A method for deriving the asymptotic behaviour of any physical field is presented. This leads to a geometrically meaningful derivation of the peeling properties for arbitrary values of the cosmological constant. Application to the outstanding case of the physical Weyl tensor provides the explicit form of all terms that determine its asymptotic behaviour along arbitrary lightlike geodesics. The results follow under the assumption of a conformal completion à la Penrose. The only freedom available is the choice of a null vector at the conformal boundary of the space-time (which determines the lightlike geodesic arriving there).
In this paper, we show that the peeling property still holds for Bondi-Sachs metrics with nonzero cosmological constant under the boundary condition given by Sommerfeld's radiation condition together with three nontrivial $Λ$-independent functions $B$, $a$, $b$. This should indicate the new boundary condition is natural. Moreover, we construct some nonstationary vacuum Bondi-Sachs metrics without Bondi news, which Newmann-Penrose quantities fall faster than usual. This provides a new feature of gravitational waves for nonzero cosmological constant.
This paper establishes two things in an asymptotically (anti-)de Sitter spacetime, by direct computations in the physical spacetime (i.e. with no involvement of spacetime compactification): (1) The peeling property of the Weyl spinor is guaranteed. In the case where there are Maxwell fields present, the peeling properties of both Weyl and Maxwell spinors similarly hold, if the leading order term of the spin coefficient $ρ$ when expanded as inverse powers of $r$ (where $r$ is the usual spherical radial coordinate, and $r\rightarrow\infty$ is null infinity, $\mathcal{I}$) has coefficient $-1$. (…
Peeling property for the Einstein scalar field equations with the nonzero cosmological constant
Peking University（北京大学）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）；Guangxi University（广西大学）
We start by studying a peeling process on finite random planar maps with faces of arbitrary degrees determined by a general weight sequence, which satisfies an admissibility criterion. The corresponding perimeter process is identified as a biased random walk, in terms of which the admissibility criterion has a very simple interpretation. The finite random planar maps under consideration were recently proved to possess a well-defined local limit known as the infinite Boltzmann planar map (IBPM). Inspired by recent work of Curien and Le Gall, we show that the peeling process on the IBPM can be o…
We determine the leading order fall-off behaviour of the Weyl tensor in higher dimensional Einstein spacetimes (with and without a cosmological constant) as one approaches infinity along a congruence of null geodesics. The null congruence is assumed to "expand" in all directions near infinity (but it is otherwise generic), which includes in particular asymptotically flat spacetimes. In contrast to the well-known four-dimensional peeling property, the fall-off rate of various Weyl components depends substantially on the chosen boundary conditions, and is also influenced by the presence of a cos…
This is the first of two papers devoted to the asymptotic structure of space-time in the presence of a non-negative cosmological constant $Λ$. This first paper is concerned with the case of $Λ=0$. Our approach is fully based on the tidal nature of the gravitational field and therefore on the `tidal energies' built with the Weyl curvature. In particular, we use the (radiant) asymptotic supermomenta computed from the rescaled Weyl tensor at infinity to provide a novel characterisation of radiation escaping from, or entering into, the space-time. Our new criterion is easy to implement and shown t…
It has been built a strict mathematical model of the thermodynamic equilibrium's establishment in the originally nonequilibrium cosmological ultrarelativistic plasma for the arbitrary accelerated Universe under the assumption that scaling of interactions of elementary particles is restored at energies above the unitary limit. It is shown, that in case of Universe positive acceleration, thermodynamic equilibrium never can be completely restored.
We briefly review of the definitions of the total energy, the total linear momentum and the angular momentum of gravitational field when the cosmological constant is zero. In particular, we show pseudo-tensor's definition of the energy and the momentum given by Prof. Duan in 1963 agree with the ADM total energy-momentum and the Bondi energy-momentum at spatial and null infinity respectively. We also review the relevant energy-momentum inequalities. Finally, we provide a short review of the positive energy theorem and the peeling property of the Newmann-Penrose quantities when the cosmological …
Anisotropic exponential cosmological solutions for a space of arbitrary dimension filled with ordinary matter in the 4th and 5th orders of Lovelock gravity are obtained. Also we have supposed a generalization of such solutions on an arbitrary order. All the solutions are represented as a set of conditions on Hubble parameters.
