28 research outputs found
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
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
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Cosmological dynamics of exponential gravity
We present a detailed investigation of the cosmological dynamics based on
gravity. We apply the dynamical system approach to both
the vacuum and matter cases and obtain exact solutions and their stability in
the finite and asymptotic regimes. The results show that cosmic histories exist
which admit a double de-Sitter phase which could be useful for describing the
early and the late-time accelerating universe.Comment: 17 pages LaTeX, 3 figure
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
Homogeneous Plane-wave Spacetimes and their Stability
We consider the stability of spatially homogeneous plane-wave spacetimes. We
carry out a full analysis for plane-wave spacetimes in (4+1) dimensions, and
find there are two cases to consider; what we call non-exceptional and
exceptional. In the non-exceptional case the plane waves are stable to
(spatially homogeneous) vacuum perturbations as well as a restricted set of
matter perturbations. In the exceptional case we always find an instability.
Also we consider the Milne universe in arbitrary dimensions and find it is also
stable provided the strong energy condition is satisfied. This implies that
there exists an open set of stable plane-wave solutions in arbitrary
dimensions.Comment: 15 pages, no figures; minor changes, new references, to appear in CQ
Magnetic Brane-worlds
We investigate brane-worlds with a pure magnetic field and a perfect fluid.
We extend earlier work to brane-worlds, and find new properties of the Bianchi
type I brane-world. We find new asymptotic behaviours on approach to the
singularity and classify the critical points of the dynamical phase space. It
is known that the Einstein equations for the magnetic Bianchi type I models are
in general oscillatory and are believed to be chaotic, but in the brane-world
model this chaotic behaviour does not seem to be possible.Comment: 21 pages, 3 ps figures; To appear in CQ
On the Viability of Bianchi Type VIIh Models with Dark Energy
We generalize the predictions for the CMB anisotropy patterns arising in
Bianchi type VIIh universes to include a dark energy component. We consider
these models in light of the result of Jaffe et al. (2005a,b) in which a
correlation was found on large angular scales between the WMAP data and the
anisotropy structure in a low density Bianchi universe. We find that by
including a term Omega_L > 0, the same best-fit anisotropy pattern is
reproduced by several combinations of cosmological parameters. This sub-set of
models can then be further constrained by current observations that limit the
values of various cosmological parameters. In particular, we consider the
so-called geometric degeneracy in these parameters imposed by the peak
structure of the WMAP data itself. Apparently, despite the additional freedom
allowed by the dark energy component, the modified Bianchi models are ruled out
at high significance.Comment: submitted to Ap
Future Asymptotic Behaviour of Tilted Bianchi models of type IV and VIIh
Using dynamical systems theory and a detailed numerical analysis, the
late-time behaviour of tilting perfect fluid Bianchi models of types IV and
VII are investigated. In particular, vacuum plane-wave spacetimes are
studied and the important result that the only future attracting equilibrium
points for non-inflationary fluids are the plane-wave solutions in Bianchi type
VII models is discussed. A tiny region of parameter space (the loophole) in
the Bianchi type IV model is shown to contain a closed orbit which is found to
act as an attractor (the Mussel attractor). From an extensive numerical
analysis it is found that at late times the normalised energy-density tends to
zero and the normalised variables 'freeze' into their asymptotic values. A
detailed numerical analysis of the type VII models then shows that there is
an open set of parameter space in which solution curves approach a compact
surface that is topologically a torus.Comment: 30 pages, many postscript figure
The Futures of Bianchi type VII0 cosmologies with vorticity
We use expansion-normalised variables to investigate the Bianchi type VII
model with a tilted -law perfect fluid. We emphasize the late-time
asymptotic dynamical behaviour of the models and determine their asymptotic
states. Unlike the other Bianchi models of solvable type, the type VII
state space is unbounded. Consequently we show that, for a general
non-inflationary perfect fluid, one of the curvature variables diverges at late
times, which implies that the type VII model is not asymptotically
self-similar to the future. Regarding the tilt velocity, we show that for
fluids with (which includes the important case of dust,
) the tilt velocity tends to zero at late times, while for a
radiation fluid, , the fluid is tilted and its vorticity is
dynamically significant at late times. For fluids stiffer than radiation
(), the future asymptotic state is an extremely tilted spacetime
with vorticity.Comment: 23 pages, v2:references and comments added, typos fixed, to appear in
CQ
A dynamical system approach to higher order gravity
The dynamical system approach has recently acquired great importance in the
investigation on higher order theories of gravity. In this talk I review the
main results and I give brief comments on the perspectives for further
developments.Comment: 6 pages, 1 figure, 2 tables, talk given at IRGAC 2006, July 200