NONLINEAR GRAVITATIONAL EVOLUTION OF PHASES AND AMPLITUDES IN ONE-DIMENSIONAL COSMOLOGICAL DENSITY FIELDS

Nonlinear evolution of density fluctuations is examined using the Zel'dovich solution in a one-dimensional cosmological field. In particular, the distributions of phases and amplitudes of density fluctuations in Fourier space are studied in detail. The higher frequency modes generated from the pre-existing modes in the lower frequencies show some systematic phase correlation among different wavenumbers. A conservation law of fluctuation power is discovered, which holds for the power-transfer due to the nonlinear mode-coupling in a one-dimensional gravitational density field; the transfer of power tends to occur in the direction to achieve the equipartition of fluctuation power per unit wavenumber. This tendency is not only limited to a one-dimensional system, but rather seems to be quite generic from the available indications from the analysis of three-dimensional cosmological systems.