3 research outputs found
Asymptotic Properties of a Supposedly Regular (Dirac-Born-Infeld) Modification of General Relativity
We apply the dynamical systems tools to study the asymptotic properties of a
cosmological model based on a non-linear modification of General Relativity in
which the standard Einstein-Hilbert action is replaced by one of
Dirac-Born-Infeld type. It is shown that the dynamics of this model is
extremely rich: there are found equilibrium points in the phase space that can
be associated with matter-dominated, matter-curvature scaling, de Sitter, and
even phantom-like solutions. Depending on the value of the overall parameters
the dynamics in phase space can show multi-attractor structure into the future
(multiple future attractors may co-exist). This is a consequence of
bifurcations in control parameter space, showing strong dependence of the
model's dynamical properties on the free parameters. Contrary to what is
expected from non-linear modifications of general relativity of this kind,
removal of the initial spacetime singularity is not a generic feature of the
corresponding cosmological model. Instead, the starting point of the cosmic
dynamics -- the past attractor in the phase space -- is a state of infinitely
large value of the Hubble rate squared, usually associated with the big bang
singularity.Comment: 12 pages, Revtex, 12 eps figures. Several new references added. Minor
changes in the main text. Discussion improve
Study Of Tachyon Dynamics For Broad Classes of Potentials
We investigate in detail the asymptotic properties of tachyon cosmology for a
broad class of self-interaction potentials. The present approach relies in an
appropriate re-definition of the tachyon field, which, in conjunction with a
method formerly applied in the bibliography in a different context, allows to
generalize the dynamical systems study of tachyon cosmology to a wider class of
self-interaction potentials beyond the (inverse) square-law one. It is revealed
that independent of the functional form of the potential, the matter-dominated
solution and the ultra-relativistic (also matter-dominated) solution, are
always associated with equilibrium points in the phase space of the tachyon
models. The latter is always the past attractor, while the former is a saddle
critical point. For inverse power-law potentials the
late-time attractor is always the de Sitter solution, while for sinh-like
potentials , depending on the region of
parameter space, the late-time attractor can be either the inflationary
tachyon-dominated solution or the matter-scaling (also inflationary) phase. In
general, for most part of known quintessential potentials, the late-time
dynamics will be associated either with de Sitter inflation, or with
matter-scaling, or with scalar field-dominated solutions.Comment: 13 pages, latex, 4 eps figures. Title changed, authors added,
motivation rewritten, discussion improved, references added. To match the
published versio