Goodness-of-fit analysis of the Cosmicflows-2 data base of velocities

Abstract

The goodness-of-fit (GoF) of the Cosmicflows-2 (CF2) data base of peculiar velocities with the Λ cold dark matter (ΛCDM) standard model of cosmology is presented. Standard application of the χ2 statistics of the full data base, of its 4838 data points, is hampered by the small-scale non-linear dynamics which is not accounted for by the (linear regime) velocity power spectrum. The bulk velocity constitutes a highly compressed representation of the data which filters out the small-scales non-linear modes. Hence the statistics of the bulk flowprovides an efficient tool for assessing the GoF of the data given a model. The particular approach introduced here is to use the (spherical top-hat window) bulk velocity extracted from theWiener filter reconstruction of the 3Dvelocity field as a linear low-pass filtered highly compressed representation of the CF2 data. An ensemble 2250 random linear realizations of the Wilkinson Microwave Anisotropy Probe (WMAP)/ΛCDM model has been used to calculate the bulk velocity autocovariance matrix. We find that the CF2 data is consistent with the WMAP/ΛCDM model to better than the 2s confidence limits. This provides a further validation that the CF2 data base is consistent with the standard model of cosmology.