scholarly journals The dynamics of brane-world cosmological models

2005 ◽  
Vol 83 (5) ◽  
pp. 475-525 ◽  
Author(s):  
A A Coley
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Initial Conditions ◽  
High Energy ◽  
Cosmological Models ◽  
Brane World ◽  
Initial Singularity ◽  
Field Equations ◽  
Cosmological Singularity ◽  
Spatially Homogeneous

Brane-world cosmology is motivated by recent developments in string/M-theory and offers a new perspective on the hierarchy problem. In the brane-world scenario, our Universe is a four-dimensional subspace or brane embedded in a higher-dimensional bulk spacetime. Ordinary matter fields are confined to the brane while the gravitational field can also propagate in the bulk, and it is not necessary for the extra dimensions to be small, or even compact, leading to modifications of Einstein's theory of general relativity at high energies. In particular, the Randall–Sundrum-type models are relatively simple phenomenological models that capture some of the essential features of the dimensional reduction of eleven-dimensional supergravity introduced by Hořava and Witten. These curved (or warped) models are self-consistent and simple and allow for an investigation of the essential nonlinear gravitational dynamics. The governing field equations induced on the brane differ from the general relativistic equations in that there are nonlocal effects from the free gravitational field in the bulk, transmitted via the projection of the bulk Weyl tensor, and the local quadratic energy-momentum corrections, which are significant in the high-energy regime close to the initial singularity. In this review, we investigate the dynamics of the five-dimensional warped Randall–Sundrum brane worlds and their generalizations, with particular emphasis on whether the currently observed high degree of homogeneity and isotropy can be explained. In particular, we discuss the asymptotic dynamical evolution of spatially homogeneous brane-world cosmological models containing both a perfect fluid and a scalar field close to the initial singularity. Using dynamical systems techniques, it is found that, for models with a physically relevant equation of state, an isotropic singularity is a past-attractor in all orthogonal spatially homogeneous models (including Bianchi type IX models). In addition, we describe the dynamics in a class of inhomogeneous brane-world models, and show that these models also have an isotropic initial singularity. These results provide support for the conjecture that typically the initial cosmological singularity is isotropic in brane-world cosmology. Consequently, we argue that, unlike the situation in general relativity, brane-world cosmological models may offer a plausible solution to the initial conditions problem in cosmology. PACS Nos.: 98.89.Cq/Jk, 04.20–q

scholarly journals Anisotropic magnetized holographic Ricci dark energy cosmological models

2017 ◽  
Vol 95 (4) ◽  
pp. 381-392 ◽  
Author(s):  
M. Vijaya Santhi ◽  
V.U.M. Rao ◽  
Y. Aditya
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Deceleration Parameter ◽  
Bianchi Type ◽  
Cosmological Models ◽  
Field Equations ◽  
Ricci Dark Energy ◽  
Theor Phys ◽  
Linearly Varying Deceleration Parameter ◽  
Spatially Homogeneous

In this paper, we have considered spatially homogeneous and anisotropic Bianchi type-III space–time filled with matter and anisotropic modified holographic Ricci dark energy in general relativity. We have solved Einstein’s field equations using the following possibilities: (i) hybrid expansion law proposed by Akarsu et al. (JCAP, 01, 022 (2014)); (ii) a varying deceleration parameter considered by Mishra et al. (Int. J. Theor. Phys. 52, 2546 (2013)); and (iii) a linearly varying deceleration parameter given by Akarsu and Dereli (Int. J. Theor. Phys. 51, 612 (2012)). We have presented the cosmological models in each of the preceding cases and studied their evolutions. We have also discussed physical and kinematical properties of the models.

General Relativity

2019 ◽  
Author(s):  
Steven Carlip
Keyword(s):  
General Relativity ◽  
High Energy Physics ◽  
Hamiltonian Formulation ◽  
Experimental Tests ◽  
High Energy ◽  
Gravitational Energy ◽  
Field Equations ◽  
Physics First ◽  
Condensed Matter Theory ◽  
Introductory Textbooks

This work is a short textbook on general relativity and gravitation, aimed at readers with a broad range of interests in physics, from cosmology to gravitational radiation to high energy physics to condensed matter theory. It is an introductory text, but it has also been written as a jumping-off point for readers who plan to study more specialized topics. As a textbook, it is designed to be usable in a one-quarter course (about 25 hours of instruction), and should be suitable for both graduate students and advanced undergraduates. The pedagogical approach is “physics first”: readers move very quickly to the calculation of observational predictions, and only return to the mathematical foundations after the physics is established. The book is mathematically correct—even nonspecialists need to know some differential geometry to be able to read papers—but informal. In addition to the “standard” topics covered by most introductory textbooks, it contains short introductions to more advanced topics: for instance, why field equations are second order, how to treat gravitational energy, what is required for a Hamiltonian formulation of general relativity. A concluding chapter discusses directions for further study, from mathematical relativity to experimental tests to quantum gravity.

