Measuring the cosmological constant with redshift surveys

Abstract

It has been proposed that the cosmological constant $\Lambda$ 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 $\beta \equiv {\Omega }^{0.6}/b$, and we show that the main practical effect of a geometrical flattening factor $F$ is to simulate gravitational instability with ${\beta }_{\mathrm{eff}}\simeq 0.5(F-1)$. Nevertheless, with datasets of sufficient size it is possible to distinguish the two effects; we discuss in detail how this should be done. 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.

MNRAS in press. 12 pages LaTeX including Postscript figures. Uses mn.sty and epsf.sty

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