  The peculiar motions of galaxies can be used to infer the distribution of
matter in the Universe. It has recently been shown that measurements of the
peculiar velocity field indicates an anomalously high bulk flow of galaxies in
our local volume. In this paper we find the implications of the high bulk flow
for the power spectrum of density fluctuations. We find that analyzing only the
dipole moment of the velocity field yields an average power spectrum amplitude
which is indeed much higher than the LCDM value. However, by also including
shear and octupole moments of the velocity field, and marginalizing over
possible values for the growth rate, an average power spectrum amplitude which
is consistent with LCDM is recovered. We attempt to infer the shape of the
matter power spectrum from moments of the velocity field, and find a slight
excess of power on scales ~ h-1 Gpc.
