235 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
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
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
On the twin paradox in static spacetimes: I. Schwarzschild metric
Motivated by a conjecture put forward by Abramowicz and Bajtlik we reconsider
the twin paradox in static spacetimes. According to a well known theorem in
Lorentzian geometry the longest timelike worldline between two given points is
the unique geodesic line without points conjugate to the initial point on the
segment joining the two points. We calculate the proper times for static twins,
for twins moving on a circular orbit (if it is a geodesic) around a centre of
symmetry and for twins travelling on outgoing and ingoing radial timelike
geodesics. We show that the twins on the radial geodesic worldlines are always
the oldest ones and we explicitly find the conjugate points (if they exist)
outside the relevant segments. As it is of its own mathematical interest, we
find general Jacobi vector fields on the geodesic lines under consideration. In
the first part of the work we investigate Schwarzschild geometry.Comment: 18 pages, paper accepted for publication in Gen. Rel. Gra
Randall-Sundrum Model in the Presence of a Brane Bulk Viscosity
The presence of a bulk viscosity for the cosmic fluid on a single
Randall-Sundrum brane is considered. The spatial curvature is assumed to be
zero. The five-dimensional Friedmann equation is derived, together with the
energy conservation equation for the viscous fluid. These governing equations
are solved for some special cases: (i) in the low-energy limit when the matter
energy density is small compared with brane tension; (ii) for a
matter-dominated universe, and (iii) for a radiation-dominated universe. Rough
numerical estimates, for the extreme case when the universe is at its Planck
time, indicate that the viscous effect can be significant.Comment: 18 pages, RevTeX4, no figures. Discussion in Sec. III expanded; new
references. To appear in Phys. Rev.
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.
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
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
Vacuum polarization on the spinning circle
Vacuum polarization of a massive scalar field in the background of a
two-dimensional version of a spinning cosmic string is investigated. It is
shown that when the `radius of the universe' is such that spacetime is globally
hyperbolic the vacuum fluctuations are well behaved, diverging though on the
`chronology horizon'. Naive use of the formulae when spacetime is nonglobally
hyperbolic leads to unphysical results. It is also pointed out that the set of
normal modes used previously in the literature to address the problem gives
rise to two-point functions which do not have a Hadamard form, and therefore
are not physically acceptable. Such normal modes correspond to a locally (but
not globally) Minkowski time, which appears to be at first sight a natural
choice of time to implement quantization.Comment: 3 pages, no figures, REVTeX4, published versio
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
- …