Measuring the Cosmic Equation of State with Counts of Galaxies

The classical dN/dz test allows the determination of 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 as such a tracer; however, in the absence of a complete theory of galaxy formation, that method is fraught with difficulties. In this paper, we propose studying instead the evolution of the apparent abundance of dark matter halos as a function of their circular velocity, observable via the linewidths or rotation speeds of visible galaxies. Upcoming redshift surveys will allow the linewidth 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 semi-analytic method for calculating the circular velocity distribution of dark halos based upon the analytic mass function of Sheth et al. (1999) and the formation time distribution of Lacey & Cole (1993). We find that if selection effects are well-controlled and minimal external constraints are applied, the planned DEEP Redshift Survey should allow the measurement of the cosmic equation-of-state parameter w to 10% (as little as 3% if Omega_m has been well-determined from other observations). This type of test has the potential also to provide a constraint on any evolution of w such as that predicted by ``tracker'' models.