scholarly journals THE NATURE OF Λ AND THE MASS OF THE GRAVITON: A CRITICAL VIEW

2011 ◽  
Vol 03 ◽  
pp. 3-26 ◽  
Author(s):  
J.-P. GAZEAU ◽  
M. NOVELLO
Keyword(s):  
Cosmological Constant ◽  
Einstein Equation ◽  
Universal Constant ◽  
Einstein Equations ◽  
Theoretical Interpretation ◽  
De Sitter ◽  
Current Estimate ◽  
Left Hand ◽  
Fundamental State ◽  
The Right

The observational evidence of a cosmological constant Λ raises natural questions. Is Λ a universal constant fixing the geometry of an empty universe, as fundamental as the Planck constant or the speed of light in the vacuum? Its natural place is then on the left-hand side of the Einstein equation. Is it instead something emerging from a perturbation calculation performed on the metric gμν solution of the Einstein equation and to which it might be given a material status of (dark or bright) "energy"? It should then be part of the content of the right-hand side of the Einstein equations. The purpose of this paper is to analyze some of the arguments in favor of each one of these interpretations of the cosmological constant. Recent estimates based on observational data give a bound on the graviton mass to be about 100 Mpc-1. If this value and the current estimate on the cosmological constant Λ are put into perspective, one faces the interesting coincidence that between the Compton wavelength of the graviton and the cosmological constant there exists the relation [Formula: see text]. Since a physical quantity like mass originates in a minkowskian conservation law, we proceed with a group theoretical interpretation of this relation in terms of the two possible Λ-deformations of the Poincaré group, namely the de Sitter and anti de Sitter groups. We use a very suitable formula, the so-called Garidi mass, and the typically dS/AdS dimensionless parameter ℏH/mc2 in order to make clear the asymptotic relations between minkowskian masses m and their possible dS/AdS counterparts. We conclude that if the fundamental state of the geometry of space-time is minkowskian, then the square of the mass of the graviton is proportional to Λ; otherwise, if the fundamental state is de Sitter, then the graviton is massless in the deSitterian sense.

scholarly journals THE NATURE OF Λ AND THE MASS OF THE GRAVITON: A CRITICAL VIEW

2011 ◽  
Vol 26 (22) ◽  
pp. 3697-3720 ◽  
Author(s):  
J.-P. GAZEAU ◽  
M. NOVELLO
Keyword(s):  
Cosmological Constant ◽  
Einstein Equation ◽  
Universal Constant ◽  
Einstein Equations ◽  
Theoretical Interpretation ◽  
De Sitter ◽  
Current Estimate ◽  
Left Hand ◽  
Fundamental State ◽  
The Right

The observational evidence of a cosmological constant Λ raises natural questions. Is Λ a universal constant fixing the geometry of an empty universe, as fundamental as the Planck constant or the speed of light in the vacuum? Its natural place is then on the left-hand side of the Einstein equation. Is it instead something emerging from a perturbation calculation performed on the metric gμν solution of the Einstein equation and to which it might be given a material status of (dark or bright) "energy"? It should then be part of the content of the right-hand side of the Einstein equations. The purpose of this paper is to analyze some of the arguments in favor of each one of these interpretations of the cosmological constant. Recent estimates based on observational data give a bound on the graviton mass to be about 100 Mpc-1. If this value and the current estimate on the cosmological constant Λ are put into perspective, one faces the interesting coincidence that between the Compton wavelength of the graviton and the cosmological constant there exists the relation [Formula: see text]. Since a physical quantity like mass originates in a minkowskian conservation law, we proceed with a group theoretical interpretation of this relation in terms of the two possible Λ-deformations of the Poincaré group, namely the de Sitter and anti de Sitter groups. We use a very suitable formula, the so-called Garidi mass, and the typically dS/AdS dimensionless parameter ħH/mc2 in order to make clear the asymptotic relations between minkowskian masses m and their possible dS/AdS counterparts. We conclude that if the fundamental state of the geometry of space-time is minkowskian, then the square of the mass of the graviton is proportional to Λ; otherwise, if the fundamental state is de Sitter, then the graviton is massless in the deSitterian sense.

scholarly journals Cosmological model favored by the holographic principle

2016 ◽  
Vol 41 ◽  
pp. 1660127
Author(s):  
Irina Dymnikova ◽  
Anna Dobosz ◽  
Bożena Sołtysek
Keyword(s):  
Cosmological Model ◽  
Cosmological Constant ◽  
Space Time ◽  
Holographic Principle ◽  
Einstein Equations ◽  
Energy Tensor ◽  
De Sitter ◽  
Quantum Evaporation ◽  
Stress Energy ◽  
De Sitter Vacua

