Errors on the measurement of via cosmological dipoles

In the light of recent studies suggesting significant amounts of power in the galaxy distribution on wavelengths of several hundred Mpc, this paper considers the likely contribution of very large-wavelength modes to the peculiar motion of the Local Group. This velocity is often compared with an estimate from redshift surveys of the gravitational acceleration generated by galaxy clustering, in order to estimate the density parameter, Ω. We show that, for Gaussian density fields, the neglect of mass concentrations beyond the survey limit can produce a large change in magnitude of predicted velocity, |υ|, while having little effect on the agreement in direction between the predicted and true velocities. We present realizations which show that spurious apparent convergence in the acceleration can occur quite commonly. Even for the deepest redshift surveys available to carry out this test, the fractional precision on Ω which can be obtained is likely to be poorer than an rms of 30–40 per cent. The results from the cosmological dipole test therefore do not at present provide definitive evidence for a high-density Universe.