Abstract:
The lensing signals involved in CMB polarization maps have already been measured with ground-based experiments such as SPTpol and POLARBEAR, and would become important as a probe of cosmological and astrophysical issues in the near future. Sizes of polarization maps from ground-based experiments are, however, limited by contamination of long wavelength modes of observational noise. To further extract the lensing signals, we explore feasibility of measuring lensing signals from a collection of small sky maps each of which is observed separately by a ground-based large telescope, i.e., lensing reconstruction from a patchwork map of large sky coverage organized from small sky patches. We show that, although the B-mode power spectrum obtained from the patchwork map is biased due to baseline uncertainty, bias on the lensing potential would be negligible if the B-mode on scales larger than the blowup scale of $1/f$ noise is removed in the lensing reconstruction. As examples of cosmological applications, we also show 1) the cross-correlations between the reconstructed lensing potential and full-sky temperature/polarization maps from satellite missions such as PLANCK and LiteBIRD, and 2) the use of the reconstructed potential for delensing B-mode polarization of LiteBIRD observation.

Abstract:
Weak gravitational lensing of distant galaxies can probe the total projected mass distribution of foreground gravitational structures on all scales and has been used successfully to map the projected mass distribution of rich intermediate redshift clusters. This paper reviews the general concepts of the lensing analysis. We focus on the relation between the observable (shapes and fluxes) and physical (mass, redshift) quantities and discuss some observational issues and recent developments on data analysis which appear promising for a better measurement of the lensing signatures (distortion and magnification) at very large scales.

Abstract:
Weak gravitational lensing by the large scale structure can be used to probe the dark matter distribution in the Universe directly and thus to probe cosmological models. The recent detection of cosmic shear by several groups has demonstrated the feasibility of this new mode of observational cosmology. In the currently most extensive analysis of cosmic shear, it was found that the shear field contains unexpected modes, so-called B-modes, which are thought to be unaccountable for by lensing. B-modes can in principle be generated by an intrinsic alignment of galaxies from which the shear is measured, or may signify some remaining systematics in the data reduction and analysis. In this paper we show that B-modes in fact {\it are produced} by lensing itself. The effect comes about through the clustering of source galaxies, which in particular implies an angular separation-dependent clustering in redshift. After presenting the theory of the decomposition of a general shear field into E- and B-modes, we calculate their respective power spectra and correlation functions for a clustered source distribution. Numerical and analytical estimates of the relative strength of these two modes show that the resulting B-mode is very small on angular scales larger than a few arcminutes, but its relative contribution rises quickly towards smaller angular scales, with comparable power in both modes at a few arcseconds. The relevance of this effect with regard to the current cosmic shear surveys is discussed.

Abstract:
Gravitational lensing has become one of the most interesting tools to study the mass distribution in the Universe. Since gravitational light deflection is independent of the nature and state of the matter, it is ideally suited to investigate the distribution of all (and thus also of dark) matter in the Universe. Lensing results have now become available over a wide range of scales, from the search for MACHOs in the Galactic halo, to the mass distribution in galaxies and clusters of galaxies, and the statistical properties of the large-scale matter distribution in the Universe. Here, after introducing the concepts of strong and weak lensing, several applications are outlined, from strong lensing by galaxies, to strong and weak lensing by clusters and the lensing properties of the large-scale structure.

Abstract:
Gravitational Lensing is an efficient tool to probe: the mass distribution of collapsed systems: galaxies and clusters; high redshift objects thanks to the gravitational amplification; and the geometry of the Universe. I will review here some important aspects of lensing and related issues in observational cosmology.

Abstract:
We apply a mass reconstruction technique to simulated large-scale structure gravitational distortion maps, from 2.5' to 10 degree scales, for different cosmological scenarii. The projected mass is reconstructed using a non-parametric least square method after noise due to the galaxy intrinsic ellipticities has been added on. The shearing of the galaxies is performed using the full lensing equation, without any hypothesis like the weak lensing approximation, or other linearization. It is shown that, in the reconstructed maps the noise acts as a perfect uncorrelated Poisson noise, with no propagation at large scales. The measured power spectrum and first four moments of the convergence can be corrected accurately for this source of noise. Using 60 realizations for each model, we show that a weak lensing survey of 5x5 degrees with a typical sheared background population of 30 gal/arcmin^2 at a redshift z_s=1, is able to probe the amplitude of the power spectrum with a few percents accuracy. Such a survey would lead to a 6 sigma separation between open (Omega=0.3) and flat (Omega=1) model. This separation is shown to be robust against different hypothesis for the normalization or the shape of the power spectrum, and does not require very deep surveys. The observational strategy for an optimal measurement of the power spectrum and the moments of the convergence is discussed.

