Measuring the Cosmic Equation of State with Counts of Galaxies. II. Error Budget for the DEEP2 Redshift Survey

In a previous paper, we described a new variant on the classical dN/dz test which could be performed using upcoming redshift surveys. By observing the velocity function of galaxies rather than their luminosity function, it is possible to avoid many of the uncertainties of galaxy evolution while employing a directly measurable quantity. We previously assumed that counting statistics would dominate the errors in this method. Here, we present the results of including cosmic variance and determine the impact of systematic effects on application of this test to the upcoming DEEP2 Redshift Survey. For DEEP2, cosmic variance should yield errors roughly twice those predicted from Poisson statistics. Through Monte Carlo simulations we find that if the functional form, but not the strength, of any of the major systematic effects (baryonic infall, velocity errors, and incompleteness) is known, the systematic may successfully be corrected for using the observed velocity function, leaving a much smaller residual error. The total uncertainty from systematics is comparable to that from cosmic variance, but correlated amongst redshift bins. We find that DEEP2 can provide a much more precise measurement of the cosmic equation of state parameter w than any available today, albeit weaker than some other proposed tests.