QUASAR CLUSTERING AND SPACETIME GEOMETRY

The non-Euclidean geometry of spacetime induces an anisotropy in the a pparent correlation function of high-redshift objects, such as quasars , if redshifts and angles are converted to distances in ''naive'' Eucl idean fashion. The degree of angular distortion depends on cosmologica l parameters, especially on the cosmological constant Lambda, so this effect can constrain Lambda independent of any assumptions about the e volution of luminosities, sizes, or clustering. We examine the prospec ts for distinguishing between low-density (Ohm(0) = 0.1-0.4) cosmologi cal models with flat and open space geometry using the large quasar sa mples anticipated from the Two Degree Field Survey (2dF) and the Sloan Digital Sky Survey (SDSS). Along the way, we derive a number of resul ts that are useful for studies of the quasar correlation function. In particular, we show that even these large quasar surveys are likely to reside in the ''sparse sampling'' regime for correlation function mea surements, so that the statistical fluctuations in measurements are si mply the Poisson fluctuations in the observed numbers of pairs. As a r esult, (1) one can devise a simple maximum likelihood scheme for estim ating clustering parameters, (2) one can generate Monte Carlo realizat ions of correlation function measurements without specifying high-orde r correlation functions or creating artificial quasar distributions, a nd (3) for a fixed number of quasars, a deeper survey over a smaller a rea has greater statistical power than a shallow, large-area survey. I f the quasar correlation length is equal to the value implied by recen t (quite uncertain) estimates, then the 2dF and SDSS samples can provi de clear discrimination between flat and open geometries for Ohm(0) le ss than or equal to 0.2 but only marginal discrimination for Ohm(0) = 0.4. Clear discrimination is possible for Ohm(0) = 0.4 if the true qua sar correlation length is a factor of 2 larger, and a high-density sur vey of 30,000 quasars in 200 deg(2) would provide clear discrimination even for the lower correlation length. Detection of quasar clustering anisotropy would confirm the cosmological spacetime curvature that is a fundamental prediction of general relativity.