scholarly journals Mass in de Sitter and Anti-de-Sitter Universes with Regard to Dark Matter

2020 ◽  
Author(s):  
Jean-Pierre Gazeau
Keyword(s):  
Dark Matter ◽  
Irreducible Representation ◽  
Rest Mass ◽  
Flat Space ◽  
Space Time ◽  
Energy Scale ◽  
Unitary Irreducible Representation ◽  
De Sitter ◽  
Rest Energy ◽  
Point Energy

An explanation of the origin of dark matter is suggested in this work. The argument is based on symmetry considerations about the concept of mass. In the Wigner's view, the rest mass and the spin of a free elementary particle in flat space-time are the two invariants that characterize the associated unitary irreducible representation of the Poincar\'e group. The Poincar\'e group has two and only two deformations with maximal symmetry. They describe respectively the de Sitter (dS) and Anti de Sitter (AdS) kinematic symmetries. Analogously to their shared flat space-time limit, two invariants, spin and energy scale for de Sitter and rest energy for Anti de Sitter, characterize the unitary irreducible representation associated with dS and AdS elementary systems. While the dS energy scale is a simple deformation of the Poincaré rest energy and so has a purely mass nature, AdS rest energy is the sum of a purely mass component and a kind of zero-point energy derived from the curvature. An analysis based on recent estimates on the chemical freeze-out temperature marking in Early Universe the phase transition quark-gluon plasma epoch to the hadron epoch supports the guess that dark matter energy might originate from an effective AdS curvature energy.

scholarly journals Mass in de Sitter and Anti-de Sitter Universes with Regard to Dark Matter

Universe ◽  
2020 ◽  
Vol 6 (5) ◽  
pp. 66 ◽  
Author(s):  
Jean-Pierre Gazeau
Keyword(s):  
Dark Matter ◽  
Irreducible Representation ◽  
Flat Space ◽  
Space Time ◽  
Energy Scale ◽  
Unitary Irreducible Representation ◽  
Poincaré Group ◽  
De Sitter ◽  
Rest Energy ◽  
Poincare Group

An explanation of the origin of dark matter is suggested in this work. The argument is based on symmetry considerations about the concept of mass. In Wigner’s view, the rest mass and the spin of a free elementary particle in flat space-time are the two invariants that characterize the associated unitary irreducible representation of the Poincaré group. The Poincaré group has two and only two deformations with maximal symmetry. They describe respectively the de Sitter (dS) and anti-de Sitter (AdS) kinematic symmetries. Analogously to their shared flat space-time limit, two invariants, spin and energy scale for de Sitter and rest energy for anti-de Sitter, characterize the unitary irreducible representation associated with dS and AdS elementary systems, respectively. While the dS energy scale is a simple deformation of the Poincaré rest energy and so has a purely mass nature, AdS rest energy is the sum of a purely mass component and a kind of zero-point energy derived from the curvature. An analysis based on recent estimates on the chemical freeze-out temperature marking in Early Universe the phase transition quark–gluon plasma epoch to the hadron epoch supports the guess that dark matter energy might originate from an effective AdS curvature energy.

New conservation laws for zero rest-mass fields in asymptotically flat space-time

1968 ◽  
Vol 305 (1481) ◽  
pp. 175-204 ◽  
Keyword(s):  
Conservation Laws ◽  
Rest Mass ◽  
Power Series Expansion ◽  
Flat Space ◽  
Arbitrary Spin ◽  
Space Time ◽  
Maxwell Theory ◽  
Asymptotically Flat ◽  
Gravitational Fields ◽  
Higher Spin

