1,398 research outputs found
Dynamical Analysis of Scalar Field Cosmologies with Spatial Curvature
We explore the dynamical behaviour of cosmological models involving a scalar
field (with an exponential potential and a canonical kinetic term) and a matter
fluid with spatial curvature included in the equations of motion. Using
appropriately defined parameters to describe the evolution of the scalar field
energy in this situation, we find that there are two extra fixed points that
are not present in the case without curvature. We also analyse the evolution of
the effective equation-of-state parameter for different initial values of the
curvature.Comment: 17 pages, 11 figures. Amended in response to peer review in the Open
Journal of Astrophysic
A Wave-Mechanical Approach to Cosmic Structure Formation
The dynamical equations describing the evolution of a self-gravitating fluid
can be rewritten in the form of a Schrodinger equation coupled to a Poisson
equation determining the gravitational potential. This wave-mechanical
representation allows an approach to cosmological gravitational instability
that has numerous advantages over standard fluid-based methods. We explore the
usefulness of the Schrodinger approach by applying it to a number of simple
examples of self-gravitating systems in the weakly non-linear regime. We show
that consistent description of a cold self-gravitating fluid requires an extra
"quantum pressure" term to be added to the usual Schrodinger equation and we
give examples of the effect of this term on the development of gravitational
instability. We also show how the simple wave equation can be modified by the
addition of a non-linear term to incorporate the effects of gas pressure
described by a polytropic equation-of-state.Comment: 9 pages, 2 figures. Minor changes. Accepted for publication in MNRA
Non-linearity and Non-Gaussianity through Phase Information
In the standard picture of structure formation, initially random-phase
fluctuations are amplified by non-linear gravitational instability to produce a
final distribution of mass which is highly non-Gaussian and has highly coupled
Fourier phases. Second-order statistics, such as the power spectrum, are blind
to this kind of phase association. We discuss the information contained in the
phases of cosmological density fluctuations and their possible use in
statistical analysis tools. In particular, we show how the bispectrum measures
a particular form of phase association called quadratic phase coupling, show
how to visualise phase association using colour models. These techniques offer
the prospect of more complete tests of initial non-Gaussianity than those
available at present.Comment: 7 pages, 1 figure (two parts). To appear in the proceedings of The
MPA/ESO/MPE Joint Astronomy Conference "Mining the Sky" held in Garching,
Germany, July 31 - August 4 2000. To be published in the Springer-Verlag
series "ESO Astrophysics Symposia
Phase Information and the Evolution of Cosmological Density Perturbations
The Fourier transform of cosmological density perturbations can be
represented in terms of amplitudes and phases for each Fourier mode. We
investigate the phase evolution of these modes using a mixture of analytical
and numerical techniques. Using a toy model of one-dimensional perturbations
evolving under the Zel'dovich approximation as an initial motivation, we
develop a statistic that quantifies the information content of the distribution
of phases. Using numerical simulations beginning with more realistic Gaussian
random-phase initial conditions, we show that the information content of the
phases grows from zero in the initial conditions, first slowly and then rapidly
when structures become non-linear. This growth of phase information can be
expressed in terms of an effective entropy: Gaussian initial conditions are a
maximum entropy realisation of the initial power spectrum, gravitational
evolution decreases the phase entropy. We show that our definition of phase
entropy results in a statistic that explicitly quantifies the information
stored in the phases of density perturbations (rather than their amplitudes)
and that this statistic displays interesting scaling behaviour for self-similar
initial conditions.Comment: Accepted for publication in MNRAS with added comments on future work.
For high-resolution Figure 1, or postscript file, please see
http://www-star.qmw.ac.uk/~lyc
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