Quasar Clustering and Spacetime Geometry

The non-Euclidean geometry of spacetime induces an anisotropy in the apparentcorrelation function of high-redshift quasars. This effect can constrain thecosmological constant \Lambda independent of any assumptions about evolution ofluminosities, sizes, or clustering. We examine the prospects for distinguishingbetween low-density (\Omega_0=0.1-0.4) cosmological models with flat and openspace geometry using the quasar samples anticipated from the 2dF and Sloanredshift surveys. We show that even these large quasar surveys are likely toreside in the "sparse sampling" regime, so that measurement errors in thecorrelation function obey Poisson statistics. As a result: (a) one can devise asimple maximum-likelihood scheme for estimating clustering parameters, (b) onecan generate Monte Carlo realizations of correlation function measurementswithout creating artificial quasar distributions, and (c) for fixed quasarnumber, a deeper survey over a smaller area has greater statistical power thana shallow, large-area survey. Adopting recent (quite uncertain) estimates ofthe quasar correlation length, we find that the 2dF and Sloan samples canprovide clear discrimination between flat and open geometries for \Omega <= 0.2but only marginal discrimination for \Omega = 0.4. Clear discrimination ispossible for \Omega = 0.4 if the true quasar correlation length is a factor oftwo larger, and a high-density survey of 30,000 quasars in 200 square degreeswould provide clear discrimination even for the lower correlation length.Comment: 37 pages, 9 figures, submitted to ApJ, (shortened abstract