THE MACH NUMBER OF THE COSMIC FLOW - A CRITICAL TEST FOR CURRENT THEORIES

We propose a new measurement of cosmological structure, the Mach number M(R) which measures the ratio of the mean velocity, v̄(R) of a patch of size R to the velocity dispersion of objects relative to the patch, σ(R): M(R) = v̄(R)/σ(R). To allow comparisons with linear theory, the velocity field must first be smoothed on a suitable scale. In the context of linear perturbation theory, M(R), which measures the ratio of power on scales larger than to scales smaller than R, is independent of the perturbation amplitude and also of bias. Comparing values of M(R) predicted by popular models with tentative available observations, we find an apparent inconsistency, if the standard values of power-law index n = 1 and cosmological density parameter, Ω = 1, are adopted. Nonstandard models based on adiabatic perturbations with either negative n or small Q, which can pass this test, also fail, because they produce unacceptably large microwave background fluctuations.