We present a new method for measuring the projected mass distributions of galaxy clusters, based solely on the gravitational lens amplification of background galaxies by the cluster potential field. The gravitational amplification is measured by comparing the joint distribution in redshift and magnitude of galaxies behind the cluster with that of the average distribution of field galaxies. Lensing shifts the magnitude distribution in a characteristic redshift-dependent way, and simultaneously dilutes the surface density of galaxies. These effects oppose, with the latter dominating at low redshift and the former at high redshift, owing to the curvature of the galaxy luminosity function. Lensing by a foreground cluster thus induces an excess of bright high-redshift galaxies, from which the lens amplification may be inferred.We show that the total amplification is directly related to the surface mass density in the weak field limit, and so it is possible to map the mass distribution of the cluster. The method is shown to be limited by discreteness noise and galaxy clustering behind the lens. Galaxy clustering sets a lower limit to the error along the redshift direction, but a clustering independent lensing signature may be obtained from the magnitude distribution at fixed redshift. Provided the luminosity function deviates from a pure power law, the lens-induced brightening can be measured directly by comparison with the field. In the limit that galaxy luminosities are independent of environment, this method is only shot-noise limited.Statistical techniques are developed for estimating the surface mass density of the cluster. We extend these methods to account for any obscuration by cluster halo dust, which may be mapped independently of the dark matter. We apply the method to a series of numerical simulations and show the the feasibility of the approach. We consider the use of approximate redshift information, and show how the mass estimates are degraded; finally we discuss the data required to map the dark matter in clusters from photometry alone.

We re-examine the e ects of redshift space distortion in all{sky galaxy redshift surveys in the formalism of spherical harmonics. This natural decomposition of the density eld into radial and angular eigenfunctions of the Laplacian operator complements both the spherical symmetry of the survey geometry and the dynamical basis for the redshift distortion.Within this framework we show how one can treat both the large{scale linear e ects, and the small-scale nonlinear clustering, exactly to rst order. We show, contrary to earlier claims, that the redshifted density eld is no longer homogeneous, as well as being anisotropic.We construct a likelihood function for each mode in the decomposition, based on the random Gaussian eld hypothesis. This function nds its maximum when the underlying eld is homogeneous and isotropic, and has the correct amplitude at each mode. As the level of distortion in the eld is governed by the cosmological density parameter, via 0:6 0 =b, where b is the galaxy bias parameter, strong limits can be placed on cosmological models.The method also allows in principle a determination of the power spectrum of perturbations, requiring no assumptions beyond that of linear theory. The method therefore o ers signi cant advantages over Fourier techniques when dealing with all-sky surveys.We apply our likelihood analysis to both simulated data, and real data, using the IRAS 1.2-Jy galaxy catalogue, for which we nd a maximum likelihood ' 1:1 0:3, and a real-space uctuation amplitude corresponding to 8;IRAS = 0:68 0:05. The 1errors should be treated cautiously and are discussed in the paper. We also relax the gravitational instability assumption, to nd a more general determination of the velocity power spectrum required to reconcile the anisotropic redshift space map with the assumed isotropic real-space map.

We perform a cosmic shear analysis of the COMBO-17 survey -- a unique dataset with shear quality R-band imaging and accurate photometric redshift estimates (dz=0.05) for ~90% of galaxies to R=24.0. We undertake a full maximum likelihood analysis to measure the weak lensing power spectra, Cl^kk, Cl^bb & Cl^kb from l=400 to l=10^4. We find a strong measurement of the convergence power over five fields. The b-field has a much lower significance, indicating our data is free of major systematics, while the cross-correlation of k & b is consistent with zero. We have also calculated the shear correlation functions and variance over a range of scales between 0.5 and 20 arcmin. In addition, we have used our results to measure cosmological parameters, constraining the normalisation of the matter power spectrum to be sigma_8=(0.72 \pm 0.09)(Omega_m/0.3)^-0.49, where the errors quoted are 1-sigma due to the intrinsic dispersion in galaxy ellipticities, cosmic and sampling variance. We have significantly reduced the usual additional uncertainty in the median redshift (z_m) of the survey by estimating z_m directly from the data. To demonstrate the power of accurate redshift information, we have also measured parameters from a shear analysis of only those galaxies with accurate redshifts. In this case, we have eliminated the uncertainty in the redshift distribution of sources and we show that the uncertainty in the resulting parameter constraints are reduced by more than a factor of 2 compared to the typical uncertainties found in cosmic shear surveys to date. Finally, we combine our parameter measurements with constraints from the 2dFGRS and from the CMB. With these additional constraints, we measure sigma_8=0.73 +0.05/-0.03 and Omega_m=0.27 +/- 0.02.Comment: Matches version to appear in 1st May edition of MNRAS (vol. 341, pp.100-118

We develop the pseudo-C method for reconstructing the cosmic microwave background (CMB) temperature and polarization auto-and cross-power spectra, and estimate the pseudo-C covariance matrix for a realistic experiment on the cut sky. We calculate the full coupling equations for all six possible CMB power spectra, relating the observed pseudo-C values to the underlying all-sky C values, and test the reconstruction on both full-sky and cut-sky simulated CMB data sets. In particular we consider the reconstruction of the C from upcoming ground-based polarization experiments covering areas of a few hundred deg 2 and find that the method is fast, unbiased and performs well over a wide range of multipoles from = 2 to = 2500. We then calculate the full covariance matrix between the modes of the pseudo-temperature and polarization power spectra, assuming that the underlying CMB fields are Gaussian randomly distributed. The complexity of the covariance matrix prohibits its rapid calculation, required for parameter estimation. Hence we present an approximation for the covariance matrix in terms of convolutions of the underlying power spectra. The coupling matrices in these expressions can be estimated by fitting to numerical simulations, circumventing direct and slow calculation, and further, inaccurate analytic approximations. We show that these coupling matrices are mostly independent of cosmology, and that the full covariance matrix for all six pseudo-C power spectra can be quickly and accurately calculated for any given cosmological model using this method. We compare these semi-analytic covariance matrices against simulations and find good agreement, the accuracy of which depends mainly on survey area and the range of cosmological parameters considered.