scholarly journals THE COSMOLOGICAL CONSTANT PROBLEM AND KALUZA–KLEIN THEORY

2001 ◽  
Vol 10 (06) ◽  
pp. 905-912 ◽  
Author(s):  
PAUL S. WESSON ◽  
HONGYA LIU
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Energy Density ◽  
Cosmological Constant ◽  
Field Equations ◽  
Cosmological Constant Problem ◽  
Klein Theory ◽  
Kaluza Klein

We present technical results which extend previous work and show that the cosmological constant of general relativity is an artefact of the reduction to 4D of 5D Kaluza–Klein theory (or 10D superstrings and 11D supergravity). We argue that the distinction between matter and vacuum is artificial in the context of ND field theory. The concept of a cosmological "constant" (which measures the energy density of the vacuum in 4D) should be replaced by that of a series of variable fields whose sum is determined by a solution of ND field equations in a well-defined manner.

scholarly journals Generalized Phenomenological Models of Dark Energy

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Prasenjit Paul ◽  
Rikpratik Sengupta
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Energy Density ◽  
Cosmological Constant ◽  
Phenomenological Models ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Free Parameters ◽  
The Universe ◽  
Matter Energy

It was first observed at the end of the last century that the universe is presently accelerating. Ever since, there have been several attempts to explain this observation theoretically. There are two possible approaches. The more conventional one is to modify the matter part of the Einstein field equations, and the second one is to modify the geometry part. We shall consider two phenomenological models based on the former, more conventional approach within the context of general relativity. The phenomenological models in this paper consider a Λ term firstly a function of a¨/a and secondly a function of ρ, where a and ρ are the scale factor and matter energy density, respectively. Constraining the free parameters of the models with the latest observational data gives satisfactory values of parameters as considered by us initially. Without any field theoretic interpretation, we explain the recent observations with a dynamical cosmological constant.

scholarly journals THE NATURE OF THE COSMOLOGICAL CONSTANT PROBLEM

2009 ◽  
Vol 24 (08n09) ◽  
pp. 1545-1548 ◽  
Author(s):  
M. D. MAIA ◽  
A. J. S. CAPISTRANO ◽  
E. M. MONTE
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Energy Density ◽  
Cosmological Constant ◽  
Ground State ◽  
Vacuum Energy ◽  
Dimensional Space ◽  
Brane World ◽  
Vacuum Energy Density ◽  
Cosmological Constant Problem

General relativity postulates the Minkowski space-time as the standard (flat) geometry against which we compare all curved space-times and also as the gravitational ground state where particles, quantum fields and their vacua are defined. On the other hand, experimental evidences tell that there exists a non-zero cosmological constant, which implies in a deSitter ground state, which not compatible with the assumed Minkowski structure. Such inconsistency is an evidence of the missing standard of curvature in Riemann's geometry, which in general relativity manifests itself in the form of the cosmological constant problem. We show how the lack of a curvature standard in Riemann's geometry can be fixed by Nash's theorem on metric perturbations. The resulting higher dimensional gravitational theory is more general than general relativity, similar to brane-world gravity, but where the propagation of the gravitational field along the extra dimensions is a mathematical necessity, rather than a postulate. After a brief introduction to Nash's theorem, we show that the vacuum energy density must remain confined to four-dimensional space-times, but the cosmological constant resulting from the contracted Bianchi identity represents a gravitational term which is not confined. In this case, the comparison between the vacuum energy and the cosmological constant in general relativity does not make sense. Instead, the geometrical fix provided by Nash's theorem suggests that the vacuum energy density contributes to the perturbations of the gravitational field.

scholarly journals Unification of the Maxwell-Einstein-Dirac Correspondence

2019 ◽  
Author(s):  
Wim Vegt
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
String Theory ◽  
Dimensional Space ◽  
Space Time ◽  
Unified Field ◽  
S Matrix ◽  
Klein Theory ◽  
Dimensional Space Time ◽  
Kaluza Klein

Albert Einstein, Lorentz and Minkowski published in 1905 the Theory of Special Relativity and Einstein published in 1915 his field theory of general relativity based on a curved 4-dimensional space-time continuum to integrate the gravitational field and the electromagnetic field in one unified field. Since then the method of Einstein’s unifying field theory has been developed by many others in more than 4 dimensions resulting finally in the well-known 10-dimensional and 11-dimensional “string theory”. String theory is an outgrowth of S-matrix theory, a research program begun by Werner Heisenberg in 1943 (following John Archibald Wheeler‘s(3) 1937 introduction of the S-matrix), picked up and advocated by many prominent theorists starting in the late 1950’s.Theodor Franz Eduard Kaluza (1885-1954), was a German mathematician and physicist well-known for the Kaluza–Klein theory involving field equations in curved five-dimensional space. His idea that fundamental forces can be unified by introducing additional dimensions re-emerged much later in the “String Theory”.The original Kaluza-Klein theory was one of the first attempts to create an unified field theory i.e. the theory, which would unify all the forces under one fundamental law. It was published in 1921 by Theodor Kaluza and extended in 1926 by Oskar Klein. The basic idea of this theory was to postulate one extra compactified space dimension and introduce nothing but pure gravity in a new (1 + 4)-dimensional space-time. Klein suggested that the fifth dimension would be rolled up into a tiny, compact loop on the order of 10-35 [m]The presented "New Unification Theory" unifies Classical Electrodynamics with General Relativity and Quantum Physics

scholarly journals Revisiting the Cosmological Constant Problem within Quantum Cosmology