We present a regular spherically symmetric cosmological model of the Lemaitre class distinguished by the holographic principle as the thermodynamically stable end-point of quantum evaporation of the cosmological horizon. A source term in the Einstein equations connects smoothly two de Sitter vacua with different values of cosmological constant and corresponds to anisotropic vacuum dark fluid defined by symmetry of its stress-energy tensor which is invariant under the radial boosts. Global structure of space-time is the same as for the de Sitter space-time. Cosmological evolution goes from a big initial value of the cosmological constant towards its presently observed value.

scholarly journals Comparative Analysis of Standard ΛCDM and ΛCS Models

2021 ◽  
Vol 57 (11) ◽  
pp. 1169
Author(s):  
V.E. Kuzmichev ◽  
V.V. Kuzmichev
Keyword(s):  
Cosmological Constant ◽  
Semiclassical Approximation ◽  
Cosmic Strings ◽  
Cosmological Parameters ◽  
Einstein Equations ◽  
Scale Transformation ◽  
De Sitter ◽  
Field Equations ◽  
Low Velocity ◽  
Sitter Model

We draw a comparison of time-dependent cosmological parameters calculated in the standard ΛCDM model with those of the model of a homogeneous and isotropic Universe with non-zero cosmological constant filled with a perfect gas of low-velocity cosmic strings (ΛCS model). It is shown that pressure-free matter can obtain the properties of a gas of low-velocity cosmic strings in the epoch, when the global geometry and the total amount of matter in the Universe as a whole obey an additional constraint. This constraint follows from the quantum geometrodynamical approach in the semiclassical approximation. In terms of general relativity, its effective contribution to the field equations can be linked to the time evolution of the equation of state of matter caused by the processes of redistribution of the energy between matter components. In the present article, the exact solutions of the Einstein equations for the ΛCS model are found. It is demonstrated that this model is equivalent to the open de Sitter model. After the scale transformation of the time variable of the ΛCS model, the standard ΛCDM and ΛCS models provide the equivalent descriptions of cosmological parameters as functions of time at equal values of the cosmological constant. The exception is the behavior of the deceleration parameter in the early Universe.

scholarly journals Fingerprints of the Cosmological Constant: Folds in the Profiles of the Axionic Dark Matter Distribution in a Dyon Exterior

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 455 ◽  
Author(s):  
Alexander Balakin ◽  
Dmitry Groshev
Keyword(s):  
Dark Matter ◽  
Cosmological Constant ◽  
Electric Fields ◽  
Double Electric Layer ◽  
De Sitter ◽  
Electric Structure ◽  
Near Zone ◽  
Sitter Model ◽  
Dark Matter Distribution ◽  
The Right

We consider the magnetic monopole in the axionic dark matter environment (axionic dyon) in the framework of the Reissner-Nordström-de Sitter model. Our aim is to study the distribution of the pseudoscalar (axion) and electric fields near the so-called folds, which are characterized by the profiles with the central minimum, the barrier on the left, and the maximum on the right of this minimum. The electric field in the fold-like zones is shown to change the sign twice, i.e., the electric structure of the near zone of the axionic dyon contains the domain similar to a double electric layer. We have shown that the described fold-like structures in the profile of the gravitational potential, and in the profiles of the electric and axion fields can exist, when the value of the dyon mass belongs to the interval enclosed between two critical masses, which depend on the cosmological constant.

scholarly journals EXACT SOLUTIONS OF EMBEDDING THE 4D UNIVERSE IN A 5D EINSTEIN MANIFOLD

2008 ◽  
Vol 17 (02) ◽  
pp. 257-263 ◽  
Author(s):  
XIN-HE MENG ◽  
JIE REN ◽  
HONG-GUANG ZHANG
Keyword(s):  
Cosmological Constant ◽  
Exact Solutions ◽  
Einstein Equation ◽  
Power Law ◽  
Einstein Manifold ◽  
Spatial Dimension ◽  
Λcdm Model ◽  
Extra Spatial Dimension ◽  
The Right ◽  
Real Universe

One of the simplest ways to extend 4D cosmological models is to add another spatial dimension to make them 5D. In particular, it has been shown that the simplest of such 5D models, i.e. one in which the right-hand side of the Einstein equation is empty, induces a 4D nonempty universe. Accordingly, the origin of matter in a real 4D universe might be mathematically attributed to the existence of one (fictitious) extra spatial dimension. Here we consider the case of an empty 5D universe possessing a cosmological constant Λ and obtain exact solutions for both positive and negative values of the Λ. It is seen that such a model can naturally reduce to a power law ΛCDM model for the real universe. Further, it can be seen that the arbitrary constants and functions appearing in this model are endowed with definite physical meanings.

scholarly journals Designer de Sitter spacetimes

2008 ◽  
Vol 86 (4) ◽  
pp. 591-595
Author(s):  
K Schleich ◽  
D M Witt
Keyword(s):  
Cosmological Constant ◽  
Infinite Family ◽  
Einstein Equations ◽  
Global Dynamics ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Isotropic Solution ◽  
Accelerating Expansion ◽  
Sitter Spacetime ◽  
Expansion Of The Universe

