.
The study of gravitational waves in the presence of a cosmological constant has led to interesting forms of the de Sitter and anti-de Sitter line elements based on families of null hypersurfaces. The forms are interesting because they focus attention on the geometry of null hypersurfaces in space-times of constant curvature. Two examples are worked out in some detail. The first originated in the study of collisions of impulsive gravitational waves in which the post-collision space-time is a solution of Einstein's field equations with a cosmological constant, and the second originated in the ge…
There is constructed, for each member of a one-parameter family of cosmological models, which is obtained from the Kottler-Schwarzschild-de Sitter spacetime by identification under discrete isometries, a slicing by spherically symmetric Cauchy hypersurfaces of constant mean curvature. These slicings are unique up to the action of the static Killing vector. Analytical and numerical results are found as to when different leaves of these slicings do not intersect, i.e. when the slicings form foliations.
Two metric perturbations in Einstein-Cartan cosmology are examined.The first case is the scalar mode perturbation of de Sitter metric in Einstein-Cartan cosmology.In this case small perturbations of de Sitter metric shows that this metric is unstable for a universe with spin-torsion density and dilaton fields.In the second case we show that the Friedmann metric in the same space is also unstable under the small perturbations.
In this paper I examine the phase space dynamics in the framework of Non-Projectable Hořava-Lifshitz bouncing cosmologies. By considering a closed Friedmann-Lemaître-Robertson-Walker (FLRW) geometry, the first integral contains a correction term that leads to nonsingular metastable bounces in the early evolution of the universe. The matter content of the model is a massive conformally coupled scalar field, dust and radiation. A nonvanishing cosmological constant connected to a de Sitter attractor in the phase space is also assumed. In narrow windows of the parameter space, labeled by an intege…
We study, using Mean Curvature Flow methods, 3+1 dimensional cosmologies with a positive cosmological constant, matter satisfying the dominant and the strong energy conditions, and with spatial slices that can be foliated by 2-dimensional surfaces that are the closed orbits of a symmetry group. If these surfaces have non-positive Euler characteristic (or in the case of 2-spheres, if the initial 2-spheres are large enough) and also if the initial spatial slice is expanding everywhere, then we prove that asymptotically the spacetime becomes physically indistinguishable from de Sitter space on ar…
In the framework of massive gravity with a de Sitter reference metric, we study homogeneous and isotropic solutions with positive spatial curvature. Remarkably, we find that bounces can occur when cosmological matter satisfies the strong energy condition, in contrast to what happens in classical general relativity. This is due to the presence in the Friedmann equations of additional terms, which depend on the scale factor and its derivatives and can be interpreted as an effective fluid. We present a detailed study of the system using a phase space analysis. After having identified the fixed po…
In this global study of solutions to the linear wave equation on Schwarzschild de Sitter spacetimes we attend to the cosmological region of spacetime which is bounded in the past by cosmological horizons and to the future by a spacelike hypersurface at infinity. We prove an energy estimate capturing the expansion of that region which combined with earlier results for the static region yields a global boundedness result for linear waves. It asserts that a general finite energy solution to the global initial value problem has a limit on the future boundary at infinity that can be viewed as a fun…
The stability of the de Sitter era of cosmic expansion in spatially curved homogeneous isotropic universes is studied. The source of the gravitational field is an imperfect fluid such that the parameters that characterize it may change with time. In this way we extend our previous analysis for spatially-flat spaces as well as the work of Barrow.
We construct two types of phase spaces for asymptotically de Sitter Einstein-Hilbert gravity in each spacetime dimension $d \ge 3$. One type contains solutions asymptotic to the expanding spatially-flat ($k=0$) cosmological patch of de Sitter space while the other is asymptotic to the expanding hyperbolic $(k=-1)$ patch. Each phase space has a non-trivial asymptotic symmetry group (ASG) which includes the isometry group of the corresponding de Sitter patch. For $d=3$ and $k=-1$ our ASG also contains additional generators and leads to a Virasoro algebra with vanishing central charge. Furthermor…
Spherical collapse has turned out to be a successful semi-analytic model to study structure formation in different DE models and theories of gravity. Nevertheless, the process of virialization is commonly studied on the basis of the virial theorem of classical mechanics. In the present paper, a fully generally-relativistic virial theorem based on the Tolman-Oppenheimer-Volkoff (TOV) solution for homogeneous, perfect-fluid spheres is constructed for the Einstein-de Sitter and ΛCDM cosmologies. We investigate the accuracy of classical virialization studies on cosmological scales and consider vir…
We shall discuss cosmological models in extended theories of gravitation. We shall define a surface, called the model surface, in the space of observable parameters which characterises families of theories. We also show how this surface can be used to compare with observations. The model surface can potentially be used to falsify whole families of models instead reasoning on a single model basis as it is usually done by best fit arguments with observations.
