scholarly journals L.R.S. Bianchi type II stiff fluid cosmological model with decaying vacuum energy density Λ in general relativity

2011 ◽  
Vol 697 (5) ◽  
pp. 429-433 ◽  
Author(s):  
Hassan Amirhashchi
Keyword(s):  
General Relativity ◽  
Energy Density ◽  
Cosmological Model ◽  
Vacuum Energy ◽  
Bianchi Type ◽  
Vacuum Energy Density ◽  
Type Ii ◽  
Stiff Fluid

scholarly journals Locally rotationally symmetric Bianchi type I massive string cosmological model with vacuum energy density and magnetic field in general relativity

2016 ◽  
Vol 94 (3) ◽  
pp. 267-270
Author(s):  
Raj Bali ◽  
Swati Singh
Keyword(s):  
Magnetic Field ◽  
Energy Density ◽  
Cosmological Model ◽  
Vacuum Energy ◽  
Bianchi Type ◽  
Vacuum Energy Density ◽  
Type I ◽  
Massive String ◽  
Total Energy Density ◽  
Rotationally Symmetric

A locally rotationally symmetric (LRS) Bianchi type I massive string cosmological model with vacuum energy density (Λ) and magnetic field is investigated. To get a deterministic model of the universe, we assume that shear (σ) is proportional to expansion (θ) and Λ ∼ 1/R2 as considered by Chen and Wu (Phys. Rev. D, 41, 695 (1990)) where R is a scale factor. We find that the total energy density (ρ), the particle density ρp decreases with time. The strong energy conditions as given by Hawking and Ellis (The large scale structure of space–time. Cambridge University Press, Cambridge, UK. p. 88. (1974)) are satisfied. The vacuum energy density decreases with time, which matches with astronomical observation. The model in general represents anisotropic space–time because of the presence of strings. The total energy density and string tension density decrease because of the presence of a magnetic field. Both the models have point-type singularities at T = 0 and τ = 0, respectively. The other physical aspects of the models are also discussed.

scholarly journals Space-Time Curvature Of General Relativity And Energy Density Of A Three-Dimensional Quantum Vacuu

2015 ◽  
Vol 69 (1) ◽  
Author(s):  
Davide Fiscaletti ◽  
Amrit Sorli
Keyword(s):  
General Relativity ◽  
Energy Density ◽  
Vacuum Energy ◽  
Three Dimensional ◽  
Space Time ◽  
Vacuum Energy Density ◽  
Quantum Vacuum ◽  
Vacuum Condensate ◽  
Interesting Solution ◽  
Variable Energy

AbstractA three-dimensional quantum vacuum condensate is introduced as a fundamental medium from which gravity emerges in a geometro-hydrodynamic limit. In this approach, the curvature of space-time characteristic of general relativity is obtained as a mathematical value of a more fundamental actual variable energy density of quantum vacuum which has a concrete physical meaning. The fluctuations of the quantum vacuum energy density suggest an interesting solution for the dark energy problem.

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.

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.

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