Universe ◽  
2020 ◽  
Vol 6 (8) ◽  
pp. 108
Author(s):  
Vesselin Gueorguiev ◽  
Andre Maeder
Keyword(s):  
Energy Density ◽  
Cosmological Constant ◽  
Quantum Cosmology ◽  
Vacuum Energy ◽  
Planck Scale ◽  
Vacuum Energy Density ◽  
Characteristic Scale ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Cosmological Constant Problem

A new perspective on the Cosmological Constant Problem (CCP) is proposed and discussed within the multiverse approach of Quantum Cosmology. It is assumed that each member of the ensemble of universes has a characteristic scale a that can be used as integration variable in the partition function. An averaged characteristic scale of the ensemble is estimated by using only members that satisfy the Einstein field equations. The averaged characteristic scale is compatible with the Planck length when considering an ensemble of solutions to the Einstein field equations with an effective cosmological constant. The multiverse ensemble is split in Planck-seed universes with vacuum energy density of order one; thus, Λ˜≈8π in Planck units and a-derivable universes. For a-derivable universe with a characteristic scale of the order of the observed Universe a≈8×1060, the cosmological constant Λ=Λ˜/a2 is in the range 10−121–10−122, which is close in magnitude to the observed value 10−123. We point out that the smallness of Λ can be viewed to be natural if its value is associated with the entropy of the Universe. This approach to the CCP reconciles the Planck-scale huge vacuum energy–density predicted by QFT considerations, as valid for Planck-seed universes, with the observed small value of the cosmological constant as relevant to an a-derivable universe as observed.

PHYSICAL PROPERTIES OF MATTER DERIVED FROM GEOMETRY OF KALUZA-KLEIN THEORY

1993 ◽  
Vol 02 (02) ◽  
pp. 163-170 ◽  
Author(s):  
P.S. WESSON ◽  
J. PONCE DE LEON ◽  
P. LIM ◽  
H. LIU
Keyword(s):  
General Relativity ◽  
Physical Properties ◽  
Field Equations ◽  
Klein Theory ◽  
Kaluza Klein

We ask if it is possible to geometrize properties of matter such as the density and pressure in terms of a Kaluza-Klein extension of general relativity. We find that this is possible for at least three important classes of problems, where acceptable 4D properties of matter are recovered as the extra parts of a 5D geometry with “empty” field equations. This suggests to us that matter may be purely geometrical in origin.

On the cosmological constant problem and brane-world geometry

Open Physics ◽  
2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Abraão Capistrano ◽  
Pedro Odon
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Energy Density ◽  
Cosmological Constant ◽  
Vacuum Energy ◽  
Extrinsic Curvature ◽  
Brane World ◽  
Vacuum Energy Density ◽  
Cosmological Constant Problem ◽  
Riemannian Geometries

AbstractThe cosmological constant problem is examined within the context of the covariant brane-world gravity, based on Nash’s embedding theorem for Riemannian geometries. We show that the vacuum structure of the brane-world is more complex than General Relativity’s because it involves extrinsic elements, in specific, the extrinsic curvature. In other words, the shape (or local curvature) of an object becomes a relative concept, instead of the “absolute shape” of General Relativity. We point out that the immediate consequence is that the cosmological constant and the energy density of the vacuum quantum fluctuations have different physical meanings: while the vacuum energy density remains confined to the four-dimensional brane-world, the cosmological constant is a property of the bulk’s gravitational field that leads to the conclusion that these quantities cannot be compared, as it is usually done in General Relativity. Instead, the vacuum energy density contributes to the extrinsic curvature, which in turn generates Nash’s perturbation of the gravitational field. On the other hand, the cosmological constant problem ceases to be in the brane-world geometry, reappearing only in the limit where the extrinsic curvature vanishes.

scholarly journals The spacetime between Einstein and Kaluza–Klein

2020 ◽  
Vol 35 (36) ◽  
pp. 2030020
Author(s):  
Chris Vuille
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Differential Operators ◽  
Mathematical Structure ◽  
Field Equations ◽  
Five Dimensions ◽  
Four Dimensions ◽  
Klein Theory ◽  
Klein Gordon ◽  
Kaluza Klein

