8 research outputs found
Spike Oscillations
According to Belinskii, Khalatnikov and Lifshitz (BKL), a generic spacelike
singularity is characterized by asymptotic locality: Asymptotically, toward the
singularity, each spatial point evolves independently from its neighbors, in an
oscillatory manner that is represented by a sequence of Bianchi type I and II
vacuum models. Recent investigations support a modified conjecture: The
formation of spatial structures (`spikes') breaks asymptotic locality. The
complete description of a generic spacelike singularity involves spike
oscillations, which are described by sequences of Bianchi type I and certain
inhomogeneous vacuum models. In this paper we describe how BKL and spike
oscillations arise from concatenations of exact solutions in a
Hubble-normalized state space setting, suggesting the existence of hidden
symmetries and showing that the results of BKL are part of a greater picture.Comment: 38 pages, 14 figure
Bianchi Cosmologies with Anisotropic Matter: Locally Rotationally Symmetric Models
The dynamics of cosmological models with isotropic matter sources (perfect
fluids) is extensively studied in the literature; in comparison, the dynamics
of cosmological models with anisotropic matter sources is not. In this paper we
consider spatially homogeneous locally rotationally symmetric solutions of the
Einstein equations with a large class of anisotropic matter models including
collisionless matter (Vlasov), elastic matter, and magnetic fields. The
dynamics of models of Bianchi types I, II, and IX are completely described; the
two most striking results are the following: (i) There exist matter models,
compatible with the standard energy conditions, such that solutions of Bianchi
type IX (closed cosmologies) need not necessarily recollapse; there is an open
set of forever expanding solutions. (ii) Generic type IX solutions associated
with a matter model like Vlasov matter exhibit oscillatory behavior toward the
initial singularity. This behavior differs significantly from that of
vacuum/perfect fluid cosmologies; hence "matter matters". Finally, we indicate
that our methods can probably be extended to treat a number of open problems,
in particular, the dynamics of Bianchi type VIII and Kantowski-Sachs solutions.Comment: 64 pages, 19 Figure
Thermodynamics and Kinetic Theory of Relativistic Gases in 2-D Cosmological Models
A kinetic theory of relativistic gases in a two-dimensional space is
developed in order to obtain the equilibrium distribution function and the
expressions for the fields of energy per particle, pressure, entropy per
particle and heat capacities in equilibrium. Furthermore, by using the method
of Chapman and Enskog for a kinetic model of the Boltzmann equation the
non-equilibrium energy-momentum tensor and the entropy production rate are
determined for a universe described by a two-dimensional Robertson-Walker
metric. The solutions of the gravitational field equations that consider the
non-equilibrium energy-momentum tensor - associated with the coefficient of
bulk viscosity - show that opposed to the four-dimensional case, the cosmic
scale factor attains a maximum value at a finite time decreasing to a "big
crunch" and that there exists a solution of the gravitational field equations
corresponding to a "false vacuum". The evolution of the fields of pressure,
energy density and entropy production rate with the time is also discussed.Comment: 23 pages, accepted in PR
Irreversible Processes in Inflationary Cosmological Models
By using the thermodynamic theory of irreversible processes and Einstein
general relativity, a cosmological model is proposed where the early universe
is considered as a mixture of a scalar field with a matter field. The scalar
field refers to the inflaton while the matter field to the classical particles.
The irreversibility is related to a particle production process at the expense
of the gravitational energy and of the inflaton energy. The particle production
process is represented by a non-equilibrium pressure in the energy-momentum
tensor. The non-equilibrium pressure is proportional to the Hubble parameter
and its proportionality factor is identified with the coefficient of bulk
viscosity. The dynamic equations of the inflaton and the Einstein field
equations determine the time evolution of the cosmic scale factor, the Hubble
parameter, the acceleration and of the energy densities of the inflaton and
matter. Among other results it is shown that in some regimes the acceleration
is positive which simulates an inflation. Moreover, the acceleration decreases
and tends to zero in the instant of time where the energy density of matter
attains its maximum value.Comment: 13 pages, 2 figures, to appear in PR