Some recently discovered exact conservation laws for asymptotically flat gravitational fields are discussed in detail. The analogous conservation laws for zero rest-mass fields of arbitrary spin s = 0,½,1,...) in flat or asymptotically flat space-time are also considered and their connexion with a generalization of Kirchoff’s integral is pointed out. In flat space-time, an infinite hierarchy of such conservation laws exists for each spin value, but these have a somewhat trivial interpretation, describing the asymptotic incoming field (in fact giving the coefficients of a power series expansion of the incoming field). The Maxwell and linearized Einstein theories are analysed here particularly. In asymptotically flat space-time, only the first set of quantities of the hierarchy remain absolutely conserved. These are 4 s + 2 real quantities, for spin s , giving a D ( s , 0) representation of the Bondi-Metzner-Sachs group. But even for these quantities the simple interpretation in terms of incoming waves no longer holds good: it emerges from a study of the stationary gravitational fields that a contribution to the quantities involving the gravitational multipole structure of the field must also be present. Only the vacuum Einstein theory is analysed in this connexion here, the corresponding discussions of the Einstein-Maxwell theory (by Exton and the authors) and the Einstein-Maxwell-neutrino theory (by Exton) being given elsewhere. (A discussion of fields of higher spin in curved space-time along these lines would encounter the familiar difficulties first pointed out by Buchdahl.) One consequence of the discussion given here is that a stationary asymptotically flat gravitational field cannot become radiative and then stationary again after a finite time, except possibly if a certain (origin independent) quadratic combination of multipole moments returns to its original value. This indicates the existence of ‘tails’ to the outgoing waves (or back-scattered field),which destroys the stationary nature of the final field.

Unification of dark energy and dark matter based on the Petrov classification and space-time symmetry

2016 ◽  
Vol 31 (02n03) ◽  
pp. 1641005 ◽  
Author(s):  
Irina Dymnikova
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Space Time ◽  
Cosmological Term ◽  
De Sitter ◽  
Dark Fluid ◽  
Time Symmetry ◽  
Stress Energy ◽  
Petrov Classification ◽  
De Sitter Vacuum

The Petrov classification of stress-energy tensors provides a model-independent definition of a vacuum by the algebraic structure of its stress-energy tensor and implies the existence of vacua whose symmetry is reduced as compared with the maximally symmetric de Sitter vacuum associated with the Einstein cosmological term. This allows to describe a vacuum in general setting by dynamical vacuum dark fluid, presented by a variable cosmological term with the reduced symmetry which makes vacuum dark fluid essentially anisotropic and allows it to be evolving and clustering. The relevant regular solutions to the Einstein equations describe regular cosmological models with time-evolving and spatially inhomogeneous vacuum dark energy, and compact vacuum objects generically related to a dark energy through the de Sitter vacuum interior: regular black holes, their remnants and self-gravitating vacuum solitons — which can be responsible for observational effects typically related to a dark matter. The mass of objects with de Sitter interior is generically related to vacuum dark energy and to breaking of space-time symmetry.

scholarly journals SUPERSYMMETRY BREAKING IN ANTI-DE SITTER SPACE–TIME

2013 ◽  
Vol 28 (13) ◽  
pp. 1350053
Author(s):  
BIN ZHU ◽  
KUN MENG ◽  
RAN DING
Keyword(s):  
Supersymmetry Breaking ◽  
Flat Space ◽  
De Sitter Space ◽  
Space Time ◽  
Time Limit ◽  
Quantum Corrections ◽  
De Sitter ◽  
R Symmetry

We study the questions of how supersymmetry is spontaneously broken in anti-de Sitter space–time. We verify that the would-be R-symmetry in AdS4 plays a central role for the existence of meta-stable supersymmetry breaking. To illustrate, some well-known models such as Poloyni models and O'Raifeartaigh models are investigated in detail. Our calculations are reliable in flat space–time limit and confirm us that meta-stable vacua are generic even though quantum corrections are taken into account.

COORDINATE-INDEPENDENT DEFINITION OF TIME AND VACUUM IN CURVED SPACE–TIME

1994 ◽  
Vol 09 (08) ◽  
pp. 1239-1260 ◽  
Author(s):  
A. Z. CAPRI ◽  
S. M. ROY
Keyword(s):  
Particle Production ◽  
Dimensional Space ◽  
Flat Space ◽  
Space Time ◽  
Physical Principle ◽  
De Sitter ◽  
Timelike Vector ◽  
Time Translation ◽  
Pass Through ◽  
Definition Of

