Cosmic shear is the distortion of images of distant galaxies due to weak gravitational lensing by the large-scale structure in the Universe. Such images are coherently deformed by the tidal field of matter inhomogeneities along the line of sight. By
measuring galaxy shape correlations, we can study the properties and evolution of structure on large scales as well as the geometry of the Universe. Thus, cosmic shear has become a powerful probe into the nature of dark matter and the origin of the current accelerated expansion of the Universe. Over the last years, cosmic shear has evolved into a reliable and robust cosmological probe, providing measurements of the expansion history of the Universe and the growth of its structure. We review here the principles of weak gravitational lensing and show how cosmic shear is interpreted in a cosmological context. Then we give an overview of weak-lensing measurements, and present the main observational cosmic-shear results since it was discovered 15 years ago, as well as the implications for cosmology. We then conclude with an outlook on the various future surveys and missions, for which cosmic shear is one of the main science drivers, and discuss promising new weak cosmological lensing techniques for future observations.
Using a sample of 25683 star-forming and 2821 passive galaxies at $zsim2$, selected in the COSMOS field following the BzK color criterion, we study the hosting halo mass and environment of galaxies as a function of their physical properties. Spitzer
and Herschel provide accurate SFR estimates for starburst galaxies. We measure the auto- and cross-correlation functions of various galaxy sub-samples and infer the properties of their hosting halos using both an HOD model and the linear bias at large scale. We find that passive and star-forming galaxies obey a similarly rising relation between the halo and stellar mass. The mean host halo mass of star forming galaxies increases with the star formation rate between 30 and 200 M$_odot$.yr$^{-1}$, but flattens for higher values, except if we select only main-sequence galaxies. This reflects the expected transition from a regime of secular co-evolution of the halos and the galaxies to a regime of episodic starburst. We find similar large scale biases for main-sequence, passive, and starburst galaxies at equal stellar mass, suggesting that these populations live in halos of the same mass. We detect an excess of clustering on small scales for passive galaxies and showed, by measuring the large-scale bias of close pairs, that this excess is caused by a small fraction ($sim16%$) of passive galaxies being hosted by massive halos ($sim 3 times 10^{13}$ M$_odot$) as satellites. Finally, extrapolating the growth of halos hosting the z$sim$2 population, we show that M$_star sim 10^{10}$ M$_odot$ galaxies at z$sim$2 will evolve, on average, into massive (M$_star sim 10^{11}$ M$_odot$), field galaxies in the local Universe and M$_star sim 10^{11}$ M$_odot$ galaxies at z=2 into local, massive, group galaxies. The most massive main-sequence galaxies and close pairs of massive, passive galaxies end up in todays clusters.
Higher-order, non-Gaussian aspects of the large-scale structure carry valuable information on structure formation and cosmology, which is complementary to second-order statistics. In this work we measure second- and third-order weak-lensing aperture-
mass moments from CFHTLenS and combine those with CMB anisotropy probes. The third moment is measured with a significance of $2sigma$. The combined constraint on $Sigma_8 = sigma_8 (Omega_{rm m}/0.27)^alpha$ is improved by 10%, in comparison to the second-order only, and the allowed ranges for $Omega_{rm m}$ and $sigma_8$ are substantially reduced. Including general triangles of the lensing bispectrum yields tighter constraints compared to probing mainly equilateral triangles. Second- and third-order CFHTLenS lensing measurements improve Planck CMB constraints on $Omega_{rm m}$ and $sigma_8$ by 26% for flat $Lambda$CDM. For a model with free curvature, the joint CFHTLenS-Planck result is $Omega_{rm m} = 0.28 pm 0.02$ (68% confidence), which is an improvement of 43% compared to Planck alone. We test how our results are potentially subject to three astrophysical sources of contamination: source-lens clustering, the intrinsic alignment of galaxy shapes, and baryonic effects. We explore future limitations of the cosmological use of third-order weak lensing, such as the nonlinear model and the Gaussianity of the likelihood function.
We present cosmological constraints from 2D weak gravitational lensing by the large-scale structure in the Canada-France Hawaii Telescope Lensing Survey (CFHTLenS) which spans 154 square degrees in five optical bands. Using accurate photometric redsh
ifts and measured shapes for 4.2 million galaxies between redshifts of 0.2 and 1.3, we compute the 2D cosmic shear correlation function over angular scales ranging between 0.8 and 350 arcmin. Using non-linear models of the dark-matter power spectrum, we constrain cosmological parameters by exploring the parameter space with Population Monte Carlo sampling. The best constraints from lensing alone are obtained for the small-scale density-fluctuations amplitude sigma_8 scaled with the total matter density Omega_m. For a flat LambdaCDM model we obtain sigma_8(Omega_m/0.27)^0.6 = 0.79+-0.03. We combine the CFHTLenS data with WMAP7, BOSS and an HST distance-ladder prior on the Hubble constant to get joint constraints. For a flat LambdaCDM model, we find Omega_m = 0.283+-0.010 and sigma_8 = 0.813+-0.014. In the case of a curved wCDM universe, we obtain Omega_m = 0.27+-0.03, sigma_8 = 0.83+-0.04, w_0 = -1.10+-0.15 and Omega_K = 0.006+0.006-0.004. We calculate the Bayesian evidence to compare flat and curved LambdaCDM and dark-energy CDM models. From the combination of all four probes, we find models with curvature to be at moderately disfavoured with respect to the flat case. A simple dark-energy model is indistinguishable from LambdaCDM. Our results therefore do not necessitate any deviations from the standard cosmological model.
We present the public release of the Bayesian sampling algorithm for cosmology, CosmoPMC (Cosmology Population Monte Carlo). CosmoPMC explores the parameter space of various cosmological probes, and also provides a robust estimate of the Bayesian evi
dence. CosmoPMC is based on an adaptive importance sampling method called Population Monte Carlo (PMC). Various cosmology likelihood modules are implemented, and new modules can be added easily. The importance-sampling algorithm is written in C, and fully parallelised using the Message Passing Interface (MPI). