963 research outputs found
On homothetic cosmological dynamics
We consider the homogeneous and isotropic cosmological fluid dynamics which
is compatible with a homothetic, timelike motion, equivalent to an equation of
state . By splitting the total pressure into the sum of an
equilibrium part and a non-equilibrium part , we find that on
thermodynamical grounds this split is necessarily given by and , corresponding to a dissipative stiff (Zel'dovich) fluid.Comment: 8 pages, to be published in Class. Quantum Gra
Axially Symmetric Bianchi I Yang-Mills Cosmology as a Dynamical System
We construct the most general form of axially symmetric SU(2)-Yang-Mills
fields in Bianchi cosmologies. The dynamical evolution of axially symmetric YM
fields in Bianchi I model is compared with the dynamical evolution of the
electromagnetic field in Bianchi I and the fully isotropic YM field in
Friedmann-Robertson-Walker cosmologies. The stochastic properties of axially
symmetric Bianchi I-Einstein-Yang-Mills systems are compared with those of
axially symmetric YM fields in flat space. After numerical computation of
Liapunov exponents in synchronous (cosmological) time, it is shown that the
Bianchi I-EYM system has milder stochastic properties than the corresponding
flat YM system. The Liapunov exponent is non-vanishing in conformal time.Comment: 18 pages, 6 Postscript figures, uses amsmath,amssymb,epsfig,verbatim,
to appear in CQ
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.
Dust-filled axially symmetric universes with a cosmological constant
Following the recent recognition of a positive value for the vacuum energy
density and the realization that a simple Kantowski-Sachs model might fit the
classical tests of cosmology, we study the qualitative behavior of three
anisotropic and homogeneous models: Kantowski-Sachs, Bianchi type-I and Bianchi
type-III universes, with dust and a cosmological constant, in order to find out
which are physically permitted. We find that these models undergo
isotropization up to the point that the observations will not be able to
distinguish between them and the standard model, except for the Kantowski-Sachs
model
with smaller than some critical value
. Even if one imposes that the Universe should be nearly
isotropic since the last scattering epoch (), meaning that the
Universe should have approximately the same Hubble parameter in all directions
(considering the COBE 4-Year data), there is still a large range for the matter
density parameter compatible with Kantowsky-Sachs and Bianchi type-III if
, for a very small . The
Bianchi type-I model becomes exactly isotropic owing to our restrictions and we
have in this case. Of course, all these models
approach locally an exponential expanding state provided the cosmological
constant .Comment: 12 pages, 9 figures, 1 table. Published in Physical Review D 1
Chaotic Friedmann-Robertson-Walker Cosmology
We show that the dynamics of a spatially closed Friedmann - Robertson -
Walker Universe conformally coupled to a real, free, massive scalar field, is
chaotic, for large enough field amplitudes. We do so by proving that this
system is integrable under the adiabatic approximation, but that the
corresponding KAM tori break up when non adiabatic terms are considered. This
finding is confirmed by numerical evaluation of the Lyapunov exponents
associated with the system, among other criteria. Chaos sets strong limitations
to our ability to predict the value of the field at the Big Crunch, from its
given value at the Big Bang. (Figures available on request)Comment: 28 pages, 11 figure
The stability of cosmological scaling solutions
We study the stability of cosmological scaling solutions within the class of
spatially homogeneous cosmological models with a perfect fluid subject to the
equation of state p_gamma=(gamma-1) rho_gamma (where gamma is a constant
satisfying 0 < gamma < 2) and a scalar field with an exponential potential. The
scaling solutions, which are spatially flat isotropic models in which the
scalar field energy density tracks that of the perfect fluid, are of physical
interest. For example, in these models a significant fraction of the current
energy density of the Universe may be contained in the scalar field whose
dynamical effects mimic cold dark matter. It is known that the scaling
solutions are late-time attractors (i.e., stable) in the subclass of flat
isotropic models. We find that the scaling solutions are stable (to shear and
curvature perturbations) in generic anisotropic Bianchi models when gamma <
2/3. However, when gamma > 2/3, and particularly for realistic matter with
gamma >= 1, the scaling solutions are unstable; essentially they are unstable
to curvature perturbations, although they are stable to shear perturbations. We
briefly discuss the physical consequences of these results.Comment: AMSTeX, 7 pages, re-submitted to Phys Rev Let
On the Stability of the Einstein Static Universe
We show using covariant techniques that the Einstein static universe
containing a perfect fluid is always neutrally stable against small
inhomogeneous vector and tensor perturbations and neutrally stable against
adiabatic scalar density inhomogeneities so long as c_{s}^2>1/5, and unstable
otherwise. We also show that the stability is not significantly changed by the
presence of a self-interacting scalar field source, but we find that spatially
homogeneous Bianchi type IX modes destabilise an Einstein static universe. The
implications of these results for the initial state of the universe and its
pre-inflationary evolution are also discussed.Comment: some additional comments and references; version to appear in Class.
Quant. Gra
Exponential potentials and cosmological scaling solutions
We present a phase-plane analysis of cosmologies containing a barotropic
fluid with equation of state , plus a scalar
field with an exponential potential where . In addition to the well-known inflationary
solutions for in which the scalar field energy density tracks that of the barotropic
fluid (which for example might be radiation or dust). We show that the scaling
solutions are the unique late-time attractors whenever they exist. The
fluid-dominated solutions, where at late times, are
always unstable (except for the cosmological constant case ). The
relative energy density of the fluid and scalar field depends on the steepness
of the exponential potential, which is constrained by nucleosynthesis to
. We show that standard inflation models are unable to solve
this `relic density' problem.Comment: 6 pages RevTeX file with four figures incorporated (uses RevTeX and
epsf). Matches published versio
Collective traffic-like movement of ants on a trail: dynamical phases and phase transitions
The traffic-like collective movement of ants on a trail can be described by a
stochastic cellular automaton model. We have earlier investigated its unusual
flow-density relation by using various mean field approximations and computer
simulations. In this paper, we study the model following an alternative
approach based on the analogy with the zero range process, which is one of the
few known exactly solvable stochastic dynamical models. We show that our theory
can quantitatively account for the unusual non-monotonic dependence of the
average speed of the ants on their density for finite lattices with periodic
boundary conditions. Moreover, we argue that the model exhibits a continuous
phase transition at the critial density only in a limiting case. Furthermore,
we investigate the phase diagram of the model by replacing the periodic
boundary conditions by open boundary conditions.Comment: 8 pages, 6 figure
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