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 data on a local observer's past null cone. It is demonstrated that, at an earlier epoch of the LTB model, the observational data would not be consistent with that of the $Λ$CDM model.
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…
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.
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.
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…
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 investigate the dynamics of the chameleonic Generalised Brans--Dicke model in flat FRW cosmology. In a new approach, a framework to study stability and attractor solutions in the phase space is developed for the model by simultaneously best fitting the stability and model parameters with the observational data. The results show that for an accelerating universe the phantom crossing does not occur in the past and near future.
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.
In this paper within the scope of FRW cosmology for k = 0, \pm1 we study the dynamics of the universe for a cosmological model with a scalar field nonminimally coupled to matter. By best- fitting the model parameters with the observational data for the direct interaction between the dark sectors in the model we obtain observational constraints on cosmological parameters. The result shows that with the best fitted model parameters, only in flat universe, the phantom crossing occurs twice in the past and once in the future, whereas no crossing occurs for open and closed models of the universe.
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.
In this paper, we explore a fractal model of the universe proposed by Calcagni [JHEP{\bf03}(2010)120] for a power-counting renormalizable field theory living in a fractal spacetime. Considering a timelike fractal profile, we derived field equations in fractal cosmology, in order to explore the structure formation and the expansion history in fractal universe. Numerical investigations based on matter power spectra diagrams report higher structure growth in fractal cosmology, being in contrast to local galaxy surveys. Additionally, according to the evolution of Hubble parameter diagrams, it can …
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…
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…
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…
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 Hund…
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…
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 …
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…
Although many people have thought that the difference between the Copenhagen and many-worlds versions of quantum theory was merely metaphysical, quantum cosmology may allow us to make a physical test to distinguish between them empirically. The difference between the two versions shows up when the various components of the wavefunction have different numbers of observers and observations. In the Copenhagen version, a random observation is selected from the sample within the component that is selected by wavefunction collapse, but in the many-worlds version, a random observation is selected fro…
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…
Most of current cosmological theories are built combining an isotropic and homogeneous manifold with a scale factor that depends on time. If one supposes a hyperconical universe with linear expansion, an inhomogeneous metric can be obtained by an appropriate transformation that preserves the proper time. This model locally tends to a flat Friedman-Robertson-Walker metric with linear expansion. The objective of this work is to analyse the observational compatibility of the inhomogeneous metric considered. For this purpose, the corresponding luminosity distance was obtained and was compared with…
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 …
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…
An integral kernel representation for the commutative $\star$-product on curved classical spacetime is introduced. Its convergence conditions and relationship to a Drin'feld differential twist are established. A $\star$-Einstein field equation can be obtained, provided the matter-based twist's vector generators are fixed to self-consistent values during the variation in order to maintain $\star$-associativity. Variations not of this type are non-viable as classical field theories. $\star$-Gauge theory on such a spacetime can be developed using $\star$-Ehresmann connections. While the theory pr…
In this thesis we are interested in the problem of dark energy in cosmology. In particular, we consider the possibility that this effect is due to an infrared non-local modification of the theory of General Relativity. Inspired by massive gravity, we construct non-local theories in which gravity may be massive, but where the symmetry of diffeomorphisms is preserved. We focus on the cosmology of these theories and confront them with observational constraints. On a more theoretical level, we discuss some subtleties of non-local field theory and address in a novel way the issue of stability. This…
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…
Poincaré gauge theory of gravity offers opportunities to solve some principal problems of general relativity theory and modern cosmology. In the frame of this theory the gravitational interaction can have the repulsion character in the case of usual gravitating matter with positive values of energy density and pressure satisfying energy dominance condition. Cosmological consequences of gravitational repulsion are considered in the case of homogeneous isotropic models in connection with the problem of cosmological singularity and dark energy problem of general relativity theory. Regular Big Ban…
The field equation of orthodox general relativity are written in the context of a geometry with non-vanishing torsion, the Absolute Parallelism (AP) geometry. An AP-structure, with homogeneity and isotropy, is used for cosmological applications. The resulting dynamical equations are those of FRW-Standard cosmology, which have many problems e.g. singularity, particle horizons, ...etc. We suggest a new scheme for investigating the effect of torsion on the dynamics of FRW-Cosmology, without changing the basic structure of general relativity. It is shown that some of these problems will disappear …
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.