We study, using Mean Curvature Flow methods, 2+1 dimensional cosmologies with a positive cosmological constant and matter satisfying the dominant and the strong energy conditions. If the spatial slices are compact with non-positive Euler characteristic and are initially expanding everywhere, then we prove that the spatial slices reach infinite volume, asymptotically converge on average to de Sitter and they become, almost everywhere, physically indistinguishable from de Sitter. This holds true notwithstanding the presence of initial arbitrarily-large density fluctuations and the formation of b…
We analyse possible cosmological scenarios on a brane where the brane acts as a dynamical boundary of various black holes with anti-de Sitter or de Sitter asymptotics. In many cases, the brane is found to describe completely non-singular universe. In some cases, quantum gravity era of the brane-universe can also be avoided by properly tuning bulk parameters. We further discuss the creation of a brane-universe by studying its wave function. This is done by employing Wheeler-De Witt equation in the mini superspace formalism.
Recent observations in cosmology indicate an accelerating expansion of the universe postulated to arise from some form of dark energy, the paradigm being positive cosmological constant. De Sitter spacetime is the well-known isotropic solution to the Einstein equations with cosmological constant. However, as discussed here, it is not the most general, locally isotropic solution. One can construct an infinite family of such solutions, designer de Sitter spacetimes, which are everywhere locally isometric to a region of de Sitter spacetime. However, the global dynamics of these designer cosmologie…
We present an analysis of the phase space of cosmological models based on a non minimal coupling between the geometry and a fermionic condensate. We obtain that the strong constraint coming from the Dirac equations allows a detailed design of the cosmology of these models and at the same time guarantees an evolution towards a state indistinguishable from General Relativistic cosmological models. In this light, we show how the use of some specific potentials is able to reproduce naturally two de Sitter phases separated by a power law expansion which could be an interesting model for the unifica…
In the context of Horndeski cosmologies, we consider a dynamical adjustment mechanism able to screen any value of the vacuum energy of the matter fields leading to a fixed de Sitter geometry. Thus, we present the most general scalar-tensor cosmological models without higher than second order derivatives in the field equation that have a fixed spatially flat de Sitter critical point for any kind of material content or vacuum energy. These models allow us to understand the current accelerated expansion of the universe as the result of the evolution towards the critical point when it is an attrac…
We investigate the cosmological production of gravitational waves in a nonsingular flat cosmology powered by a "running vacuum" energy density described by $ρ_Λ\equivρ_Λ(H)$, a phenomenological expression potentially linked with the renormalization group approach in quantum field theory in curved spacetimes. The model can be interpreted as a particular case of the class recently discussed by Perico et al. (Phys. Rev. D {\bf 88}, 063531, 2013) which is termed complete in the sense that the cosmic evolution occurs between two extreme de Sitter stages (early and late time de Sitter phases). {The …
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 review a dynamical dark energy model scarcely studied in the literature and we introduce two possible generalizations. We discuss separately the behavior of the original model and a minimal extension of it by exploring some early and late times limits, we find that the cosmic components are related by their parameters state. In order to have access to the phantom regime we present two dark energy densities inspired from the holographic approach and from the emergent entropic forces model in the early universe. For the first case we obtain a Type III singularity and in the second proposal we…
Pontificia Universidad Javeriana（波哥大耶稣会天主教大学）；ICTP–South American Institute for Fundamental Research（国际理论物理中心南美基础研究所）；Universidade Federal de São Paulo (UNIFESP)（圣保罗联邦大学）
Electrodynamics for self-interacting scalar fields in spatially flat Friedmann-Robertson-Walker space-times is studied. The corresponding one-loop field equation for the expectation value of the complex scalar field in the conformal vacuum is derived. For exponentially expanding universes, the equations for the Bogoliubov coefficients describing the coupling of the scalar field to gravity are solved numerically. They yield a non-local correction to the Coleman-Weinberg effective potential which does not modify the pattern of minima found in static de Sitter space. Such a correction contains a …
A Quantum Gravitational Mechanism for Isotropization of de Sitter Cosmologies
Brown University（布朗大学）；Imperial College London（帝国理工学院）；Massachusetts Institute of Technology（麻省理工学院）；Harvard University（哈佛大学）；Flatiron Institute（平顿研究所）
A new gauge-invariant criterion for stability against inhomogeneous perturbations of de Sitter space is applied to scenarios of dark energy and inflation in scalar-tensor gravity. The results extend previous studies.
