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.Comment: 4 pages plus 3 embedded figures; version approved by Ap. J. Letters.
A greatly improved error analysis has been added, along with a figure showing
complementarity to other cosmological test