This article is devoted to static spherically symmetric black hole solutions of dRGT (de Rham-Gabadadze-Tolley) massive gravity in the presence of cosmological constant. The unitary and non-unitary gauges are used to find the solutions in three, four and five dimensions. We show that there are two general classes of solutions. In one of them, the effect of massive potential is appeared as the effective cosmological constant. By investigating these solutions in different dimensions, we find an expression for effective cosmological constant in arbitrary dimensions.
We study the imprint of a massive scalar particle on cosmological correlation functions, and suggest the way to determine the mass of the newly introduced particle, which is expected to be around 10^14 GeV. After reviewing the basic theory by Maldacena and the effective field theory (EFT) of inflation by Cheung et al., we apply these two theories to construct new couplings of a massive scalar field with primordial fluctuations including an arbitrary number of gravitons. We compute some correlation functions including these couplings in the soft-graviton limit. We show that when the number of s…
Results of numerical simulation constructed before strict mathematical model of an establishment of thermodynamic equilibrium in originally nonequilibrium cosmological ultrarelativistic plasma for the Universe with any acceleration in the assumption of restoration of a scalling of interactions of elementary particles are presented at energies above a unitary limit. Limiting parametres of residual nonequilibrium distribution of nonequilibrium relic particles of ultrahigh energies are found.
We proved that strictly stationary Einstein-Maxwell-axion-dilaton spacetime with negative cosmological constant could not support a nontrivial configuration of complex scalar fields. We considered the general case of the arbitrary number of U(1) gauge fields in the theory under consideration.
We consider the Lovelock theory of gravity that assumes a nonlinearity of the field equations in the second-order derivatives of the metric. We prove the opportunity of obtaining cosmological solutions without isotropization in the presence of matter in the form of a perfect fluid, which is necessary for invisibility of extra dimensions that inevitably emerge in the Lovelock theory. In particular, the Jacobs solution has been generalized to an arbitrary order of the theory, and in the third order, an anisotropic exponential solution has been found.
Following an earlier suggestion by Dolgov, we present a specific model of two massless vector fields which dynamically cancel a cosmological constant of arbitrary magnitude and sign. Flat Minkowski spacetime appears asymptotically as an attractor of the field equations. Unlike the original model, the new model does not upset the local Newtonian gravitational dynamics.
A modified-gravity-type model of two hypothetical massless vector fields is presented. These vector fields are gravitationally coupled to standard matter and an effective cosmological constant. Considered in a cosmological context, the vector fields dynamically cancel an arbitrary cosmological constant, and flat Minkowski spacetime appears as the limit of attractor-type solutions of the field equations. Asymptotically, the field equations give rise to a standard Friedmann-Robertson-Walker universe and standard Newtonian gravitational dynamics of small systems.