Recent work on $N=2$ supersymmetric Bianchi type IX cosmologies coupled to a scalar field is extended to a general treatment of homogeneous quantum cosmologies with explicitely solvable momentum constraints, i.e. Bianchi types I, II, VII, VIII besides the Bianchi type IX, and special cases, namely the Friedmann universes, the Kantowski-Sachs space, and Taub-NUT space. Besides the earlier explicit solution of the Wheeler DeWitt equation for Bianchi type IX, describing a virtual wormhole fluctuation, an additional explicit solution is given and identified with the `no-boundary state'.
It has been proposed that on (anti)-de Sitter background, the Heisenberg uncertainty principle should be modified by the introduction of a term proportional to the cosmological constant. We show that this modification of the uncertainty principle can be derived straightforwardly from the geometric properties of (anti)-de Sitter spacetime. We also discuss the connection between the so-called extended generalized uncertainty principle and triply special relativity.
Painlevé-Gullstrand coordinates, a very useful tool in spherical horizon thermodynamics, fail in anti-de Sitter space and in the inner region of Reissner-Nordström. We predict this breakdown to occur in any region containing negative Misner-Sharp-Hernandez quasilocal mass because of repulsive gravity stopping the motion of PG observers in radial free fall with zero initial velocity. PG coordinates break down also in the static Einstein universe for completely different reasons. The more general Martel-Poisson family of charts, which normally has PG coordinates as a limit, is reported for stati…
An effective Lagrangian approach based on an extended Einstein-Aether (EA) model is presented and formulated in a generic non flat Fridman-Lemaitre-Robertson-Walker (FLRW) space-time. For a flat FLRW space-time, a Friedmann equation similar to the one obtained in Quantum Loop Cosmology (QLC) is reproduced, with related non singular bounce solution. Finally, the Static Spherically Symmetric (SSS) solutions are investigated.
We have examined, repeated and extended earlier numerical calculations of Berger and Moncrief for the evolution of unpolarized Gowdy T3 cosmological models. Our results are consistent with theirs and we support their claim that the models exhibit AVTD behaviour, even though spatial derivatives cannot be neglected. The behaviour of the curvature invariants and the formation of structure through evolution both backwards and forwards in time is discussed.
The conformal equivalence of some cosmological models in Brans-Dicke theory to general relativistic cosmologies with a scalar field is discussed. In the case of radiation-dominated universes, it is shown that the presence of the scalar field has a negligible impact upon the evolution of the models in the Einstein frame. It is also shown that power-law inflation in general relativity, which is conformal to ``extended'' power-law inflation in Brans-Dicke theory, is not a unique attractor for expanding closed universes, but rather that the occurence of inflation depends upon the initial kinetic e…
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…
We analyze the effect of Planck-scale modified radiation equation of state on the Reissner-Nodström-anti-de Sitter black hole inspired by Kiselev's ansatz. Deformed thermodynamic quantities are found, phase transitions and black holes as heat engines are described for the Carnot and square cycles. Non-trivial differences between linear and quadratic Planck-scale corrections are discussed in detail.
For dynamical systems of dimension three or more the question of integrability or nonintegrability is extended by the possibility of chaotic behaviour in the general solution. We determine the integrability of isotropic cosmological models in general relativity and string theory with a variety of matter terms, by a performance of the Painlevé analysis in an effort to examine whether or not there exists a Laurent expansion of the solution about a movable pole which contains the number of arbitrary constants necessary for a general solution.
The no-boundary proposal provides a compelling theory for the initial conditions of our universe. We study the implications of such initial conditions for ekpyrotic and cyclic cosmologies. These cosmologies allow for the existence of a new type of "ekpyrotic instanton", which describes the creation of a universe in the ekpyrotic contraction phase. Remarkably, we find that the ekpyrotic attractor can explain how the universe became classical. In a cyclic context, in addition to the ekpyrotic instantons there exist de Sitter-like instantons describing the emergence of the universe in the dark en…
We discuss the production and evolution of cosmological gravitons showing how the cosmological background affects their dynamics. Besides, the detection of cosmological gravitons could constitute an extremely important signature to discriminate among different cosmological models. Here we consider the cases of scalar-tensor gravity and $f(R)$ gravity where it is demonstrated the amplification of graviton amplitude changes if compared with General Relativity. Possible observational constraints are discussed.
