15 pages PDF, 4 figures, to appear as introductory chapter in "One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity"
发表信息：
International Journal of Modern Physics D Vol. 24, No. 14 (2015) 1530030 (15 pages)
This year marks the hundredth anniversary of Einstein's 1915 landmark paper "Die Feldgleichungen der Gravitation" in which the field equations of general relativity were correctly formulated for the first time, thus rendering general relativity a complete theory. Over the subsequent hundred years physicists and astronomers have struggled with uncovering the consequences and applications of these equations. This contribution, which was written as an introduction to six chapters dealing with the connection between general relativity and cosmology that will appear in the two-volume book "One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity," endeavors to provide a historical overview of the connection between general relativity and cosmology, two areas whose development has been closely intertwined.
Cosmology is a field of physics in which the use of General Relativity theory is indispensable. However, a cosmology based on Newtonian gravity theory for gravity is possible in certain circumstances. The applicability of Newtonian theory can be substantially extended if it is modified in such way that pressure has a more active role as source of the gravitational field. This was done in the neo-Newtonian cosmology. The limitation on the construction of a Newtonian cosmology, and the need for a relativistic theory in cosmology are reviewed. The neo-Newtonian proposal is presented, and its cons…
General Relativity (GR) revolutionized the way we thought about gravity. After briefly describing the key successes of GR and its impact, I will discuss the major conceptual challenges it faces today. I conclude by outlining the prospective future directions of development, which hold the promise of deepening our understanding of the nature of gravity.
We perform three-dimensional numerical relativity simulations of homogeneous and inhomogeneous expanding spacetimes, with a view towards quantifying non-linear effects from cosmological inhomogeneities. We demonstrate fourth-order convergence with errors less than one part in 10^6 in evolving a flat, dust Friedmann-Lemaitre-Roberston-Walker (FLRW) spacetime using the Einstein Toolkit within the Cactus framework. We also demonstrate agreement to within one part in 10^3 between the numerical relativity solution and the linear solution for density, velocity and metric perturbations in the Hubble …
In this Letter we present strong arguments in favour of thoroughly revising the negative mass cosmology (NMC), which has been proposed as a simple alternative explanation of dark energy and dark matter effects, within the framework of General Relativity. We show that there are various physical predictions in this model which require fine-tuning in order to make them compatible with current cosmological surveys. In this way, the original motivation of the NMC model becomes obscured due to the imposition of fine-tuned unknown variables. We conclude that a more rigorous theoretical treatment is n…
Advances in our understanding of the origin, evolution and structure of the universe have long been driven by cosmological perturbation theory, model building and effective field theory. In this review, we introduce numerical relativity as a powerful new complementary tool for fundamental cosmology. To illustrate its power, we discuss applications of numerical relativity to studying the robustness of slow contraction and inflation in homogenizing, isotropizing and flattening the universe beginning from generic unsmooth initial conditions. In particular, we describe how recent numerical relativ…
The Averaging problem in general relativity and cosmology is discussed. The approach of macroscopic gravity to resolve the problem is presented. An exact cosmological solution to the equations of macroscopic gravity is given and its properties are discussed. Contents: 1. Introduction to General Relativity 2. General Relativity -> Relativistic Cosmology 3. Introduction to Relativistic Cosmology 4. Relativistic Cosmology -> Mathematical Cosmology 5. Averaging Problem in Relativistic Cosmology 6. History of the Averaging Problem 7. Averaging and FLRW Cosmologies 8. Averaging Problem in General Re…
This article presents a simple model that reproduces key concepts of modern cosmology within the framework of special relativity, at a level that is suitable for an undergraduate or high school setting. The model includes cosmic expansion governed by a universal scale factor, the Hubble relation, proper distances between galaxies and the associated recession speeds, comoving coordinates, angular and luminosity distances, and the relation between the cosmic scale factor and the cosmological redshift. It allows for a pedagogical discussion of the role of superluminal recession speeds of galaxies…
In these lectures my aim is to review enough of conformal differential geometry in four dimensions to give an account of Penrose's conformal cyclic geometry.
The widely accepted description of the present cosmic acceleration and the neutrino oscillations in terms of a cosmological constant and neutrino masses, respectively, seems conceptually not very satisfactory. From a phenomenological perspective, the possibility that those phenomena are instead the first windows to new physics at very low energies is explored.