A spatially homogeneous gravitational field

1966 ◽  
Vol 62 (1) ◽  
pp. 87-89 ◽  
Author(s):  
V. Joseph
Keyword(s):  
Gravitational Field ◽  
Canonical Form ◽  
Riemann Tensor ◽  
Vacuum Field ◽  
Type I ◽  
Field Equations ◽  
Parameter Group ◽  
Spatially Homogeneous ◽  
Homogeneous Gravitational Field ◽  
Type V

AbstractA solution of Einstein's vacuum field equations, apparently new, is exhibited. The metric, which is homogeneous (that is, admits a three-parameter group of motions transitive on space-like hypersurfaces), belongs to Taub Type V. The canonical form of the Riemann tensor, which is of Petrov Type I, is determined.

HIGHER-DIMENSIONAL COSMOLOGICAL MODELS WITH STRANGE QUARK MATTER

2006 ◽  
Vol 15 (04) ◽  
pp. 477-483 ◽  
Author(s):  
IHSAN YILMAZ ◽  
ATTILA ALTAY YAVUZ
Keyword(s):  
General Relativity ◽  
Quark Gluon Plasma ◽  
Quark Matter ◽  
Strange Quark ◽  
Gluon Plasma ◽  
Strange Quark Matter ◽  
Cosmological Models ◽  
Field Equations ◽  
Higher Dimensional ◽  
Different Types

In this article, we study higher-dimensional cosmological models with quark–gluon plasma in the context of general relativity. For this purpose, we consider quark–gluon plasma as a perfect fluid in the higher-dimensional universes. After solving Einstein's field equations, we have analyzed this matter for the different types of universes in the higher- and four-dimensional universes. Also, we have discussed the features of obtained solutions.

scholarly journals Gravitational Redshifts and the Mass-Radius Relation

1989 ◽  
Vol 114 ◽  
pp. 401-407
Author(s):  
Gary Wegner
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Solar System ◽  
White Dwarf ◽  
Sufficient Accuracy ◽  
Gravitational Redshift ◽  
Principle Of Equivalence ◽  
Field Equations ◽  
Tests Of General Relativity ◽  
Gravitational Field Equations

The gravitational redshift is one of Einstein’s three original tests of General Relativity and derives from time’s slowing near a massive body. For velocities well below c, this is represented with sufficient accuracy by:As detailed by Will (1981), Schiff’s conjecture argues that the gravitational redshift actually tests the principle of equivalence rather than the gravitational field equations. For low redshifts, solar system tests give highest accuracy. LoPresto & Pierce (1986) have shown that the redshift at the Sun’s limb is good to about ±3%. Rocket experiments produce an accuracy of ±0.02% (Vessot et al. 1980), while for 40 Eri B the best white dwarf, the observed and predicted VRS agree to only about ±_5% (Wegner 1980).

scholarly journals An Alternative to the Alcubierre Theory: Warp Fields by the Gravitation via Accelerated Particles Assertion

2016 ◽  
Vol 8 (5) ◽  
pp. 44
Author(s):  
Edward A. Walker
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Equilibrium Point ◽  
Space Time ◽  
Particle Accelerators ◽  
Field Equations ◽  
Time Curve ◽  
Published Paper ◽  
Accelerated Particles ◽  
Gravitational Equilibrium

<p class="1Body">A summarization of the Alcubierre metric is given in comparison to a new metric that has been formulated based on the theoretical assertion of a recently published paper entitled “gravitational space-time curve generation via accelerated particles”. The new metric mathematically describes a warp field where particle accelerators can theoretically generate gravitational space-time curves that compress or contract a volume of space-time toward a hypothetical vehicle traveling at a sub-light velocity contingent upon the amount of voltage generated. Einstein’s field equations are derived based on the new metric to show its compatibility to general relativity. The “time slowing” effects of relativistic gravitational time dilation inherent to the gravitational field generated by the particle accelerators is mathematically shown to be counteracted by a gravitational equilibrium point between an arrangement of two equal magnitude particle accelerators. The gravitational equilibrium point produces a volume of flat or linear space-time to which the hypothetical vehicle can traverse the region of contracted space-time without experiencing time slippage. The theoretical warp field possessing these attributes is referred to as the two gravity source warp field which is mathematically described by the new metric.</p>

A NOETHER SYMMETRY STUDY IN SCALAR-TENSOR THEORY

1998 ◽  
Vol 13 (24) ◽  
pp. 4163-4171 ◽  
Author(s):  
B. MODAK ◽  
S. KAMILYA ◽  
S. BISWAS
Keyword(s):  
General Relativity ◽  
Functional Form ◽  
Noether Symmetry ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Tensor Theory ◽  
Exponential Expansion ◽  
General Scalar ◽  
Spatially Homogeneous ◽  
The Universe

In this work we study a general scalar-tensor theory in which the coupling and potential functions are determined from Noether symmetry arguments. We also obtain exact solutions of the field equations and found that the universe asymptotically follows an exponential expansion having no graceful exit. The study of the functional form of ω(φ) reveals that the theory asymptotically becomes an attractor of general relativity. We restrict ourselves to spatially homogeneous, isotropic flat universe.

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.

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