In present paper we construct the classical and minisuperspace quantum models of an extended charged particle. The modelling is based on the radiation fluid singular hypersurface filled with physical vacuum. We demonstrate that both at classical and quantum levels such a model can have equilibrium states at the radius equal to the classical radius of a charged particle. In the cosmological context the model could be considered also as the primary stationary state, having the huge internal energy being nonobservable for an external observer, from which the Universe was born by virtue of the qua…
The gravitino problem is investigated in the framework of Extended Gravity cosmologies. In particular, we consider $f(R)$ gravity, the most natural extension of the Hilbert-Einstein action, and $f(\cal T)$ gravity, the extension of teleparallel equivalent gravity. Since in these theories the expansion laws of the Universe are modified, as compared to the standard $Λ$CDM cosmology, it follows that also the thermal history of particles gets modified. We show that $f(R)$ models allow to avoid the late abundance of gravitinos. In particular, we found that for an appropriate choice of the parameter…
We use phase space method to study possible consequences of fixed points in flat FLRW models. One of these consequences is that a fluid with a finite sound speed, or a differentiable pressure, reaches a fixed point in an infinite time and has no finite-time singularities of types I, II and III described in hep-th/0501025. It is impossible for such a fluid to cross the phantom divide in a finite time. We show that a divergent $dp/dH$, or a speed of sound is necessary but not sufficient condition for phantom crossing. We use pressure properties, such as asymptotic behavior and fixed points, to q…
The throttling process of the Kerr-Newman-anti-de Sitter (KN-AdS) black holes is systematically studied in the extended phase space. In this framework, the cosmological constant is interpreted as a varying thermodynamic pressure, and the black hole mass is identified with enthalpy. The throttling process is essentially an isenthalpic (i.e., constant-mass) process for the KN-AdS black holes. The Joule-Thomson coefficient, inversion temperature, inversion curve, and isenthalpic curve are investigated in order, with both analytical and numerical methods. It is found that there are no maximum inve…
One possible explanation for the present observed acceleration of the Universe is the breakdown of homogeneity and isotropy due to the formation of non-linear structures. How inhomogeneities affect the averaged cosmological expansion rate and lead to late-time acceleration is generally considered to be due to some backreaction mechanism. General Relativity together with pressure-free matter have until recently been considered as the sole ingredients for averaged calculations. In this communication we focus our attention on more general scenarios, including imperfect fluids as well as alternati…
In this paper we compare outcomes of some extended phantom-like cosmologies with each other and also with $Λ$CDM\, and $Λ$DGP. We focus on the variation of the luminosity distances, the age of the universe and the deceleration parameter versus the redshift in these scenarios. In a dynamical system approach, we show that the accelerating phase of the universe in the $f(R)$-DGP scenario is stable if one consider the \emph{curvature fluid} as a phantom scalar field in the equivalent scalar-tensor theory, otherwise it is a transient and unstable phenomenon. Up to the parameters values adopted in t…
Chaplygin anisotropic matter governing the cosmological evolution in two identical universes with an intermediate static spherically symmetric region is considered. The static region contains a wormhole allowing one to pass etween two horizons. The metric in the non-static region represents a kind of an anisotropic Kantowski-Sachs cosmological model starting from a horizon instead the initial singularity. A classification of the cosmologies with a monotonic late stage is presented. It is shown that only one scenario can involve a de Sitter regime. The scales in the de Sitter phase allows one t…
We consider a spacetime with empty Schwarzschild-de Sitter exterior and Schwarzschild-de Sitter interior metric for a spherical fluid with constant density. The fluid interior may be taken to represent a galaxy supercluster, for which the proper distance from the center of the supercluster to the cosmological horizon has the same order of magnitude as the Hubble radius derived from Friedmann-Robertson-Walker (FRW) cosmologies. The fluid interior and surrounding vacuum may also be considered as a model of the Local Group of galaxies in the far future. Particle motion is subject both to the attr…
For self-gravitating, static, spherically symmetric, minimally coupled scalar fields with arbitrary potentials and negative kinetic energy (favored by the cosmological observations), we give a classification of possible regular solutions to the field equations with flat, de Sitter and AdS asymptotic behavior. Among the 16 presented classes of regular rsolutions are traversable wormholes, Kantowski-Sachs (KS) cosmologies beginning and ending with de Sitter stages, and asymptotically flat black holes (BHs). The Penrose diagram of a regular BH is Schwarzschild-like, but the singularity at $r=0$ i…
