134 research outputs found
Tilted two-fluid Bianchi type I models
In this paper we investigate expanding Bianchi type I models with two tilted
fluids with the same linear equation of state, characterized by the equation of
state parameter w. Individually the fluids have non-zero energy fluxes w.r.t.
the symmetry surfaces, but these cancel each other because of the Codazzi
constraint. We prove that when w=0 the model isotropizes to the future. Using
numerical simulations and a linear analysis we also find the asymptotic states
of models with w>0. We find that future isotropization occurs if and only if . The results are compared to similar models investigated previously
where the two fluids have different equation of state parameters.Comment: 14 pages, 3 figure
All metrics have curvature tensors characterised by its invariants as a limit: the \epsilon-property
We prove a generalisation of the -property, namely that for any
dimension and signature, a metric which is not characterised by its polynomial
scalar curvature invariants, there is a frame such that the components of the
curvature tensors can be arbitrary close to a certain "background". This
"background" is defined by its curvature tensors: it is characterised by its
curvature tensors and has the same polynomial curvature invariants as the
original metric.Comment: 6 page
Late-time behaviour of the tilted Bianchi type VI models
We study tilted perfect fluid cosmological models with a constant equation of
state parameter in spatially homogeneous models of Bianchi type VI
using dynamical systems methods and numerical simulations. We study models with
and without vorticity, with an emphasis on their future asymptotic evolution.
We show that for models with vorticity there exists, in a small region of
parameter space, a closed curve acting as the attractor.Comment: 13 pages, 1 figure, v2: typos fixed, minor changes, matches published
versio
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
Uniqueness of Petrov type D spatially inhomogeneous irrotational silent models
The consistency of the constraint with the evolution equations for spatially
inhomogeneous and irrotational silent (SIIS) models of Petrov type I, demands
that the former are preserved along the timelike congruence represented by the
velocity of the dust fluid, leading to \emph{new} non-trivial constraints. This
fact has been used to conjecture that the resulting models correspond to the
spatially homogeneous (SH) models of Bianchi type I, at least for the case
where the cosmological constant vanish. By exploiting the full set of the
constraint equations as expressed in the 1+3 covariant formalism and using
elements from the theory of the spacelike congruences, we provide a direct and
simple proof of this conjecture for vacuum and dust fluid models, which shows
that the Szekeres family of solutions represents the most general class of SIIS
models. The suggested procedure also shows that, the uniqueness of the SIIS of
the Petrov type D is not, in general, affected by the presence of a non-zero
pressure fluid. Therefore, in order to allow a broader class of Petrov type I
solutions apart from the SH models of Bianchi type I, one should consider more
general ``silent'' configurations by relaxing the vanishing of the vorticity
and the magnetic part of the Weyl tensor but maintaining their ``silence''
properties i.e. the vanishing of the curls of and the pressure
.Comment: Latex, 19 pages, no figures;(v2) some clarification remarks and an
appendix are added; (v3) minor changes to match published versio
The late-time behaviour of vortic Bianchi type VIII Universes
We use the dynamical systems approach to investigate the Bianchi type VIII
models with a tilted -law perfect fluid. We introduce
expansion-normalised variables and investigate the late-time asymptotic
behaviour of the models and determine the late-time asymptotic states. For the
Bianchi type VIII models the state space is unbounded and consequently, for all
non-inflationary perfect fluids, one of the curvature variables grows without
bound. Moreover, we show that for fluids stiffer than dust (), the
fluid will in general tend towards a state of extreme tilt. For dust
(), or for fluids less stiff than dust (), we show that
the fluid will in the future be asymptotically non-tilted. Furthermore, we show
that for all the universe evolves towards a vacuum state but
does so rather slowly, .Comment: 19 pages, 3 ps figures, v2:typos fixed, refs and more discussion
adde
Fluid observers and tilting cosmology
We study perfect fluid cosmological models with a constant equation of state
parameter in which there are two naturally defined time-like
congruences, a geometrically defined geodesic congruence and a non-geodesic
fluid congruence. We establish an appropriate set of boost formulae relating
the physical variables, and consequently the observed quantities, in the two
frames. We study expanding spatially homogeneous tilted perfect fluid models,
with an emphasis on future evolution with extreme tilt. We show that for
ultra-radiative equations of state (i.e., ), generically the tilt
becomes extreme at late times and the fluid observers will reach infinite
expansion within a finite proper time and experience a singularity similar to
that of the big rip. In addition, we show that for sub-radiative equations of
state (i.e., ), the tilt can become extreme at late times and
give rise to an effective quintessential equation of state. To establish the
connection with phantom cosmology and quintessence, we calculate the effective
equation of state in the models under consideration and we determine the future
asymptotic behaviour of the tilting models in the fluid frame variables using
the boost formulae. We also discuss spatially inhomogeneous models and tilting
spatially homogeneous models with a cosmological constant
A spacetime not characterised by its invariants is of aligned type II
By using invariant theory we show that a (higher-dimensional) Lorentzian
metric that is not characterised by its invariants must be of aligned type II;
i.e., there exists a frame such that all the curvature tensors are
simultaneously of type II. This implies, using the boost-weight decomposition,
that for such a metric there exists a frame such that all positive boost-weight
components are zero. Indeed, we show a more general result, namely that any set
of tensors which is not characterised by its invariants, must be of aligned
type II. This result enables us to prove a number of related results, among
them the algebraic VSI conjecture.Comment: 14pages, CQG to appea
Essential Constants for Spatially Homogeneous Ricci-flat manifolds of dimension 4+1
The present work considers (4+1)-dimensional spatially homogeneous vacuum
cosmological models. Exact solutions -- some already existing in the
literature, and others believed to be new -- are exhibited. Some of them are
the most general for the corresponding Lie group with which each homogeneous
slice is endowed, and some others are quite general. The characterization
``general'' is given based on the counting of the essential constants, the
line-element of each model must contain; indeed, this is the basic contribution
of the work. We give two different ways of calculating the number of essential
constants for the simply transitive spatially homogeneous (4+1)-dimensional
models. The first uses the initial value theorem; the second uses, through
Peano's theorem, the so-called time-dependent automorphism inducing
diffeomorphismsComment: 26 Pages, 2 Tables, latex2
Quantum creation of an Inhomogeneous universe
In this paper we study a class of inhomogeneous cosmological models which is
a modified version of what is usually called the Lema\^itre-Tolman model. We
assume that we have a space with 2-dimensional locally homogeneous spacelike
surfaces. In addition we assume they are compact. Classically we investigate
both homogeneous and inhomogeneous spacetimes which this model describe. For
instance one is a quotient of the AdS space which resembles the BTZ black
hole in AdS.
Due to the complexity of the model we indicate a simpler model which can be
quantized easily. This model still has the feature that it is in general
inhomogeneous. How this model could describe a spontaneous creation of a
universe through a tunneling event is emphasized.Comment: 21 pages, 5 ps figures, REVTeX, new subsection include
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