The Primeval Mass Fluctuation Spectrum and the Distribution of the Nearby Galaxies

Abstract

The initial peculiar velocities of tracers of the extragalactic mass distribution computed by a numerical application of the action principle offer a measure of the primeval mass fluctuation power spectrum P(k). Presented here is a method of estimating the spectrum from the fit of the velocity correlation function expressed as an integral over P(k) in linear perturbation theory to the products of pairs of initial velocities of the mass tracers. The method is applied to numerical action solutions for the motions of the galaxies in and near the Local Group. The distributions of products of pairs of the initial velocities are in satisfactory agreement with the predictions from the correlation function. The range of initial separations in the sample is too small to constrain the shape of P(k), but the value is reasonably well determined at wavenumber km ~ 0.4 Mpc–1 in a low-density cosmological model, or km Mpc~ 0.75 Mpc–1 in an Einstein-de Sitter model. In a low-density open or cosmologically flat model, the value of P(km) extrapolated to the present in linear perturbation theory agrees with estimates from the galaxy distribution under the assumption that galaxies trace mass. This adds to the evidence that galaxies are useful mass tracers. In the low-density models, the galaxy distribution near the Local Group grew out of a primeval mass fluctuation δM/M ~ 1 extrapolated to the present in linear theory.