Measuring the Cosmic Equation of State with Counts of Galaxies

The classical dN/dz test allows one to determine fundamental cosmological parameters from the evolution of the cosmic volume element. This test is applied by measuring the redshift distribution of a tracer whose evolution in number density is known. In the past, ordinary galaxies have been used for this; however, in the absence of a complete theory of galaxy formation, that method is fraught with difficulties. In this Letter, we propose studying instead the evolution of the apparent numbers of dark matter halos as a function of their circular velocity, observable via the line widths or rotation speeds of visible galaxies. Upcoming redshift surveys will allow the line width distribution of galaxies to be determined at both z ~ 1 and the present day. In the course of studying this test, we have devised a rapid, improved semianalytic method for calculating the circular velocity distribution of dark halos based on the analytic mass function of Sheth, Mo, & Tormen and the formation time distribution of Lacey & Cole. We find that if selection effects are well controlled and minimal external constraints are applied, the planned DEEP Redshift Survey could allow us to measure the cosmic equation-of-state parameter w to ±10% (as little as 3% if Ω_m has been well determined from other observations). This type of test also has the potential to provide a constraint on any evolution of w, such as that predicted by "tracker" models.