28 research outputs found
Regular and Chaotic Regimes in Scalar Field Cosmology
A transient chaos in a closed FRW cosmological model with a scalar field is studied. We describe two different chaotic regimes and show that the type of chaos in this model depends on the scalar field potential. We have found also that for sufficiently steep potentials or for potentials with large cosmological constant the chaotic behavior disappears
Certain aspects of regularity in scalar field cosmological dynamics
We consider dynamics of the FRW Universe with a scalar field. Using
Maupertuis principle we find a curvature of geodesics flow and show that zones
of positive curvature exist for all considered types of scalar field potential.
Usually, phase space of systems with the positive curvature contains islands of
regular motion. We find these islands numerically for shallow scalar field
potentials. It is shown also that beyond the physical domain the islands of
regularity exist for quadratic potentials as well.Comment: 15 pages with 4 figures; typos corrected, final version to appear in
Regular and Chaotic Dynamic
Quantum Oscillations Can Prevent the Big Bang Singularity in an Einstein-Dirac Cosmology
We consider a spatially homogeneous and isotropic system of Dirac particles
coupled to classical gravity. The dust and radiation dominated closed
Friedmann-Robertson-Walker space-times are recovered as limiting cases. We find
a mechanism where quantum oscillations of the Dirac wave functions can prevent
the formation of the big bang or big crunch singularity. Thus before the big
crunch, the collapse of the universe is stopped by quantum effects and reversed
to an expansion, so that the universe opens up entering a new era of classical
behavior.
Numerical examples of such space-times are given, and the dependence on
various parameters is discussed. Generically, one has a collapse after a finite
number of cycles. By fine-tuning the parameters we construct an example of a
space-time which is time-periodic, thus running through an infinite number of
contraction and expansion cycles.Comment: 8 pages, LaTeX, 4 figures, statement on energy conditions correcte
Brane cosmology with an anisotropic bulk
In the context of brane cosmology, a scenario where our universe is a
3+1-dimensional surface (the ``brane'') embedded in a five-dimensional
spacetime (the ``bulk''), we study geometries for which the brane is
anisotropic - more specifically Bianchi I - though still homogeneous. We first
obtain explicit vacuum bulk solutions with anisotropic three-dimensional
spatial slices. The bulk is assumed to be empty but endowed with a negative
cosmological constant. We then embed Z_2-symmetric branes in the anisotropic
spacetimes and discuss the constraints on the brane energy-momentum tensor due
to the five-dimensional anisotropic geometry. We show that if the bulk is
static, an anisotropic brane cannot support a perfect fluid. However, we find
that for some of our bulk solutions it is possible to embed a brane with a
perfect fluid though its energy density and pressure are completely determined
by the bulk geometry.Comment: 20 pages, 1 figur
Big Crunch Avoidance in k = 1 Semi-Classical Loop Quantum Cosmology
It is well known that a closed universe with a minimally coupled massive
scalar field always collapses to a singularity unless the initial conditions
are extremely fine tuned. We show that the corrections to the equations of
motion for the massive scalar field, given by loop quantum gravity in high
curvature regime, always lead to a bounce independently of the initial
conditions. In contrast to the previous works in loop quantum cosmology, we
note that the singularity can be avoided even at the semi-classical level of
effective dynamical equations with non-perturbative quantum gravity
modifications, without using a discrete quantum evolution.Comment: Minor changes, To appear in Physical Review
Bianchi type IX asymptotical behaviours with a massive scalar field: chaos strikes back
We use numerical integrations to study the asymptotical behaviour of a
homogeneous but anisotropic Bianchi type IX model in General Relativity with a
massive scalar field. As it is well known, for a Brans-Dicke theory, the
asymptotical behaviour of the metric functions is ruled only by the Brans-Dicke
coupling constant with respect to the value -3/2. In this paper we examine if
such a condition still exists with a massive scalar field. We also show that,
contrary to what occurs for a massless scalar field, the singularity
oscillatory approach may exist in presence of a massive scalar field having a
positive energy density.Comment: 31 pages, 7 figures (low resolution
Inflationary Theory and Alternative Cosmology
Recently Hollands and Wald argued that inflation does not solve any of the
major cosmological problems. We explain why we disagree with their arguments.
They also proposed a new speculative mechanism of generation of density
perturbations. We show that in their scenario the inhomogeneities responsible
for the large scale structure observed today were generated at an epoch when
the energy density of the hot universe was 10^{95} times greater than the
Planck density. The only way to avoid this problem is to assume that there was
a stage of inflation in the early universe.Comment: 17 pages, 1 fig, a discussion of a canonical measure of probability
of inflation is adde
Chaotic Inflationary Universe on Brane
The chaotic inflationary model of the early universe, proposed by Linde is
explored in the brane world considering matter described by a minimally coupled
self interacting scalar field. We obtain cosmological solutions which admit
evolution of a universe either from a singularity or without a singularity. It
is found that a very weakly coupled self-interacting scalar field is necessary
for a quartic type potential in the brane world model compared to that
necessary in general relativity. In the brane world sufficient inflation may be
obtained even with an initial scalar field having value less than the Planck
scale. It is found that if the universe is kinetic energy dominated to begin
with, it transits to an inflationary stage subsequently.Comment: 13 pages, no fig., accepted in Physical Review
Simple Dynamics on the Brane
We apply methods of dynamical systems to study the behaviour of the
Randall-Sundrum models. We determine evolutionary paths for all possible
initial conditions in a 2-dimensional phase space and we investigate the set of
accelerated models. The simplicity of our formulation in comparison to some
earlier studies is expressed in the following: our dynamical system is a
2-dimensional Hamiltonian system, and what is more advantageous, it is free
from the degeneracy of critical points so that the system is structurally
stable. The phase plane analysis of Randall-Sundrum models with isotropic
Friedmann geometry clearly shows that qualitatively we deal with the same types
of evolution as in general relativity, although quantitatively there are
important differences.Comment: an improved version, 34 pages, 9 eps figure
Homogeneous cosmologies in generalized modified gravity
Dynamical system methods are used in the study of the stability of spatially
flat homogeneous cosmologies within a large class of generalized modified
gravity models in the presence of a relativistic matter-radiation fluid. The
present approach can be considered as the generalization of previous works in
which only cases were considered. Models described by an arbitrary
function of all possible geometric invariants are investigated and general
equations giving all critical points are derived.Comment: 13 pages, no figure