We consider $d$-dimensional static spacetimes in Einstein gravity with a cosmological constant in the presence of a minimally coupled massless scalar field. The spacetimes have a $(d-2)$-dimensional base manifold given by an Einstein space and the massless scalar field depends only on the radial coordinate. The field equations are decoupled in the general case, and can be solved exactly for the cases when either the cosmological constant vanishes or the base manifold is Ricci flat. We focus on the case of a negative cosmological constant and a Ricci-flat base manifold. The solution has a curva…
The mechanism of the initial inflationary scenario of the universe and of its late-time acceleration can be described by assuming the existence of some gravitationally coupled scalar fields $ϕ$, with the inflaton field generating inflation and the quintessence field being responsible for the late accelerated expansion. Various inflationary and late-time accelerated scenarios are distinguished by the choice of an effective self-interaction potential $V(ϕ)$, which simulates a temporarily non-vanishing cosmological term. In this work, we present a new formalism for the analysis of scalar fields i…
We prove the existence of a large class of one parameter families of solutions to the Einstein-Euler equations that depend on the singular parameter $\ep=v_T/c$ $(0<\ep < \ep_0)$, where $c$ is the speed of light, and $v_T$ is a typical speed of the gravitating fluid. These solutions are shown to exist on a common spacetime slab $M\cong [0,T)\times \Tbb^3$, and converge as $\ep \searrow 0$ to a solution of the cosmological Poisson-Euler equations of Newtonian gravity. Moreover, we establish that these solutions can be expanded in the parameter $\ep$ to any specified order with expansion coeffic…
We present the asymptotic solutions for spacetimes with non-zero cosmological constant $Λ$ coupled to Maxwell fields, using the Newman-Penrose formalism. This extends a recent work that dealt with the vacuum Einstein (Newman-Penrose) equations with $Λ\neq0$. The results are given in two different null tetrads: the Newman-Unti and Szabados-Tod null tetrads, where the peeling property is exhibited in the former but not the latter. Using these asymptotic solutions, we discuss the mass-loss of an isolated electro-gravitating system with cosmological constant. In a universe with $Λ>0$, the physics …
We consider massless fields of arbitrary spin in de Sitter space. We introduce a spinor-helicity formalism, which encodes the field data on a cosmological horizon. These variables reduce the free S-matrix in an observer's causal patch, i.e. the evolution of free fields from one horizon to another, to a simple Fourier transform. We show how this result arises via twistor theory, by decomposing the horizon<->horizon problem into a pair of (more symmetric) horizon<->twistor problems.
Recently Horava proposed a renormalizable gravity theory in four dimensions which reduces to Einstein gravity with a non-vanishing cosmological constant in IR but with improved UV behaviors. Here, I study an IR modification which breaks "softly" the detailed balance condition in Horava model and allows the asymptotically flat limit as well. I obtain the black hole and cosmological solutions for "arbitrary" cosmological constant that represent the analogs of the standard Schwartzschild-(A)dS solutions which can be asymptotically (A)dS as well as flat and I discuss some thermodynamical propertie…
Detailed analysis of the dependence of the one-loop counterterms on the gauge and parametrization in the Einstein gravity with the cosmological constant
In the framework of the recently proposed models of massive gravity, defined with respect to a de Sitter reference metric, we obtain new homogeneous and isotropic solutions for arbitrary cosmological matter and arbitrary spatial curvature. These solutions can be classified into three branches. In the first two, the massive gravity terms behave like a cosmological constant. In the third branch, the massive gravity effects can be described by a time evolving effective fluid with rather remarkable features, including the property to behave as a cosmological constant at late time.
E. Verlinde obtained a generalized formula for the entropy of a conformal field theory. For this we consider a (n+1) dimensional closed radiation dominated FLWR in the context of the holographic principle. In this work we construct a extension of the Cardy-Verlinde formula to positive cosmological constant spaces (dS spaces) with arbitrary topology
A method is developed for dealing with ultraviolet divergences in calculations of cosmological correlations, which does not depend on dimensional regularization. An extended version of the WKB approximation is used to analyze the divergences in these calculations, and these divergences are controlled by the introduction of Pauli--Villars regulator fields. This approach is illustrated in the theory of a scalar field with arbitrary self-interactions in a fixed flat-space Robertson--Walker metric with arbitrary scale factor $a(t)$. Explicit formulas are given for the counterterms needed to cancel…
We show that the energy-momentum tensor of homogeneous fields of arbitrary spin in an expanding universe is always isotropic in average provided the fields remain bounded and evolve rapidly compared to the rate of expansion. An analytic expression for the average equation of state is obtained for Lagrangians with generic power-law kinetic and potential terms. As an example we consider the behavior of a spin-two field in the standard Fierz-Pauli theory of massive gravity. The results can be extended to general space-time geometries for locally inertial observers.
A particular compensation-type solution of the main cosmological constant problem has been proposed recently, with two massless vector fields dynamically canceling an arbitrary cosmological constant Λ. The naive expectation is that such a compensation mechanism does not allow for the existence of an inflationary phase in the very early Universe. However, it is shown that certain initial boundary conditions on the vector fields can in fact give rise to an inflationary phase.
