Gravity and Non-gravity Modes in the VIRMOS-DESCART Weak Lensing Survey

We analyze the weak lensing data of the VIRMOS imaging survey using projections (called E and B-modes) of the two independents observed correlation functions. The E-mode contains all the lensing signal, while noise and systematics contribute equally to the E and B modes provided that intrinsic alignment is negligible. The mode separation allows a measurement of the signal with a \sqrt{2} smaller error bars, and a separate channel to test for systematic errors. We apply various transformations, including a spherical harmonic space power spectrum C^E_l and C^B_l, which provides a direct measurement of the projected dark matter distribution for 500<l<10^4.Comment: accepted version, minor changes, 18 pages including 6 figure

Cross-Correlating Probes of Primordial Gravitational Waves

One of the most promising ways of detecting primordial gravitational waves generated during inflation is to observe B-modes of polarization, generated by Thomson scattering after reionization, in the cosmic microwave background (CMB). Large scale foregrounds though are expected to be a major systematic issue, so -- in the event of a tentative detection -- an independent confirmation of large scale gravitational waves would be most welcome. Previous authors have suggested searching for the analogous mode of cosmic shear in weak lensing surveys but have shown that the signal to noise of this mode is marginal at best. This argument is reconsidered here, accounting for the cross-correlations of the polarization and lensing B-modes. A lensing survey can potentially strengthen the argument for a detection of primordial gravitational waves, although it is unlikely to help constrain the amplitude of the signal.Comment: 13 pages, 8 figure

Breaking the Degeneracy: Optimal Use of Three-point Weak Lensing Statistics

We study the optimal use of third order statistics in the analysis of weak lensing by large-scale structure. These higher order statistics have long been advocated as a powerful tool to break measured degeneracies between cosmological parameters. Using ray-tracing simulations, incorporating important survey features such as a realistic depth-dependent redshift distribution, we find that a joint two- and three-point correlation function analysis is a much stronger probe of cosmology than the skewness statistic. We compare different observing strategies, showing that for a limited survey time there is an optimal depth for the measurement of third-order statistics, which balances statistical noise and cosmic variance against signal amplitude. We find that the chosen CFHTLS observing strategy was optimal and forecast that a joint two- and three-point analysis of the completed CFHTLS-Wide will constrain the amplitude of the matter power spectrum $\sigma_8$ to 10% and the matter density parameter $\Omega_m$ to 17%, a factor of ~2.5 improvement on the two-point analysis alone. Our error analysis includes all non-Gaussian terms, finding that the coupling between cosmic variance and shot noise is a non-negligible contribution which should be included in any future analytical error calculations.Comment: 27 pages, 13 figures, 3 table

Measuring the Deviation from the Linear and Deterministic Bias through Cosmic Gravitational Lensing Effects

Since gravitational lensing effects directly probe inhomogeneities of dark matter, lensing-galaxy cross-correlations can provide us important information on the relation between dark matter and galaxy distributions, i.e., the bias. In this paper, we propose a method to measure the stochasticity/nonlinearity of the galaxy bias through correlation studies of the cosmic shear and galaxy number fluctuations. Specifically, we employ the aperture mass statistics $M_{ap}$ to describe the cosmic shear. We divide the foreground galaxy redshift $z_f<z_s$ into several bins, where $z_s$ is the redshift of the source galaxies, and calculate the quantity $^2/$ for each redshift bin. Then the ratio of the summation of $^2/< N_g^2(z_f)>$ over the bins to $$ gives a measure of the nonlinear/stochastic bias. Here $N_g(z_f)$ is the projected surface number density fluctuation of foreground galaxies at redshift $z_f$, and $M_{ap}$ is the aperture mass from the cosmic-shear analysis. We estimate that for a moderately deep weak-lensing survey with $z_s=1$, source galaxy surface number density $n_b=30 \hbox {gal}/\hbox {arcmin}^2$ and a survey area of $25 \hbox {deg}^2$, the effective $r$-parameter that represents the deviation from the linear and deterministic bias is detectable in the angular range of 1'-10' if |r-1|\gsim 10%. For shallow, wide surveys such as the Sloan Digital Sky Survey with $z_s=0.5$, $n_b=5 \hbox {gal}/\hbox {arcmin}^2$, and a survey area of $10^4 \hbox {deg}^2$, a 10% detection of $r$ is possible over the angular range $1'-100'$.Comment: ApJ in pres