Geometric Distortion of the Correlation Function of Lyman-Break Galaxies

The present number of galaxies with measured redshifts z ≳ 1 is increasing rapidly, thus allowing for measurements of their correlation function. The correlation function ξ(ψ,v) is measured in redshift space as a function of the angular separation and velocity difference v. The relation between angle and velocity difference depends on the cosmological model via the factor H(z)D(z), where H(z) is the Hubble parameter and D(z) is the angular diameter distance. Therefore, the cosmological model can be constrained by measuring this factor from the shape of the contours of the ξ(ψ,v), if the effect of peculiar velocities can be taken into account. Here, we investigate the application of this method to the high-redshift Lyman-break galaxies. The high bias factor of this galaxy population should suppress peculiar velocity effects, leaving the cosmological distortion as the main contribution to the anisotropy of the correlation function. We estimate the shot noise and cosmic variance errors using linear theory. A field size of at least 0.2 deg² is required to distinguish the Einstein-de Sitter model from the flat Λ = 0.7 model, if 1.25 Lyman-break galaxies are measured per square arcminute. With a field of 1 deg², the cosmological constant can be measured to ~20% accuracy if it is large (≳0.5). Other equations of state for a scalar field can also be constrained.