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…
5-dimensional special relativity can be considered as the 5-dimensional extension of Carmeli's cosmological special relativity, as well as the flat specialization of 5-d brane world theory. To this framework we add a 5-dimensional perfect fluid stress-energy tensor, and unify the equations of perfect hydrodynamics in a single 5-dimensional tensor conservation law. This picture permits to interpret particle production phenomena as cosmological effects, in the spirit of open system cosmology. The source of particle production vanishes if the fluid is isentropic. Moreover the hydrodynamical equat…
We apply the variable speed of light into general relativity in order to solve the problems we met in the standard cosmology. We're surprised to find that, the results from the general relativity in cosmology are exactly the same as those we got from Newtonian dynamics. The relation between the Newtonian dynamics and the relativistic dynamics can be demonstrated with the variable speed of light. With this approach, some problems in the standard cosmology such as the flatness problem and the horizon problem doesn't arise any more. All the cosmological results and the physical results are reason…
Taking into account a fractal structure for the black hole horizon, Barrow argued that the area law of entropy is modified due to quantum-gravitational effects (Barrow in Phys Lett B 808:135643, https://doi.org/10.1016/j.physletb.2020.135643, 2020). Accordingly, the corrected entropy takes the form $S \sim A^{1+\mathrmΔ/2}$, where $0\leq\mathrmΔ\leq1$, indicates the amount of the quantum-gravitational deformation effects. In this paper, based on Barrow entropy, we first derive the modified gravitational field equations through the Clausius relation. We then consider the Friedmann-Lemaître-Robe…
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…
In loop quantum cosmology there may be a super-inflation phase in the very early universe, in which a single scalar field with a negative power-law potential $V= -M^4(ϕ/M)^β$ plays important roles. Since the effective horizon $\sqrt{SD}/H$ controls the behavior of quantum fluctuation instead of the usual Hubble horizon, we assume the following inflation scenario; the super-inflation starts when the quantum state of the scalar field emerges into the classical regime,and ends when the effective horizon becomes the Hubble horizon, and the effective horizon scale never gets shorter than the Planck…
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 …
We study the validity of cosmic distance duality relation between angular diameter and luminosity distances. To test this duality relation we use the latest Union2 Supernovae Type Ia (SNe Ia) data for estimating the luminosity distance. The estimation of angular diameter distance comes from the samples of galaxy clusters (real and mock) and FRIIb radio galaxies. We parameterize the distance duality relation as a function of redshift in four different ways and we find that the mock data set, which assumes a spherical isothermal $β$ model for the galaxy clusters does not accommodate the distance…
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…
This work is an analytical study of the main differences between classical inflationary effects of a fast-roll regime and imprints of hybrid Loop Quantum Cosmology (LQC) on the primordial power spectrum. Effective LQC solutions of phenomenological interest typically contain a classical period of kinetic dominance prior to slow-roll inflation, with consequences on the power spectrum that here we try and tell apart from those of phenomena occuring in the vicinity of a bounce in hybrid LQC. For this comparison, we use the same criterion for the choice of a vacuum state of the primordial perturbat…
We investigate the late-time cosmological behaviour of scalar-tensor theories with a universal multiplicative coupling between the scalar field and the matter Lagrangian in the matter era. This class of theory encompasses the case of the massless string dilaton (see Damour and Polyakov, General Relativity and Gravitation, 26, 1171) as well as a theory with an intrinsic decoupling mechanism in the solar system (see Minazzoli and Hees, Phys. Rev. D 88, 041504). The cosmological evolution is studied in the General Relativity limit justified by solar system constraints on the gravitation theory. T…
The configuration space of general relativity is superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms and conformal transformations. Taking this conformal nature seriously leads to a new theory of gravity which although very similar to general relativity has some very different features particularly in cosmology and quantisation. It should reproduce the standard tests of general relativity. The cosmology is stud…
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…
The de Sitter invariant special relativity is a natural extension of the usual Einstein special relativity. Within this framework a generalization of special relativity (SR) for the de Sitter space-time introduces a new length scale $R$, serving an origin of geometrical cosmological constant $Λ=3/R^2$. De Sitter relativity predicts the departure from the Lorentz invariance due to spacetime curvature, related to the geometrical cosmological constant. In this paper the possible impact of de Sitter special relativity effects on threshold particle processes and equivalence principle violation is c…
I give a compact, pedagogical review of our present understanding of the universe as based on general relativity. This includes the uniform models, with special reference to the cosmological 'constant'; and the equations for spherically-symmetric systems, in a particularly convenient form that aids their application to astrophysics. New ideas in research are also outlined, notably involving extra dimensions.
This is a summary of the lectures presented at the Xth Brazilian school on cosmology and gravitation. The style of the text is that of a lightly written descriptive summary of ideas with almost no formulas, with pointers to the literature. We hope this style can encourage new people to take a look into these results. We discuss the variables that Ashtekar introduced 18 years ago that gave rise to new momentum in this field, the loop representation, spin networks, measures in the space of connections modulo gauge transformations, the Hamiltonian constraint, application to cosmology and the conn…
Lee. et.al. (1976) analysed the bimetric theory with the help of parameterized post Newtonian (PPN) formalism. They found that the post Newtonian limit of the theory is identical with that of general theory of relativity except for their PPN parameter $α_{2}$, on the basis of cosmological considerations. In the present paper it is pointed out that feasibility of such considerations are doubtful in five dimensional bimetric theory of relativity. As the universe is unique and is governed by physical laws, many different cosmologies are possible. Examples are given for some possible cosmological …
This article proposes some cosmological reflections at the qualitative and conjectural level, suggested by the Fantappie & Arcidiacono projective relativity theory. The difference will firstly be discussed between two types of singularity in this theory: geometric (de Sitter horizon) and physical (big bang, big crunch). The reasons for the existence of geometric singularities are deeply rooted in the principle of inertia and in the principle of relativity, while physical singularities are associated with the creation or destruction of matter. In this framework, quantum mechanics is introduced …