We propose a definition of time and of the vacuum such that they are intrinsic to a given globally hyperbolic 1 + (n − 1)-dimensional space–time geometry and independent of the choice of coordinates. To arrive at this definition we use the new physical principle that a 1 + 1-dimensional Poincaré algebra, including Killing conditions on the generators, should be valid on the hypersurface of instantaneity. Given a timelike vector at a point (an observer's velocity) we define "an instant of time" to be the spacelike surface of geodesics which pass through that point and are orthogonal to that timelike vector. Gaussian coordinates erected on this surface yield 1 + 1-dimensional subspaces with Poincaré symmetry valid on that surface. The generator associated with time translation now uniquely picks out the direction of time on that surface. This fact permits unambiguous quantization on the surface of a field evolving in this background metric. For flat space–time the corresponding vacuum is always the Minkowski vacuum. We also consider in detail the case of static and Robertson–Walker metrics in 1 + 1 dimensions and find our vacuum to be different from those given before. The vacuum for the de Sitter metric in 1 + 1 dimensions is compared with the results in the literature and found to be different. Our definition of particles, and hence particle production, is consequently different also.

scholarly journals EXACT STRING SOLUTIONS IN (2 + 1)-DIMENSIONAL DE SITTER SPACE-TIME

1994 ◽  
Vol 09 (29) ◽  
pp. 2745-2754 ◽  
Author(s):  
H. J. DE VEGA ◽  
A. V. MIKHAILOV ◽  
N. SÁNCHEZ
Keyword(s):  
Flat Space ◽  
De Sitter Space ◽  
Space Time ◽  
The Other ◽  
De Sitter ◽  
Expansion Factor ◽  
New Feature ◽  
The Universe ◽  
Time Analogy

Exact and explicit string solutions in de Sitter space-time are found. (Here, the string equations reduce to a sinh-Gordon model). A new feature without flat space-time analogy appears: starting with a single worldsheet, several (here two) strings emerge. One string is stable and the other (unstable) grows as the universe grows. Their invariant size and energy either grow as the expansion factor or tend to constant. Moreover, strings can expand (contract) for large (small) universe radius at a different rate than the universe does.

scholarly journals Propagators of the Dirac fermions on spatially flat FLRW space–times

2019 ◽  
Vol 34 (05) ◽  
pp. 1950024 ◽  
Author(s):  
Ion I. Cotăescu
Keyword(s):  
Integral Representation ◽  
Flat Space ◽  
Space Time ◽  
Integral Representations ◽  
Dirac Fermions ◽  
De Sitter ◽  
3 Dimensional ◽  
Left Handed ◽  
New Type ◽  
Change Of Variable

The general formalism of the free Dirac fermions on spatially flat (1[Formula: see text]+[Formula: see text]3)-dimensional Friedmann-Lemaître–Robertson–Walker (FLRW) space–times is developed in momentum representation. The mode expansions in terms of the fundamental spinors satisfying the charge conjugation and normalization conditions are used for deriving the structure of the anticommutator matrix-functions and, implicitly, of the retarded, advanced, and Feynman fermion propagators. The principal result is that the new type of integral representation we proposed recently in the de Sitter case can be applied to the Dirac fermions in any spatially flat FLRW geometry. Moreover, the Dirac equation of the left-handed massless fermions can be analytically solved finding a general spinor solution and deriving the integral representations of the neutrino propagators. It is shown that in the Minkowski flat space–time our new integral representation is up to a change of variable just like the usual Fourier representation of the fermion propagators. The form of the Feynman propagator of the massive fermions on a spatially flat FLRW space–time with a scale factor of Milne-type is also outlined.

scholarly journals SEMICLASSICAL (QUANTUM FIELD THEORY) AND QUANTUM (STRING) DE SITTER REGIMES: NEW RESULTS

2007 ◽  
Vol 16 (06) ◽  
pp. 1053-1074 ◽  
Author(s):  
A. BOUCHAREB ◽  
M. RAMÓN MEDRANO ◽  
N. G. SÁNCHEZ
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Emission Cross Section ◽  
Hubble Constant ◽  
Flat Space ◽  
De Sitter Space ◽  
Space Time ◽  
De Sitter ◽  
Entropy Formula ◽  
New Phase