For the last 100 years, General Relativity (GR) has taken over the gravitational theory mantle held by Newtonian Gravity for the previous 200 years. This article reviews the status of GR in terms of its self-consistency, completeness, and the evidence provided by observations, which have allowed GR to remain the champion of gravitational theories against several other classes of competing theories. We pay particular attention to the role of GR and gravity in cosmology, one of the areas in which one gravity dominates and new phenomena and effects challenge the orthodoxy. We also review other ar…
In this article we propose some Maple procedures, for teaching purposes, to study the basics of General Relativity (GR) and Cosmology. After presenting some features of GRTensorII, a package specially built to deal with GR, we give two examples of how one can use these procedures. In the first example we build the Schwarzschild solution of Einstein equations, while in the second one we study some simple cosmological models.
The characteristic formalism in numerical relativity, which has been developed to study gravitational waves, and the observer metric approach in observational cosmology both make use of coordinate systems based on null cones. In this paper, these coordinate systems are compared and it is then demonstrated how characteristic numerical relativity can be used to investigate problems in observational cosmology. In a numerical experiment using the characteristic formalism, it is shown how the historical evolution of a LTB universe compares to that of the $Λ$CDM model given identical observational d…
General Very Special Relativity (GVSR) is the curved space-time of Very Special Relativity (VSR) proposed by Cohen and Glashow. The geometry of GVSR possesses a line element of Finsler Geometry proposed by Bogoslovsky. We calculate the Einstein field equations and derive a modified FRW cosmology, for an osculating Riemannian space. The Friedman equation of motion leads to an explanation of the cosmological acceleration in terms of an alternative non-Lorentz invariant theory. A first order approach for a primordial spurionic vector field introduced into the metric, gives back an estimation of t…
Formalising the logical dependence of physical quantities on material referents of scale, I show that both Hubble's law and the cosmological constant are in fact exactly replicable by a spatial contraction of referents locally on earth, and that the Pioneer anomaly is irrefutable indication that this is the case. The formalism literally embodies Feynman's ``hot-plate'' model, predictably yielding a logical derivation of the relativity postulates, and importantly, suffices to demonstrate the inherent logical consistency of general relativity and quantum mechanics, whose foundations I have shown…
The main consequences of de Sitter Special Relativity to the Standard Cosmological Model of Physical Cosmology are examined. The cosmological constant Lambda appears, in this theory, as a manifestation of the proper conformal current, which must be added to the usual energy-momentum density. As that conformal current itself vanishes in absence of sources, Lambda is ultimately dependent on the matter content, and can in principle be calculated. A present-day value very close to that given by the crossed supernova/BBR data is obtained through simple and reasonable approximations. Also a primeval…
We study flat Friedmann-Lemaitre-Robertson-Walker cosmological models for a scalar field coupled nonminimally to teleparallel gravity with generic coupling and potential functions. The goal of this paper is to determine the conditions under which the cosmological evolution tends to the limit where the variation of the gravitational "constant" ceases and the system evolves close to general relativity. These conditions can be read off from the approximate analytical solutions describing the process in matter and potential domination eras. Only those models where the GR limit exists and is an att…
Even though it is not possible to differentiate General Relativity from Teleparallel Gravity using classical experiments, it could be possible to discriminate between them by quantum gravitational effects. These effects have motivated the introduction of nonlocal deformations of General Relativity, and similar effects are also expected to occur in Teleparallel Gravity. Here, we study nonlocal deformations of Teleparallel Gravity along with its cosmological solutions. We observe that Nonlocal Teleparallel Gravity (like nonlocal General Relativity) is consistent with the present cosmological dat…
Numerical N-body simulations of large scale structure formation in the universe are based on Newtonian gravity. However, according to our current understanding, the most correct theory of gravity is general relativity. It is therefore important to understand which degrees of freedom and which features are lost when the relativistic universe is approximated, or rather replaced, by a Newtonian one. This is the main purpose of our investigation. We first define Newtonian cosmology and we give an overview on general relativity, both in its standard and covariant formulations. We show how the two t…
We show that a class of nonlocal gravity models, proposed to explain current cosmic acceleration without dark energy, passes two major tests: First, they can be defined so as not to alter the, observationally correct, general relativity predictions for gravitationally bound systems. Second, they are stable, ghost-free, with no additional excitations beyond those of general relativity. In this they differ from their, ghostful, localized versions. The systems' initial value constraints are the same as in general relativity, and our nonlocal modifications never convert the original gravitons into…
