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 that could be performed using data from the next generation of redshift surveys. By studying the apparent abundance of galaxies as a function of their circular velocity or velocity dispersion rather than luminosity, it is possible to avoid many of the uncertainties of galaxy evolution while using quantities that may be measured directly. In that work, we assumed that counting statistics would dominate the resulting errors. Here we present the results of including cosmic variance and determine the impact of systematic effects on attempts to perform the test with the upcoming DEEP2 Redshift Survey. For the DEEP2 survey geometry, cosmic variance yields 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 free parameter may be determined from the observed velocity function. The systematic may then be corrected for, leaving a much smaller residual error. The total uncertainty from systematics is comparable to that from cosmic variance but is correlated among redshift bins. Based on these analyses, we present error budgets for a dN/dz measurement with DEEP2 and determine the resulting constraints on cosmological parameters. We find that the uncertainty in the cosmic equation of state parameter w are similar to2 times higher than previously derived, providing a measurement much stronger than any available today but weaker than some other proposed tests.