In this paper I introduce tensor multinomials, an algebra that is dense in the space of nonlinear smooth differential operators, and use a subalgebra to create an extension of Einstein’s theory of general relativity. In a mathematical sense this extension falls between Einstein’s original theory of general relativity in four dimensions and the Kaluza–Klein theory in five dimensions. The theory has elements in common with both the original Kaluza–Klein and Brans–Dicke, but emphasizes a new and different underlying mathematical structure. Despite there being only four physical dimensions, the use of tensor multinomials naturally leads to expanded operators that can incorporate other fields. The equivalent Ricci tensor of this geometry is robust and yields vacuum general relativity and electromagnetism, as well as a Klein–Gordon-like quantum scalar field. The formalism permits a time-dependent cosmological function, which is the source for the scalar field. I develop and discuss several candidate Lagrangians. Trial solutions of the most natural field equations include a singularity-free dark energy dust cosmology.

scholarly journals A SOLUTION TO THE COSMOLOGICAL CONSTANT PROBLEM

2005 ◽  
Vol 14 (10) ◽  
pp. 1667-1673 ◽  
Author(s):  
ROLAND TRIAY
Keyword(s):  
General Relativity ◽  
Energy Density ◽  
Cosmological Constant ◽  
Vacuum Energy ◽  
Fundamental Constant ◽  
Quantum Fluctuations ◽  
Vacuum Energy Density ◽  
Cosmological Constant Problem

According to general relativity, the present analysis shows on geometrical grounds that the cosmological constant problem is an artifact due to the unfounded link of this fundamental constant to vacuum energy density of quantum fluctuations.

scholarly journals Time Dependence of Various Cosmological Parameters in the Framework of Kaluza-Klein Space-Time

2019 ◽  
pp. 211-220
Author(s):  
Sudipto Roy ◽  
Anirban Sarkar ◽  
Pritha Ghosh
Keyword(s):  
Cosmological Constant ◽  
Time Dependence ◽  
Cosmological Parameters ◽  
Accelerated Expansion ◽  
Accelerating Universe ◽  
Field Equations ◽  
Eos Parameter ◽  
Klein Theory ◽  
Time Variations ◽  
Kaluza Klein

A theoretical model, regarding the time dependence of several cosmological parameters, has been constructed in the present study, in the framework of Kaluza-Klein theory, using its field equations for a spatially flat metric. Time dependent empirical expressions of the cosmological constant and the equation of state (EoS) parameter have been substituted into the field equations to determine the time dependence of various cosmological parameters. Time variations of these parameters have been shown graphically. The cosmological features obtained from this model are found to be in agreement with the observed characteristics of the accelerating universe. Interestingly, the signature flipping of the deceleration parameter, from positive to negative, is predicted by this model, indicating a transformation of the universe from a state of decelerated expansion to accelerated expansion, as obtained from astrophysical observations. Time dependence of the gravitational constant (G), energy density (?), cosmological constant (?) and the EoS parameter (?) have been determined and depicted graphically in the present study.

scholarly journals Unification of the Maxwell-Einstein-Dirac Correspondence

2019 ◽  
Author(s):  
Wim Vegt
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
String Theory ◽  
Dimensional Space ◽  
Space Time ◽  
Unified Field ◽  
S Matrix ◽  
Klein Theory ◽  
Dimensional Space Time ◽  
Kaluza Klein

Albert Einstein, Lorentz and Minkowski published in 1905 the Theory of Special Relativity and Einstein published in 1915 his field theory of general relativity based on a curved 4-dimensional space-time continuum to integrate the gravitational field and the electromagnetic field in one unified field. Since then the method of Einstein’s unifying field theory has been developed by many others in more than 4 dimensions resulting finally in the well-known 10-dimensional and 11-dimensional “string theory”. String theory is an outgrowth of S-matrix theory, a research program begun by Werner Heisenberg in 1943 (following John Archibald Wheeler‘s(3) 1937 introduction of the S-matrix), picked up and advocated by many prominent theorists starting in the late 1950’s.Theodor Franz Eduard Kaluza (1885-1954), was a German mathematician and physicist well-known for the Kaluza–Klein theory involving field equations in curved five-dimensional space. His idea that fundamental forces can be unified by introducing additional dimensions re-emerged much later in the “String Theory”.The original Kaluza-Klein theory was one of the first attempts to create an unified field theory i.e. the theory, which would unify all the forces under one fundamental law. It was published in 1921 by Theodor Kaluza and extended in 1926 by Oskar Klein. The basic idea of this theory was to postulate one extra compactified space dimension and introduce nothing but pure gravity in a new (1 + 4)-dimensional space-time. Klein suggested that the fifth dimension would be rolled up into a tiny, compact loop on the order of 10-35 [m]The presented "New Unification Theory" unifies Classical Electrodynamics with General Relativity and Quantum Physics

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