We investigate a particular type of classical nonsingular bouncing cosmology, which results from general relativity if we allow for degenerate metrics. The simplest model has a matter content with a constant equation-of-state parameter and we get the modified Hubble diagrams for both the luminosity distance and the angular diameter distance. Based on these results, we present a Gedankenexperiment to determine the length scale of the spacetime defect which has replaced the big bang singularity. A possibly more realistic model has an equation-of-state parameter which is different before and afte…
We derive the equations of motion for scalar metric perturbations in a particular nonsingular bouncing cosmology, where the big bang singularity is replaced by a spacetime defect with a degenerate metric. The adiabatic perturbation solution is obtained for nonrelativistic hydrodynamic matter. We get the same result by working with conformal coordinates. This last method is also valid for vector and tensor metric perturbations, and selected results are presented. We, finally, discuss several new effects from the linear perturbations of this nonsingular bouncing cosmology, such as across-bounce …
In earlier work it was shown that a weak modification of general relativity, in the linearized approach, renders a spherically symmetric and stationary model of the Universe. This was due to the presence of a third mode of polarization in the linearized gravity in which a "curvature energy" term is present. Such term was identified as the Dark Energy of the Universe. In this letter a more realistic model is discussed. A different cosmological solution to the Einstein-Vlasov System is analysed. This solution shows reasonable results which are within the standard bounds predicted by the cosmolog…
We find initial data for numerical relativity simulations of inhomogeneous cosmologies. This involves treating an exceptional case of the general relativity constraint equations. We devise analytic and numerical methods to treat this exceptional case. We apply the analytic method to the standard case of cosmology with a single scalar field. The numerical method is applied to the two-field ekpyrotic cosmology.
The modelling of light-like signals in General Relativity taking the form of impulsive gravitational waves and light-like shells of matter is examined. Systematic deductions from the Bianchi identities are made. These are based upon Penrose's hierarchical classification of the geometry induced on the null hypersurface history of the surface by its imbedding in the space-times to the future and to the past of it. The signals are not confined to propagate in a vacuum and thus their interaction with matter (a burst of radiation propagating through a cosmic fluid, for example) is also studied. Res…
We review an attempt to set a suitable foundational principle for consistent quantization of gravity based on the canonical formulation. It requires extending the spacetime description of the relativistic postulates to also encompass an alternative formulation in momentum-energy continuum where the inertial physical laws can be equivalently described. The extension to noninertial frames breaks such an equivalence, leaving a new dynamical field which, together with gravity, allows to construct a canonical scenario where the Dirac's quantization method leads to consistent definitions of hermitia…
We consider the correspondence between the Jordan frame and the Einstein frame descriptions of scalar-tensor theory of gravitation. We argue that since the redefinition of the scalar field is not differentiable at the limit of general relativity the correspondence between the two frames is lost at this limit. To clarify the situation we analyse the dynamics of the scalar field in different frames for two distinct scalar-tensor cosmologies with specific coupling functions and demonstrate that the corresponding scalar field phase portraits are not equivalent for regions containing the general re…
We provide a consistency relation between cosmological observables in general relativity without relying on the equation of state of dark energy. The consistency relation should be satisfied if general relativity is the correct theory of gravity and dark energy clustering is negligible. As an extension, we also provide the DGP counterpart of the relation.
We develop a gauge invariant canonical perturbation scheme for perturbations around symmetry reduced sectors in generally covariant theories, such as general relativity. The central objects of investigation are gauge invariant observables which encode the dynamics of the system. We apply this scheme to perturbations around a homogeneous and isotropic sector (cosmology) of general relativity. The background variables of this homogeneous and isotropic sector are treated fully dynamically which allows us to approximate the observables to arbitrary high order in a self--consistent and fully gauge …
In the homogeneous and isotropic Friedmann-Robertson-Walker minisuperspace model, it is known that there are no Euclidean wormhole solutions in the pure gravity system. Here it is demonstrated explicitly that in Taub cosmology, which is one of the simplest anisotropic cosmology models, wormhole solutions do exist in pure general relativity in both classical and quantum contexts.
We review recent developments and results in testing general relativity (GR) at cosmological scales. The subject has witnessed rapid growth during the last two decades with the aim of addressing the question of cosmic acceleration and the dark energy associated with it. However, with the advent of precision cosmology, it has also become a well-motivated endeavor by itself to test gravitational physics at cosmic scales. We overview cosmological probes of gravity, formalisms and parameterizations for testing deviations from GR at cosmological scales, selected modified gravity (MG) theories, grav…
Two lattice based methods for numerical relativity, the Regge Calculus and the Smooth Lattice Relativity, will be compared with respect to accuracy and computational speed in a full 3+1 evolution of initial data representing a standard Kasner cosmology. It will be shown that both methods provide convergent approximations to the exact Kasner cosmology. It will also be shown that the Regge Calculus is of the order of 110 times slower than the Smooth Lattice method.