We compute the quantum string entropy S s (m, H) from the microscopic string density of states ρ s (m, H) of mass m in de Sitter space–time. We find for high m (high Hm → c/α') a new phase transition at the critical string temperature T s = (1/2πk B )L cl c2/α', higher than the flat space (Hagedorn) temperature t s (L cl = c/H, the Hubble constant H acts at the transition, producing a smaller string constant α' and thus, a higher tension). T s is the precise quantum dual of the semiclassical (QFT Hawking–Gibbons) de Sitter temperature T sem = ħ c/(2πk B L cl ). By precisely identifying the semiclassical and quantum (string) de Sitter regimes, we find a new formula for the full de Sitter entropy S sem (H), as a function of the usual Bekenstein–Hawking entropy [Formula: see text]. For L cl ≫ ℓ Planck , i.e. for low [Formula: see text] is the leading term, but for high H near c/ℓ Planck , a new phase transition operates and the whole entropy S sem (H) is drastically different from the Bekenstein–Hawking entropy [Formula: see text]. We compute the string quantum emission cross-section σ string by a black hole in de Sitter (or asymptotically de Sitter) space–time (bhdS). For T sem bhdS ℓ T s (early evaporation stage), it shows the QFT Hawking emission with temperature T sem bhdS (semiclassical regime). For T sem bhdS → T s , σ string exhibits a phase transition into a string de Sitter state of size [Formula: see text], [Formula: see text], and string de Sitter temperature T s . Instead of featuring a single pole singularity in the temperature (Carlitz transition), it features a square root branch point (de Vega–Sanchez transition). New bounds on the black hole radius r g emerge in the bhdS string regime: it can become r g = L s /2, or it can reach a more quantum value, r g = 0.365 ℓ s .

Zero rest-mass fields including gravitation: asymptotic behaviour

1965 ◽  
Vol 284 (1397) ◽  
pp. 159-203 ◽  
Keyword(s):  
Asymptotic Behaviour ◽  
Scalar Potential ◽  
Rest Mass ◽  
Asymptotic Properties ◽  
Empty Space ◽  
Space Time ◽  
De Sitter ◽  
Complex Scalar ◽  
General Technique ◽  
Peeling Off

A zero rest-mass field of arbitrary spin s determines, at each event in space-time, a set of 2 s principal null directions which are related to the radiative behaviour of the field. These directions exhibit the characteristic ‘peeling-off' behaviour of Sachs, namely that to order r - k -1 ( k = 0, . . . , 2 s ), 2 s - k of them coincide radially, r being a linear parameter in any advanced or retarded radial direction. This result is obtained in part I for fields of any spin in special relativity, by means of an inductive spinor argument which depends ultimately on the appropriate asymptotic behaviour of a very simple Hertz-type complex scalar potential. Spin ( s - ½) fields are used as potentials for spin s fields, etc. Several examples are given to illustrate this, In particular, the method is used to obtain physically sensible singularity-free waves for each spin which can be of any desired algebraic type. In part II, a general technique is described, for discussing asymptotic properties of fields in curved space-times which is applicable to all asymptotically flat or asymptotically de Sitter space-times. This involves the introduction of ‘points at infinity’ in a consistent way. These points constitute a hypersurface boundary I to a manifold whose interior is conformally identical with the original space-time. Zero rest-mass fields exhibit an essential conformal invariance, so their behaviour at ‘infinity’ can be studied at this hypersurface. Continuity at I for the transformed field implies that the ‘peeling-off’ property holds. Furthermore, if the Einstein empty-space equations hold near I then continuity at I for the transformed gravitational field is a consequence. This leads to generalizations of results due to Bondi and Sachs. The case when the Einstein-Maxwell equations hold near I is also similarly treated here. The hypersurface I is space-like, time-like or null according as the cosmological constant is positive, negative or absent. The technique affords a covariant approach to the definition of radiation fields in general relativity. If I is not null, however, the radiation field concept emerges as necessarily origin dependent. Further applications of the technique are also indicated.

The scalar wave equation in a Schwarzschild space-time

1979 ◽  
Vol 367 (1731) ◽  
pp. 503-525 ◽  
Keyword(s):  
Wave Equation ◽  
Rest Mass ◽  
Flat Space ◽  
Cauchy Data ◽  
Space Time ◽  
Scalar Wave ◽  
Spatial Infinity ◽  
Null Infinity ◽  
Scalar Wave Equation ◽  
Near Future

This paper studies the asymptotic behaviour of solutions of the zero rest mass scalar wave equation in the Schwarzschild space-time in a neighbourhood of spatial infinity which includes parts of future and past null infinity. The behaviour of such fields is essentially different from that which occurs in a flat space-time. In particular fields which have a Bondi-type expansion in powers of ' r -1 ’ near past null infinity do not have such an expansion near future null infinity. Further solutions which have physically reasonable Cauchy data probably fail to have Bondi-type expansions near null infinity.

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