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 cosmologies is very different than that of de Sitter spacetime itself. The construction and dynamics of these designer de Sitter spacetimes is detailed along with some comments about their implications for the structure of our Universe.PACS Nos.: 04.20.–q, 04.20.Ex, 04.20.Gz, 98.80.–k

scholarly journals “MODULI SPACE” OF ASYMPTOTICALLY ANTI-DE-SITTER SPACE-TIMES IN 2+1 DIMENSIONS

1995 ◽  
Vol 10 (29) ◽  
pp. 4139-4160 ◽  
Author(s):  
KIYOSHI EZAWA
Keyword(s):  
Black Holes ◽  
General Solution ◽  
Power Series ◽  
Cosmological Constant ◽  
Moduli Space ◽  
Three Dimensional ◽  
Einstein Equations ◽  
Quadratic Differentials ◽  
De Sitter ◽  
Inverse Radius

Setting an ansatz that the metric is expressible by a power series of the inverse radius and taking a particular gauge choice, we construct a “general solution” of (2+1)-dimensional Einstein equations with a negative cosmological constant in the case where the space-time is asymptotically anti-de-Sitter. Our general solution turns out to be parametrized by two centrally extended quadratic differentials on S1. In order to include three-dimensional black holes naturally in our general solution, it is necessary to exclude the region inside the horizon. We also discuss the relation of our general solution to the moduli space of flat [Formula: see text] connections.

scholarly journals Bardeen–de Sitter black holes

2017 ◽  
Vol 26 (07) ◽  
pp. 1750071 ◽  
Author(s):  
Sharmanthie Fernando
Keyword(s):  
Black Hole ◽  
Cosmological Constant ◽  
Cross Sections ◽  
Einstein Equations ◽  
Nonlinear Electrodynamics ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
De Sitter ◽  
Third Order ◽  
Regular Black Hole

In this paper, we present a regular black hole with a positive cosmological constant. The regular black hole considered is the well known Bardeen black hole and it is a solution to the Einstein equations coupled to nonlinear electrodynamics with a magnetic monopole. The paper discusses the properties of the Bardeen–de Sitter black hole. We have computed the gray body factors and partial absorption cross-sections for massless scalar field impinges on this black hole with the third-order WKB approximation. A detailed discussion on how the behavior of the gray body factors depend on the parameters of the theory such as the mass, charge and the cosmological constant is given. Possible extensions of the work is discussed at the end of the paper.

THEOREM TO GENERATE NON-SPHERICAL RADIATING BLACK HOLE SOLUTIONS

2008 ◽  
Vol 23 (15) ◽  
pp. 1115-1127
Author(s):  
V. S. MOROZOVA ◽  
S. G. GHOSH
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Cosmological Constant ◽  
Einstein Equations ◽  
Energy Conditions ◽  
Type I ◽  
De Sitter ◽  
Sitter Background ◽  
Two Parameter ◽  
Black Hole Solutions

We prove a theorem that characterizes a two-parameter family of solutions to Einstein equations with a negative cosmological constant, representing, in general, non-spherical radiating black holes in an anti-de Sitter background. It is shown that the best known non-spherical radiating black hole solutions are particular cases and static non-spherical black hole solutions, for Type I fluid, are also retrieved. A brief discussion on the energy conditions, singularities and horizons is provided.

New Bondi-type outgoing boundary condition for the Einstein equations with cosmological constant

2015 ◽  
Vol 24 (10) ◽  
pp. 1550081 ◽  
Author(s):  
Xiaokai He ◽  
Zhoujian Cao
Keyword(s):  
Boundary Condition ◽  
Cosmological Constant ◽  
Minkowski Spacetime ◽  
Einstein Equations ◽  
Conformally Flat ◽  
De Sitter ◽  
Positive Cosmological Constant ◽  
Original Boundary ◽  
Sitter Spacetime ◽  
The One

In the middle of last century, Bondi and his coworkers proposed an outgoing boundary condition for the Einstein equations. Recently, more and more observations imply that the Einstein equations should include a nonzero cosmological constant. A spacetime with a positive cosmological constant approaches to a de Sitter space asymptotically. Bondi's original boundary condition is not valid for these asymptotically de Sitter spacetimes. But the traditional conformally flat boundary condition excludes the gravitational radiation for the asymptotically de Sitter spacetimes. In this work, a new Bondi-type outgoing boundary condition based on Bondi–Sachs coordinates is considered. With this new boundary condition, the gravitational wave behavior for the asymptotically de Sitter spacetime is similar to the one for the asymptotically Minkowski spacetime. The traditional conformally flat boundary condition falls into a special subclass of the new boundary condition.

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