234 research outputs found
Classical and quantum massive cosmology for the open FRW universe
In an open Friedmann-Robertson-Walker (FRW) space background, we study the
classical and quantum cosmological models in the framework of the recently
proposed nonlinear massive gravity theory. Although the constraints which are
present in this theory prevent it from admitting the flat and closed FRW models
as its cosmological solutions, for the open FRW universe, it is not the case.
We have shown that, either in the absence of matter or in the presence of a
perfect fluid, the classical field equations of such a theory adopt physical
solutions for the open FRW model, in which the mass term shows itself as a
cosmological constant. These classical solutions consist of two distinguishable
branches: One is a contacting universe which tends to a future singularity with
zero size, while another is an expanding universe having a past singularity
from which it begins its evolution. A classically forbidden region separates
these two branches from each other. We then employ the familiar canonical
quantization procedure in the given cosmological setting to find the
cosmological wave functions. We use the resulting wave function to investigate
the possibility of the avoidance of classical singularities due to quantum
effects. It is shown that the quantum expectation values of the scale factor,
although they have either contracting or expanding phases like their classical
counterparts, are not disconnected from each other. Indeed, the classically
forbidden region may be replaced by a bouncing period in which the scale factor
bounces from the contraction to its expansion eras. Using the Bohmian approach
of quantum mechanics, we also compute the Bohmian trajectory and the quantum
potential related to the system, which their analysis shows are the direct
effects of the mass term on the dynamics of the universe.Comment: 18 pages, 7 figures, typos corrected, refs. adde
Relativistic contraction and related effects in noninertial frames
Although there is no relative motion among different points on a rotating
disc, each point belongs to a different noninertial frame. This fact, not
recognized in previous approaches to the Ehrenfest paradox and related
problems, is exploited to give a correct treatment of a rotating ring and a
rotating disc. Tensile stresses are recovered, but, contrary to the prediction
of the standard approach, it is found that an observer on the rim of the disc
will see equal lengths of other differently moving objects as an inertial
observer whose instantaneous position and velocity are equal to that of the
observer on the rim. The rate of clocks at various positions, as seen by
various observers, is also discussed. Some results are generalized for
observers arbitrarily moving in a flat or a curved spacetime. The generally
accepted formula for the space line element in a non-time-orthogonal frame is
found inappropriate in some cases. Use of Fermi coordinates leads to the result
that for any observer the velocity of light is isotropic and is equal to ,
providing that it is measured by propagating a light beam in a small
neighborhood of the observer.Comment: 15 pages, significantly revised version, title changed, to appear in
Phys. Rev.
Entropy of gravitationally collapsing matter in FRW universe models
We look at a gas of dust and investigate how its entropy evolves with time
under a spherically symmetric gravitational collapse. We treat the problem
perturbatively and find that the classical thermodynamic entropy does actually
increase to first order when one allows for gravitational potential energy to
be transferred to thermal energy during the collapse. Thus, in this situation
there is no need to resort to the introduction of an intrinsic gravitational
entropy in order to satisfy the second law of thermodynamics.Comment: 9 pages, 4 figures. Major changes from previous version. We consider
only thermodynamic entropy in this version. Published in PR
Time-Symmetrization and Isotropization of Stiff-Fluid Kantowski-Sachs Universes
It is shown that growing-entropy stiff-fluid Kantowski-Sachs universes become
time-symmetric (if they start with time-asymmetric phase) and isotropize.
Isotropization happens without any inflationary era during the evolution since
there is no cosmological term here. It seems that this approach is an
alternative to inflation since the universe gets bigger and bigger approaching
'flatness'.Comment: 9 pages, no figure
Magnetohydrodynamics in the Inflationary Universe
Magnetohydrodynamic (MHD) waves are analysed in the early Universe, in the
inflationary era, assuming the Universe to be filled with a nonviscous fluid of
the Zel'dovich type () in a metric of the de Sitter form. A spatially
uniform, time dependent, magnetic field is assumed to be present.