Abstract:
As pointed out in previous studies, the measurement of the skewness of the convergence field $\kappa$ will be useful in breaking the degeneracy among the cosmological parameters constrained from weak lensing observations. The combination of shot noise and finite survey volume implies that such a measurement is likely to be done in a range of intermediate scales ($0.5'$ to 20') where neither perturbation theory nor the hierarchical ansatz apply. Here we explore the behavior of the skewness of $\kappa$ at these intermediate scales, based on results for the non-linear evolution of the mass bispectrum. We combined different ray-tracing simulations to test our predictions, and we find that our calculations describe accurately the transition from the weakly non-linear to the strongly non-linear regime. We show that the single lens-plane approximation remains accurate even in the non-linear regime, and we explicitly calculate the corrections to this approximation. We also discuss the prospects of measuring the skewness in upcoming weak lensing surveys.

Abstract:
A convincing detection of primordial non-Gaussianity in the local form of the bispectrum, whose amplitude is given by the fNL parameter, offers a powerful test of inflation. In this paper we calculate the modification of two-point cross-correlation statistics of weak lensing - galaxy-galaxy lensing and galaxy-Cosmic Microwave Background (CMB) cross-correlation - due to fNL. We derive and calculate the covariance matrix of galaxy-galaxy lensing including cosmic variance terms. We focus on large scales (l<100) for which the shape noise of the shear measurement becomes irrelevant and cosmic variance dominates the error budget. For a modest degree of non-Gaussianity, fNL=+/-50, modifications of the galaxy-galaxy lensing signal at the 10% level are seen on scales R~300 Mpc, and grow rapidly toward larger scales as \propto R^2. We also see a clear signature of the baryonic acoustic oscillation feature in the matter power spectrum at ~150 Mpc, which can be measured by next-generation lensing experiments. In addition we can probe the local-form primordial non-Gaussianity in the galaxy-CMB lensing signal by correlating the lensing potential reconstructed from CMB with high-z galaxies. For example, for fNL=+/-50, we find that the galaxy-CMB lensing cross power spectrum is modified by ~10% at l~40, and by a factor of two at l~10, for a population of galaxies at z=2 with a bias of 2. The effect is greater for more highly biased populations at larger z; thus, high-z galaxy surveys cross-correlated with CMB offer a yet another probe of primordial non-Gaussianity.

Abstract:
Weak lensing surveys are expected to provide direct measurements of the statistics of the projected dark matter distribution. Most analytical studies of weak lensing statistics have been limited to quasilinear scales as they relied on perturbative calculations. On the other hand, observational surveys are likely to probe angular scales less than 10 arcminutes, for which the relevant physical length scales are in the nonlinear regime of gravitational clustering. We use the hierarchical ansatz to compute the multi-point statistics of the weak lensing convergence for these small smoothing angles. We predict the multi-point cumulants and cumulant correlators up to fourth order and compare our results with high resolution ray tracing simulations. Averaging over a large number of simulation realizations for four different cosmological models, we find close agreement with the analytical calculations. In combination with our work on the probability distribution function, these results provide accurate analytical models for the full range of weak lensing statistics. The models allow for a detailed exploration of cosmological parameter space and of the dependence on angular scale and the redshift distribution of source galaxies. We compute the dependence of the higher moments of the convergence on the parameters Omega and Lambda and on the nature of gravitational clustering.

Abstract:
A large number of cosmological studies now suggest that roughly two-thirds of the critical energy density of the Universe exists in a component with negative pressure. If the equation of state of such an energy component varies with time, it should in principle be possible to identify such a variation using cosmological probes over a wide range in redshift. Proper detection of any time variation, however, requires cosmological probes beyond the currently studied range in redshift of $\sim$ 0.1 to 1. We extend our analysis to gravitational lensing statistics at high redshift and suggest that a reliable sample of lensed sources, out to a redshift of $\sim$ 5, can be used to constrain the variation of the equation of state, provided that both the redshift distribution of lensed sources and the selection function involved with the lensed source discovery process are known. An exciting opportunity to catalog an adequate sample of lensed sources (quasars) to probe quintessence is now available with the ongoing Sloan Digital Sky Survey. Writing $w(z)\approx w_0 + z (dw/dz)_0$, we study the expected accuracy to which the equation of state today $w_0$ and its rate of change $(dw/dz)_0$ can simultaneously be constrained. Such a determination can rule out some missing-energy candidates, such as classes of quintessence models or a cosmological constant.