Local and global phase-space descriptions and averaging methods are used to find qualitative features of solutions for the FLRW and the Bianchi I metrics in the context of scalar field cosmologies with arbitrary potentials and arbitrary couplings to matter. The stability of the equilibrium points in a phase-space as well as the dynamics in the regime where the scalar field diverges are studied. Equilibrium points that represent some solutions of cosmological interest such as: several types of scaling solutions, a kinetic dominated solution representing a stiff fluid, a solution dominated by an…
We present a survey of the known cosmological and black hole solutions in ghost-free bigravity and massive gravity theories. These can be divided into three classes. First, there are solutions with proportional metrics, which are the same as in General Relativity with a cosmological term, which can be positive, negative or zero. Secondly, for spherically symmetric systems, there are solutions with non-bidiagonal metrics. The g-metric fulfills Einstein equations with a positive cosmological term and a matter source, while the f-metric is anti-de Sitter. The third class contains solutions with b…
The so called $f(X)$ hybrid metric-Palatini gravity presents a unique viable generalisation of the $f(R)$ theories within the metric-affine formalism. Here the cosmology of the $f(X)$ theories is studied using the dynamical system approach. The method consists of formulating the propagation equation in terms of suitable (expansion-normalised) variables as an autonomous system. The fixed points of the system then represent exact cosmological solutions described by power-law or de Sitter expansion. The formalism is applied to two classes of $f(X)$ models, revealing both standard cosmological fix…
We investigate a flat Friedmann-Robertson-Walker spacetime filled with k-essence and find the set of functions F which generate three different families of extended tachyon fields and Chaplygin gases. They lead to accelerated and superaccelerated expanding scenarios. For any function F, we find the first integral of the k-field equation when the k-field is driven by an inverse square potential or by a constant one. In the former, we obtain the general solution of the coupled Einstein-k-field equations for a linear function F. This model shares the same kinematics of the background geometry wit…
We present a simple unifying gauge theoretical formulation of gravitational theories in two dimensional spacetime. This formulation includes the effects of a novel matter-gravity coupling which leads to an extended de Sitter symmetry algebra on which the gauge theory is based. Contractions of this theory encompass previously studied cases.
This paper is motivated by the non-linear stability problem for the expanding region of Kerr de Sitter cosmologies in the context of Einstein's equations with positive cosmological constant. We show that under dynamically realistic assumptions the conformal Weyl curvature of the spacetime decays towards future null infinity. More precisely we establish decay estimates for Weyl fields which are (i) uniform (with respect to a global time function) (ii) optimal (with respect to the rate) and (iii) consistent with a global existence proof (in terms of regularity). The proof relies on a geometric p…
Robertson-Walker spacetimes within a large class are geometrically extended to larger cosmologies that include spacetime points with zero and negative cosmological times. In the extended cosmologies, the big bang is lightlike, and though singular, it inherits some geometric structure from the original spacetime. Spacelike geodesics are continuous across the cosmological time zero submanifold which is parameterized by the radius of Fermi space slices, i.e, by the proper distances along spacelike geodesics from a comoving observer to the big bang. The continuous extension of the metric, and the …
Maximally extended, explicit and regular coverings of the Schwarzschild - de Sitter family of vacua are given, first in spacetime (generalizing a result due to Israel) and then for all dimensions $D$ (assuming a $D-2$ sphere). It is shown that these coordinates offer important advantages over the well known Kruskal - Szekeres procedure.
We compute 1-loop corrections to the redshift space galaxy power spectrum in cosmologies containing additional scales, and hence kernels different from Einstein-de Sitter (EdS). Specifically, our method is tailored for cosmologies in the presence of massive neutrinos and some modified gravity models; in this article we concentrate on the former case. The perturbative kernels have contributions that we notice appear either from the logarithmic growth factor $f(k,t)$, which is scale-dependent because of the neutrino free-streaming, or from the failure of the commonly used approximation $f^2=Ω_m$…
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…
We study the background cosmology of two extensions of dRGT massive gravity. The first is variable mass massive gravity, where the fixed graviton mass of dRGT is replaced by the expectation value of a scalar field. We ask whether self-inflation can be driven by the self-accelerated branch of this theory, and we find that, while such solutions can exist for a short period, they cannot be sustained for a cosmologically useful time. Furthermore, we demonstrate that there generally exist future curvature singularities of the "big brake" form in cosmological solutions to these theories. The second …