The Einstein equations are first solved to give the time dependence of the
scale factor, assuming that the matter density, but not the magnetic field,
contribute as source terms. The various modes are thereafter analysed; they
turn out to be essentially of the same kind as those encountered in
conventional nongravitational MHD, although the longitudinal magnetosonic wave
is not interpretable as a physical energy-transporting wave as the group
velocity becomes superluminal. We determine the phase speed of the various
modes; they turn out to be scale factor independent. The Alfv\'{e}n velocity of
the transverse magnetohydrodynamic wave becomes extremely small in the
inflationary era, showing that the wave is in practice 'frozen in'.Comment: 19 pages, LaTeX, no figures. Minor additions to the Summary section
and Acknowledgments section. Two new references. Version to appear in Phys.
Rev.
The Relative Space: Space Measurements on a Rotating Platform
We introduce here the concept of relative space, an extended 3-space which is
recognized as the only space having an operational meaning in the study of the
space geometry of a rotating disk. Accordingly, we illustrate how space
measurements are performed in the relative space, and we show that an old-aged
puzzling problem, that is the Ehrenfest's paradox, is explained in this purely
relativistic context. Furthermore, we illustrate the kinematical origin of the
tangential dilation which is responsible for the solution of the Ehrenfest's
paradox.Comment: 14 pages, 2 EPS figures, LaTeX, to appear in the European Journal of
Physic
Evolution of the Bianchi I, the Bianchi III and the Kantowski-Sachs Universe: Isotropization and Inflation
We study the Einstein-Klein-Gordon equations for a convex positive potential
in a Bianchi I, a Bianchi III and a Kantowski-Sachs universe. After analysing
the inherent properties of the system of differential equations, the study of
the asymptotic behaviors of the solutions and their stability is done for an
exponential potential. The results are compared with those of Burd and Barrow.
In contrast with their results, we show that for the BI case isotropy can be
reached without inflation and we find new critical points which lead to new
exact solutions. On the other hand we recover the result of Burd and Barrow
that if inflation occurs then isotropy is always reached. The numerical
integration is also done and all the asymptotical behaviors are confirmed.Comment: 22 pages, 12 figures, Self-consistent Latex2e File. To be published
in Phys. Rev.
Gravitational Entropy and Quantum Cosmology
We investigate the evolution of different measures of ``Gravitational
Entropy'' in Bianchi type I and Lema\^itre-Tolman universe models.
A new quantity behaving in accordance with the second law of thermodynamics
is introduced. We then go on and investigate whether a quantum calculation of
initial conditions for the universe based upon the Wheeler-DeWitt equation
supports Penrose's Weyl Curvature Conjecture, according to which the Ricci part
of the curvature dominates over the Weyl part at the initial singularity of the
universe. The theory is applied to the Bianchi type I universe models with dust
and a cosmological constant and to the Lema\^itre-Tolman universe models. We
investigate two different versions of the conjecture. First we investigate a
local version which fails to support the conjecture. Thereafter we construct a
non-local entity which shows more promising behaviour concerning the
conjecture.Comment: 20 pages, 7 ps figure
Relativistic anisotropic charged fluid spheres with varying cosmological constant
Static spherically symmetric anisotropic source has been studied for the
Einstein-Maxwell field equations assuming the erstwhile cosmological constant to be a space-variable scalar, viz., . Two
cases have been examined out of which one reduces to isotropic sphere. The
solutions thus obtained are shown to be electromagnetic in origin as a
particular case. It is also shown that the generally used pure charge
condition, viz., is not always required for constructing
electromagnetic mass models.Comment: 15 pages, 3 eps figure
Bianchi type I cyclic cosmology from Lie-algebraically deformed phase space
We study the effects of noncommutativity, in the form of a Lie-algebraically
deformed Poisson commutation relations, on the evolution of a Bianchi type I
cosmological model with a positive cosmological constant. The phase space
variables turn out to correspond to the scale factors of this model in ,
and directions. According to the conditions that the structure constants
(deformation parameters) should satisfy, we argue that there are two types of
noncommutative phase space with Lie-algebraic structure. The exact classical
solutions in commutative and type I noncommutative cases are presented. In the
framework of this type of deformed phase space, we investigate the possibility
of building a Bianchi I model with cyclic scale factors in which the size of
the universe in each direction experiences an endless sequence of contractions
and re-expansions. We also obtain some approximate solutions for the type II
noncommutative structure by numerical methods and show that the cyclic behavior
is repeated as well. These results are compared with the standard commutative
case, and similarities and differences of these solutions are discussed.Comment: 13 pages, to appear in PRD, typos corrected, Refs. adde
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