IMPORTANT REMARKS ON (ANTI) de SITTER SPACES AND THE COSMOLOGICAL CONSTANT

2006 ◽  
Vol 21 (35) ◽  
pp. 2685-2701 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Energy Density ◽  
Cosmological Constant ◽  
Vacuum Energy ◽  
Radial Function ◽  
Vacuum Energy Density ◽  
De Sitter ◽  
Cosmological Constant Problem ◽  
Natural Explanation ◽  
Observable Universe ◽  
Weyl Geometry

A class of proper and novel generalizations of the (anti) de Sitter solutions (parametrized by a family of radial functions R(r)) are presented that could provide a very plausible resolution of the cosmological constant problem along with a natural explanation of the ultraviolet/infrared (uv/ir) entanglement required to solve this problem. A nonvanishing value of the vacuum energy density of the order of [Formula: see text] is derived in agreement with the experimental observations. The presence of the radial function R(r) is instrumental to understand why the cosmological constant is not zero and why it is so tiny. The correct lower estimate of the mass of the observable universe related to the Dirac–Eddington's large number N = 1080 is also obtained. Finally we present our most recent findings of how Weyl Geometry via a Brans–Dicke scalar field solves the riddle of dark energy in addition to providing another derivation of the vacuum energy density.

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 Evaluation of the Cosmological Constant in Inflation with a Massive Nonminimal Scalar Field

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Jung-Jeng Huang
Keyword(s):  
Scalar Field ◽  
Dispersion Relation ◽  
Energy Density ◽  
Cosmological Constant ◽  
Vacuum Energy ◽  
Vacuum State ◽  
Energy Scale ◽  
Quantum Evolution ◽  
Vacuum Energy Density ◽  
De Sitter

In Schrödinger picture we study the possible effects of trans-Planckian physics on the quantum evolution of massive nonminimally coupled scalar field in de Sitter space. For the nonlinear Corley-Jacobson type dispersion relations with quartic or sextic correction, we obtain the time evolution of the vacuum state wave functional during slow-roll inflation and calculate explicitly the corresponding expectation value of vacuum energy density. We find that the vacuum energy density is finite. For the usual dispersion parameter choice, the vacuum energy density for quartic correction to the dispersion relation is larger than for sextic correction, while for some other parameter choices, the vacuum energy density for quartic correction is smaller than for sextic correction. We also use the backreaction to constrain the magnitude of parameters in nonlinear dispersion relation and show how the cosmological constant depends on the parameters and the energy scale during the inflation at the grand unification phase transition.

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.

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 A Unified Cosmological Model for Solution of Problems of Cosmological Constant, Cosmic Coincidence, Energy Conservation, Flatness and Homogeneity of Horizon

2021 ◽  
Author(s):  
Biswaranjan Dikshit
Keyword(s):  
Energy Density ◽  
Cosmological Model ◽  
Energy Conservation ◽  
Cosmological Constant ◽  
Vacuum Energy ◽  
Vacuum Energy Density ◽  
Zero Energy ◽  
Cosmological Constant Problem ◽  
Coincidence Problem ◽  
Horizon Problem

Cosmological constant problem is the difference by a factor of ~10123 between quantum mechanically calculated vacuum energy density and astronomically observed value. Cosmic coincidence problem questions why matter energy density is of the same order as the present vacuum energy density (former is ~32% and latter is ~68%). Recently, by quantizing zero-point field of space, we have developed a cosmological model that predicts correct value of vacuum and non-vacuum energy density. In this paper, we remove some earlier assumptions and develop a generalized version of our cosmological model to solve three more problems viz. energy conservation, flatness and horizon problem along with the above two. For creation of universe without violating law of energy conservation, net energy of the universe including (negative) gravitational potential energy must be zero. However, in conventional method, its quantitative proof needs the space to be exactly flat i.e. zero-energy universe is a consequence of flatness. But, in this paper, we will prove a zero-energy universe without using flatness of space and then show that flatness is actually a consequence of zero energy density. Finally, using our model we solve the horizon problem of universe. Although cosmic inflation can explain the flatness of space and uniformity of horizon by invoking inflaton field, it cannot predict the present value of vacuum energy density or matter density. But, our cosmological model solves in an unified manner all the above mentioned five problems viz. cosmological constant problem, cosmic coincidence problem, energy conservation, flatness and horizon problem.

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 A Resolution to the Vacuum Catastrophe

2019 ◽  
Author(s):  
Siamak Tafazoli
Keyword(s):  
Energy Density ◽  
Cosmological Constant ◽  
Vacuum Energy ◽  
Theoretical Estimate ◽  
Vacuum Energy Density ◽  
Cosmological Constant Problem

This paper presents a theoretical estimate for the vacuum energy density which turns out to be near zero and thus much more palatable than an infinite or a very large theoretical value obtained by imposing an ultraviolet frequency cut-off. This result helps address the "vacuum catastrophe" and the "cosmological constant problem".

scholarly journals Propagating q-field and q-ball solution

2017 ◽  
Vol 32 (18) ◽  
pp. 1750103 ◽  
Author(s):  
F. R. Klinkhamer ◽  
G. E. Volovik
Keyword(s):  
Energy Density ◽  
Cosmological Constant ◽  
Early Universe ◽  
Vacuum Energy ◽  
Vacuum Energy Density ◽  
Type Solution ◽  
Cosmological Constant Problem ◽  
Flat Spacetime ◽  
Q Wave

One possible solution of the cosmological constant problem involves a so-called q-field, which self-adjusts so as to give a vanishing gravitating vacuum energy density (cosmological constant) in equilibrium. We show that this q-field can manifest itself in other ways. Specifically, we establish a propagating mode (q-wave) in the nontrivial vacuum and find a particular soliton-type solution in flat spacetime, which we call a q-ball by analogy with the well-known Q-ball solution. Both q-waves and q-balls are expected to play a role for the equilibration of the q-field in the very early universe.

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