Cosmological Applications of Gravitational Lensing

The last decade has seen an enormous increase of activity in the field of gravitational lensing, mainly driven by improvements of observational capabilities. I will review the basics of gravitational lens theory, just enough to understand the rest of this contribution, and will then concentrate on several of the main applications in cosmology. Cluster lensing, and weak lensing, will constitute the main part of this review.Comment: 26 pages, including 2 figures (a third figure can be obtained from the author by request) gziped and uuencoded postscript file; to be published in Proceedings of the Laredo Advanced Summer School, Sept. 9

The redshift distribution and luminosity functions of galaxies in the Hubble Deep Field

Photometric redshifts have been determined for the galaxies in the Hubble Deep Field. The resulting redshift distribution shows two peaks: one at z ~ 0.6 and one at z ~ 2.2. Luminosity functions derived from the redshifts show strong luminosity evolution as a function of redshift. This evolution is consistent with the Babul and Rees scenario wherein massive galaxies form stars at high redshift while star formation in dwarf galaxies is delayed until after z = 1.Peer reviewed: YesNRC publication: N

The CNOC2 field galaxy redshift survey

The second Canadian Network for Observational Cosmology ( CNOC) galaxy redshift survey, CNOC2, is designed to investigate the relations between the dramatic evolution of field galaxies and their clustering over the redshift range 0 to 0.7. The sample of about 6000 galaxies with accurate velocities is spread over four sky patches with a total area of about 1.5deg2. Here we report preliminary results based on two of the sky patches and within the redshift range of 0.12 to 0.55. After classifying the galaxy spectral energy distributions relative to non–evolving references, we find that the early and intermediate–type populations can be described with nearly pure luminosity evolution, whereas the late–type population requires nearly pure density evolution. The spatial two–point correlation functions have a strong colour dependence with scale, and a weaker, apparently scale–free, luminosity dependence. The population most likely to be conserved with redshift is the high–luminosity galaxies. In particular, we choose galaxies with MRke ⩽−20 mag as our tracer population. We find that the evolution of the clustered density in proper co–ordinates at r ≲ 10h−1 Mpc, ρgg ∝ r0γ(1+z)3, is best described as a ‘de–clustering’, proportional to (1+z)0.6±0.4); or equivalently, there is a weak growth of clustering in co–moving co–ordinates, x0 ∝(1+z)(−0.3±0.2). This conclusion is supported by the pairwise peculiar velocities, which show no significant change with redshift. The cosmic virial theorem applied to the CNOC2 data gives Q3ΩM/b = 0.11 ± 0.04, where Q3 is the three–point correlation parameter and b the bias

The Average Mass Profile of Galaxy Clusters

The average mass density profile measured in the CNOC cluster survey is well described with the analytic form rho(r)=A/[r(r+a_rho)^2], as advocated on the basis on n-body simulations by Navarro, Frenk & White. The predicted core radii are a_rho=0.20 (in units of the radius where the mean interior density is 200 times the critical density) for an Omega=0.2 open CDM model, or a_rho=0.26 for a flat Omega=0.2 model, with little dependence on other cosmological parameters for simulations normalized to the observed cluster abundance. The dynamically derived local mass-to-light ratio, which has little radial variation, converts the observed light profile to a mass profile. We find that the scale radius of the mass distribution, 0.20<= a_rho <= 0.30 (depending on modeling details, with a 95% confidence range of 0.12-0.50), is completely consistent with the predicted values. Moreover, the profiles and total masses of the clusters as individuals can be acceptably predicted from the cluster RMS line-of-sight velocity dispersion alone. This is strong support of the hierarchical clustering theory for the formation of galaxy clusters in a cool, collisionless, dark matter dominated universe.Comment: Accepted for publication in ApJLetts. Also available at http://manaslu.astro.utoronto.ca/~carlberg/cnoc/nfw/ave.ps.g

The CNOC Cluster Survey: Omega, sigma\_8, Phi(L,z) Results, and Prospects for Lambda Measurement

Rich galaxy clusters are powerful probes of both cosmological and galaxy evolution parameters. The CNOC cluster survey was primarily designed to distinguish between Omega=1 and Omega~0.2 cosmologies. Projected foreground and background galaxies provide a field sample of comparable size. The results strongly support a low-density universe. The luminous cluster galaxies are about 10-30% fainter, depending on color, than the comparable field galaxies, but otherwise they show a slow and nearly parallel evolution. On the average, there is no excess star formation when galaxies fall into clusters. These data provide the basis for a simple Lambda measurement using the survey's clusters and the field data. The errors in Omega_M, Lambda, sigma_8 and galaxy evolution parameters could be reduced to a few percent with a sample of a few hundred clusters spread over the 0<z<1 range.Comment: to appear in Ringberg Workshop on Large-Scale Structure (ed. D. Hamilton) 14 pages, also available at http://manaslu.astro.utoronto.ca/~carlberg/cnoc/conference/ring2.ps.g

The Omega\_M-Omega\_Lambda Constraint from CNOC Clusters

The CNOC redshift survey of galaxy clusters measures Omega_M from Omega_e(z)= M/L x j/\rho_c which can be applied on a cluster-by-cluster basis. The mass-to-light ratios, M/L, are estimated from rich galaxy clusters, corrected to the field population over the 0.18 to 0.55 redshift range. Since the luminosity density depends on cosmological volumes, the resulting Omega_e(z) has a strong dependence on cosmology which allows us to place the results in the Omega_M-Omega_Lambda plane. The resulting Omega_M declines if Omega_Lambda>0 and we find that Omega_Lambda<1.5.Comment: 4 pages LaTeX. To appear in "Fundamental Parameters in Cosmology," the proceedings of the XXXIIIrd Rencontres de Morion