The holographic principle can lead to cosmological scenarios, i.e., holographic equipartition models. In this model, an extra driving term (corresponding to a time-varying cosmological term) in cosmological equations depends on an associated entropy on the horizon of the universe. The driving term is expected to be constrained by the second law of thermodynamics, as if the cosmological constant problem could be discussed from a thermodynamics viewpoint. In the present study, an arbitrary entropy on the horizon, $S_{H}$, is assumed, extending previous analysis based on particular entropies [Phy…
We investigate the cosmological evolution of mimetic matter model with arbitrary scalar potential. The cosmological reconstruction, which is the way to construct a model for arbitrary evolutions of the scale factor, is explicitly done for different choices of potential. The cases that mimetic matter model shows the evolution as Cold Dark Matter(CDM), wCDM model, dark matter and dark energy with dynamical $Om(z)$, where $Om(z) \equiv [ (H(z)/H_0)^2-1 ]/[(1+z)^3 -1],$ or phantom dark energy with phantom-non-phantom crossing are presented in detail. The cosmological perturbations for such evoluti…
In this paper, we describe the dynamics of a Bianchi Type V vacuum universe with an arbitrary cosmological constant. We begin by using an orthonormal frame approach to write Einstein's field equations as a coupled system of first-order ordinary differential equations. The equilibrium points of the resulting dynamical system are found to be expanding and contracting de Sitter universe solutions, a Minkowski spacetime solution, and static Anti-de Sitter universe solutions, which are characterized by a negative cosmological constant in addition to constant negative spatial curvature. While the ex…
The formation of cosmological black holes is investigated using the functional Schroedinger equation as observed by an asymptotic observer, assuming a spherical domain wall collapse process. The mass formula of the Sultana-Dyer black hole is derived using Israel's domain wall mathematical framework. This is used to examine the semi-classical and quantum nature of the collapsing domain wall in the general scale of an arbitrary scale factor, while ignoring evaporation and back reaction mass losses. Particular FLRW scale factors are then explored for black hole horizon formation times, all yieldi…
Interactions between cosmic fluids may appear in many cosmological scenarios that go far beyond the usually studied energy exchange in the dark sector. In the absence of known microscopic interaction mechanisms, phenomenological ansatzes are usually proposed in order to describe such models. In this paper, we derive a generalization of one of the most frequently used of such ansatzes:the one based on a initial proposal of Shapiro, Solà, España-Bonet and Ruiz-Lapuente who described a time-dependent cosmological "constant" whose variation arises from quantum effects near the Planck scale [I. L. …
We study the induced 4-dimensional linearized Einstein field equations in an m-dimensional bulk space by means of a confining potential. It is shown that in this approach the mass of graviton is quantized. The cosmological constant problem is also addressed within the context of this approach. We show that the difference between the values of the cosmological constant in particle physics and cosmology stems from our measurements in two different scales, small and large.
The possibility of flat metric solutions in the presence of arbitrary, in particular, Planck mass sized cosmological constants is investigated within multigravity theory, the ghost-free theory of $(N+1)$ rank-2 tensor fields comprising one massless and $N$ massive spin-2 fields. It is found that, indeed, for any $N$, no matter how large, no flat solutions exist without fine-tuning parameters in the potential. For an infinite number of fields, however, flat solutions exist within an infinite-dimensional parameter space. Such a ground state may be viewed as a collective state that cannot be appr…
In this paper, we study the geodesic deviation equation (GDE) within the context of the Brans-Dicke (BD) theory in $D$ dimensions. Then, we restrict our attention to the GDE for the fundamental observers and null vector field past directed. Concerning the latter, in order to apply the retrieved GDE for the cosmological models as well as examining exact solutions, we study some cosmological models in general relativity (GR) and in the context of the BD theory. For the BD framework, we provide two appropriate settings for dynamical system, which can be considered as the most extended case scenar…
