Measuring the cosmological constant with redshift surveys

It has been proposed that the cosmological constant A might be measured from geometric effects on large-scale structure. A positive vacuum density leads to correlation function contours which are squashed in the radial direction when calculated assuming a matter-dominated model. We show that this effect will be somewhat harder to detect than previous calculations have suggested: the squashing factor is likely to be < 1.3, given realistic constraints on the matter contribution to Omega. Moreover, the geometrical distortion risks being confused with the redshift-space distortions caused by the peculiar velocities associated with the growth of galaxy clustering. These depend on the density and bias parameters via the combination beta = Omega(0.6)/b, and we show that the main practical effect of a geometrical flattening factor F is to simulate gravitational instability with beta(eff) similar or equal to 0.5(F - 1). Nevertheless, with datasets of sufficient size it is possible to distinguish the two effects. We discuss in detail how this should be done, and give a maximum-likelihood method for extracting Lambda and beta from anisotropic power-spectrum data. New-generation redshift surveys of galaxies and quasars are potentially capable of detecting a non-zero vacuum density, if it exists at a cosmologically interesting level.