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

Abstract

In a previous paper, we described a new variant on the classical "" dN/dz ÏÏ 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 e †ects 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 Ðnd that if the functional form, but not the strength, of any of the major systematic e †ects (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 Ðnd that the uncertainty in the cosmic equation of state parameter w are D2 times higher than previously derived, providing a measurement much stronger than any available today but weaker than some other proposed tests.

Seds: The Spitzer Extended Deep Survey. Survey Design, Photometry, and Deep Irac Source Counts

“…This has significant implications for the nature of the source population. Based on tests with the QUICKCV code (Newman & Davis 2002), such a low sample variance (or "cosmic variance" as it is commonly referred to) can only be achieved in one of two ways. One possibility is that the clustering of the sources is intrinsically weak (with a correlation length r 0 ∼ 3 h −1 Mpc comoving, matching low-mass star-forming galaxies at z = 0-1; Zehavi et al 2011;Coil et al 2008) and they have a moderately broad redshift distribution spanning Δz ∼ 1.5-2.5.…”

Improved Cosmological Constraints from Gravitational Lens Statistics

“…In order to gauge these effects, we adopt an evolution model based on theoretical galaxy formation models. Following Newman & Davis (2000, we use the extended Press-Schechter theory to compute the ratio of the velocity dispersion function at two epochs, ( ; z)= ( ; 0), as a function of cosmological parameters. This ratio can be combined with the measured local velocity dispersion function ( ; 0) to estimate ( ; z) at any epoch.…”

“…Following a simplified version of the procedure in Newman & Davis (2000), we use the results of Lacey & Cole (1994) to estimate the mean formation redshift z f for a halo of mass M observed at redshift z. Lacey & Cole (1994) define a scaled variablẽ…”

“…While this effectively ignores the dispersion of formation epoch, we have checked that this approximation does not significantly affect the estimate of ( ; z)= ( ; 0) over the range of interest. Solving equation (19) for z f , and modeling each halo as an SIS, we can infer the velocity dispersion ( Newman & Davis 2000;Bryan & Norman 1998),…”

“…As just mentioned, the fact that ( ) evolves only due to occasional mergers means that it provides a more straightforward framework for incorporating evolution than the traditional route through the luminosity function. Newman & Davis (2000 present such a framework using extended Press-Schechter theory to compute the ratio of the velocity function at redshift z to the local velocity function, ( ; z)= ( ; 0). While model predictions for the full velocity function ( ; z) are sensitive to the uncertain physics that causes discrepancies between galaxy formation models and observed galaxy populations, the prediction for the ratio ( ; z)= ( ; 0) isolates the evolution piece (Newman & Davis 2002) and is therefore much less sensitive to these uncertainties.…”