1,701 research outputs found
Lorentz Invariance Violation induced time delays in GRBs in different cosmological models
Lorentz Invariance Violation (LIV) manifesting itself by energy dependent
modification of standard relativistic dispersion relation has recently
attracted a considerable attention. Ellis et al. previously investigated the
energy dependent time offsets in different energy bands on a sample of gamma
ray bursts and, assuming standard cosmological model, they found a weak
indication for redshift dependence of time delays suggestive of LIV. Going
beyond the CDM cosmology we extend this analysis considering also four
alternative models of dark energy (quintessence with constant and variable
equation of state, Chaplygin gas and brane-world cosmology). It turns out that
the effect noticed by Ellis et al. is also present in those models and is the
strongest for quintessence with variable equation of state.Comment: 14 pages, 1 figur
Dynamical System Approach to Cosmological Models with a Varying Speed of Light
Methods of dynamical systems have been used to study homogeneous and
isotropic cosmological models with a varying speed of light (VSL). We propose
two methods of reduction of dynamics to the form of planar Hamiltonian
dynamical systems for models with a time dependent equation of state. The
solutions are analyzed on two-dimensional phase space in the variables where is a function of a scale factor . Then we show how the
horizon problem may be solved on some evolutional paths. It is shown that the
models with negative curvature overcome the horizon and flatness problems. The
presented method of reduction can be adopted to the analysis of dynamics of the
universe with the general form of the equation of state .
This is demonstrated using as an example the dynamics of VSL models filled with
a non-interacting fluid. We demonstrate a new type of evolution near the
initial singularity caused by a varying speed of light. The singularity-free
oscillating universes are also admitted for positive cosmological constant. We
consider a quantum VSL FRW closed model with radiation and show that the
highest tunnelling rate occurs for a constant velocity of light if and . It is also proved that the considered class of
models is structurally unstable for the case of .Comment: 18 pages, 5 figures, RevTeX4; final version to appear in PR
Topological quantum numbers and curvature -- examples and applications
Using the idea of the degree of a smooth mapping between two manifolds of the
same dimension we present here the topological (homotopical) classification of
the mappings between spheres of the same dimension, vector fields, monopole and
instanton solutions. Starting with a review of the elements of Riemannian
geometry we also present an original elementary proof of the Gauss-Bonnet
theorem and the Poincar\'{e}-Hopf theorem.Comment: LaTeX2e, 26 pages, 4 figure
Cosmological applications in Kaluza-Klein theory
The field equations of Kaluza-Klein (KK) theory have been applied in the
domain of cosmology. These equations are solved for a flat universe by taking
the gravitational and the cosmological constants as a function of time t. We
use Taylor's expansion of cosmological function, , up to the first
order of the time . The cosmological parameters are calculated and some
cosmological problems are discussed.Comment: 14 pages Latex, 5 figures, one table. arXiv admin note: text overlap
with arXiv:gr-qc/9805018 and arXiv:astro-ph/980526
Differences between palpation and static/dynamic tests to diagnose painful temporomandibular disorders in patients with Lyme disease
A weak acceleration effect due to residual gravity in a multiply connected universe
Could cosmic topology imply dark energy? We use a weak field (Newtonian)
approximation of gravity and consider the gravitational effect from distant,
multiple copies of a large, collapsed (virialised) object today (i.e. a massive
galaxy cluster), taking into account the finite propagation speed of gravity,
in a flat, multiply connected universe, and assume that due to a prior epoch of
fast expansion (e.g. inflation), the gravitational effect of the distant copies
is felt locally, from beyond the naively calculated horizon. We find that for a
universe with a spatial section, the residual Newtonian gravitational
force (to first order) provides an anisotropic effect that repels test
particles from the cluster in the compact direction, in a way algebraically
similar to that of dark energy. For a typical test object at comoving distance
from the nearest dense nodes of the cosmic web of density perturbations,
the pressure-to-density ratio of the equation of state in an FLRW universe,
is w \sim - (\chi/L)^3, where is the size of the fundamental domain, i.e.
of the universe. Clearly, |w|<<1. For a T^3 spatial section of exactly equal
fundamental lengths, the effect cancels to zero. For a T^3 spatial section of
unequal fundamental lengths, the acceleration effect is anisotropic in the
sense that it will *tend to equalise the three fundamental lengths*. Provided
that at least a modest amount of inflation occurred in the early Universe, and
given some other conditions, multiple connectedness does generate an effect
similar to that of dark energy, but the amplitude of the effect at the present
epoch is too small to explain the observed dark energy density and its
anisotropy makes it an unrealistic candidate for the observed dark energy.Comment: 12 pages, 8 figures, accepted by Astronomy & Astrophysics; v2
includes 3D calculation and result; v3 includes analysis of numerical
simulation, matches accepted versio
Chaos in black holes surrounded by gravitational waves
The occurrence of chaos for test particles moving around Schwarzschild black
holes perturbed by a special class of gravitational waves is studied in the
context of the Melnikov method. The explicit integration of the equations of
motion for the homoclinic orbit is used to reduce the application of this
method to the study of simple graphics.Comment: 15 pages, LaTex
The tale of two centres
We study motion in the field of two fixed centres described by a family of
Einstein-dilaton-Maxwell theories. Transitions between regular and chaotic
motion are observed as the dilaton coupling is varied.Comment: 20 pages, RevTeX, 7 figures included, TeX format change
Group analysis of structure equations for stars in radiative and convective equilibrium
It is proposed to use the Lie group theory of symmetries of differential
equations to investigate the system of equations describing a static star in a
radiative and convective equilibrium. It is shown that the action of an
admissible group induces a certain algebraic structure in the set of all
solutions, which can be used to find a family of new solutions. We have
demonstrated that, in the most general case, the equations admit an infinite
parameter group of quasi-homologous transformations. We have found invariants
of the symmetries group which correspond to the fundamental relations
describing a physical characteristic of the stars such as the
Hertzsprung-Russell diagram or the mass-luminosity relation. In this way we can
suggest that group invariants have not only purely mathematical sense, but
their forms are closely associated with the basic empirical relations.Comment: LaTeX2e, 13page
Equation of state for Universe from similarity symmetries
In this paper we proposed to use the group of analysis of symmetries of the
dynamical system to describe the evolution of the Universe. This methods is
used in searching for the unknown equation of state. It is shown that group of
symmetries enforce the form of the equation of state for noninteracting scaling
multifluids. We showed that symmetries give rise the equation of state in the
form and energy density
, which
is commonly used in cosmology. The FRW model filled with scaling fluid (called
homological) is confronted with the observations of distant type Ia supernovae.
We found the class of model parameters admissible by the statistical analysis
of SNIa data. We showed that the model with scaling fluid fits well to
supernovae data. We found that and (), which can correspond to (hyper) phantom fluid, and to a
high density universe. However if we assume prior that
then the favoured model is close to concordance
CDM model. Our results predict that in the considered model with
scaling fluids distant type Ia supernovae should be brighter than in
CDM model, while intermediate distant SNIa should be fainter than in
CDM model. We also investigate whether the model with scaling fluid is
actually preferred by data over CDM model. As a result we find from
the Akaike model selection criterion prefers the model with noninteracting
scaling fluid.Comment: accepted for publication versio
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