paper

Phase Information and the Evolution of Cosmological Density Perturbations

arXiv:astro-ph/9905250 · doi:10.1046/j.1365-8711.2000.03086.x

Abstract

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.

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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