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