This article reviews basic construction and cosmological implications of a power-counting renormalizable theory of gravitation recently proposed by Horava. We explain that (i) at low energy this theory does not exactly recover general relativity but instead mimic general relativity plus dark matter; that (ii) higher spatial curvature terms allow bouncing and cyclic universes as regular solutions; and that (iii) the anisotropic scaling with the dynamical critical exponent z=3 solves the horizon problem and leads to scale-invariant cosmological perturbations even without inflation. We also comme…
We present a new approach to early universe cosmology. Inflation is replaced by a phase transition in which both matter and geometry are created simultaneously. We calculate the spectrum of metric perturbations and show that it is flat. We then argue that as a consequence of the dynamic nature of the phase transition the spectrum is likely not completely flat but tilted. We argue that the tilt is related to $η$, one of the critical exponents characterizing the phase transition. This exponent generically lies between 0.03 and 0.06. It thus coincides with the observed tilt of the perturbation sp…
We discuss cosmological implications of nonlinear supersymmetric(NLSUSY) general relativity(GR) of the form of Einstein-Hilbert(EH) action for empty spacetime, where NLSUSY GR is obtained by the geomtrical arguments on new spacetime just inspired by NLSUSY. The new action of NLSUSY GR is unstable and breaks down spontaneously to EH action with Nambu-Goldstone(NG) fermion matter. We show that NLSUSY GR elucidates the physical meanings of the cosmologically important quantities, e.g., the spontaneous SUSY breaking scale, the cosmological constant, the dark energy and the neutrino mass and descri…
Problem of cosmological singularity of general relativity theory is discussed. The possible resolution of this problem in the framework of inflationary cosmology is proposed. Physical conditions leading to bouncing inflationary solutions in the frame of general relativity theory and gauge theories of gravitation are compared. It is shown that gauge theories of gravitation allow to build regular inflationary cosmological models of closed, open and flat type with dominating ultrarelativistic matter at a bounce.
We investigate the cosmological behavior in a universe governed by time asymmetric extensions of general relativity, which is a novel modified gravity based on the addition of new, time-asymmetric, terms on the Hamiltonian framework, in a way that the algebra of constraints and local physics remain unchanged. Nevertheless, at cosmological scales these new terms can have significant effects that can alter the universe evolution, both at early and late times, and the freedom in the choice of the involved modification function makes the scenario able to produce a huge class of cosmological behavi…
We show that if the Lagrangean for a scalar field coupled to General Relativity only contains derivatives, then it is possible to completely deparametrise the theory. This means that 1.Physical observables, i.e. functions which Poisson commute with the spatial diffeomorphism and Hamiltonian constraints of General Relativity, can be easily constructed. 2. The physical time evolution of those observables is generated by a natural physical Hamiltonian which is (constrained to be) positive. The mechanism by which this works is due to Brown and Kuchař. In order that the physical Hamiltonian is clos…
The characteristic formalism of numerical relativity is based on a system of coordinates aligned with outgoing null cones. While these coordinates were designed for studying gravitational waves, they can also be easily adapted to model cosmological past null cones (PNCs). Similar to observational coordinates in the observational approach to cosmology, this then provides a model that only makes use of information causally connected to an observer. However, the diameter distance, which is used as a radial coordinate, limits the model's cosmological application to the region prior to the PNC refo…
In this paper, we describe physical effects occurring in the regularized Robertson-Walker spacetime which can reveal the presence of the defect. Our analysis is based on two main physical quantities: the compressive forces acting on (human) observers and the energy possessed by massive particles and photons during their dynamical evolution. In Sec. 3, we claim that with a characteristic length scale of the order of the Planck length compressive forces become so intense near the defect that no (human) observer is able to cross it. In Sec. 4, we show that the energy exhibits an unusual character…
In a previous paper [arXiv:1308.1852] we showed how a finite system of discrete particles interacting with each other via Newtonian gravitational attraction would lead to precisely the same dynamical equations for homothetic motion as in the case of the pressure-free Friedmann-Lemaître-Robertson-Walker cosmological models of General Relativity Theory, provided the distribution of particles obeys the central configuration equation. In this paper we show one can obtain perturbed such Newtonian solutions that give the same linearised structure growth equations as in the general relativity case. W…
It is argued that substantial portions of both Newtonian particle mechanics and general relativity can be viewed as relational (rather than absolute) theories. I furthermore use the relational particle models as toy models to investigate the problem of time in closed-universe canonical quantum general relativity. I consider thus in particular the internal time, semiclassical and records tentative resolutions of the problem of time.
