Frames of most uniform Hubble flow

It has been observed [1, 2] that the locally measured Hubble parameter converges quickest to the background value and the dipole structure of the velocity field is smallest in the reference frame of the Local Group of galaxies. We study the statistical properties of Lorentz boosts with respect to the Cosmic Microwave Background frame which make the Hubble flow look most uniform around a particular observer. We use a very large N-Body simulation to extract the dependence of the boost velocities on the local environment such as underdensities, overdensities, and bulk flows. We find that the observation [1, 2] is not unexpected if we are located in an underdensity, which is indeed the case for our position in the universe. The amplitude of the measured boost velocity for our location is consistent with the expectation in the standard cosmology.