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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 indicate 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 analysing only the dipole moment of the velocity field yields an average power spectrum amplitude which is indeed much higher than the Λ cold dark matter (ΛCDM) 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 the ΛCDM 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 ∼ 1  h  −1   Gpc.

A slight excess of large‐scale power from moments of the peculiar velocity field