This preliminary report proposes integrating the Maxwell equations in Minkowski spacetime using coordinates where the spacelike surfaces are hyperboloids asymptotic to null cones at spatial infinity. The space coordinates are chosen so that Scri+ occurs at a finite coordinate and a smooth extension beyond Scri+ is obtained. The question addressed is whether a Cauchy evolution numerical integration program can be easily modified to compute this evolution. In the spirit of the von Neumann and Richtmyer artificial viscosity which thickens a shock by many orders of magnitude to facilitate numerica…
The aim of this work is to present a series of concrete examples which illustrate how the computer algebra system Cadabra can be used to manipulate expressions appearing in General Relativity and other gravitational theories. We highlight the way in which Cadabra's philosophy differs from other systems with related functionality. The use of various new built-in packages is discussed, and we show how such packages can also be created by end-users directly using the notebook interface. The current paper focuses on fairly generic applications in gravitational theories, including the use of differ…
2015 is the centennial of Einstein General Relativity. On this occasion, we examine the General Relativity and Quantum Cosmology (GRQC) field of research by analysing 38291 papers uploaded on the electronic archives arXiv.org from 2000 to 2012. We establish a map of the countries contributing to GRQC in 2012. We determine the main journals publishing GRQC papers and which countries publish in which journals. We find that more and more papers are written by groups (instead of single) of authors with more and more international collaborations. There are huge differences between countries. Hence …
We consider spatially covariant modified gravity in which the would-be scalar degree of freedom is made non-dynamical and hence there are just two tensorial degrees of freedom, i.e., the same number of dynamical degrees of freedom as in general relativity. Focusing on a class of such modified gravity theories characterized by three functions of time, we discuss how modified gravity with two tensorial degrees of freedom can be distinguished observationally or phenomenologically from general relativity. It is checked that the theory gives the same predictions as general relativity for weak gravi…
The Friedmann equation is derived for a Newtonian universe. Changing mass density to energy density gives exactly the Friedmann equation of general relativity. Accounting for work done by pressure then yields the two Einstein equations that govern the expansion of the universe. Descriptions and explanations of radiation pressure and vacuum pressure are added to complete a basic kit of cosmology tools. It provides a basis for teaching cosmology to undergraduates in a way that quickly equips them to do basic calculations. This is demonstrated with calculations involving: characteristics of the e…
We revisit the analysis made by Hwang and Noh [JCAP 1310 (2013)] aiming the construction of a Newtonian set of equations incorporating pressure effects typical of the General Relativity theory. We explicitly derive the Hwang-Noh equations, comparing them with similar computations found in the literature. Then, we investigate $i)$ the cosmological expansion, $ii)$ linear cosmological perturbations theory and $iii)$ stellar equilibrium by using the new set of equations and comparing the results with those coming from the usual Newtonian theory, from the Neo-Newtonian theory and from the General …
The averaging problem in general relativity is briefly discussed. A new setting of the problem as that of macroscopic description of gravitation is proposed. A covariant space-time averaging procedure is described. The structure of the geometry of macroscopic space-time, which follows from averaging Cartan's structure equations, is described and the correlation tensors present in the theory are discussed. The macroscopic field equations (averaged Einstein's equations) derived in the framework of the approach are presented and their structure is analysed. The correspondence principle for macros…
In this article we review recent developments of cyclic cosmology. A typical non-singular cyclic model within General Relativity requires a non-conventional fluid with negative effective energy density, in order to cancel the matter component and lead to a non-singular bounce. However, the existence of such a non-conventional fluid usually leads to quantum instabilities and makes the theory ill-defined. In the present work we follow the alternative way, obtaining two scenarios of non-singular cyclic cosmological evolutions in the context of gravitational theories beyond General Relativity. The…
We find that general relativity can be naturally free of cosmological singularities. Several nonsingular models are currently available that either assume ad hoc matter contents, or are nonsingular only over a sector of solution space of zero measure, or depart drastically from general relativity at high energies. After much uncertainty over whether cosmological inflation could help solve the initial-singularity problem, the prevailing belief today is that general relativistic cosmology, with inflation or without, is endemically singular. This belief was reinforced by recent singularity theore…
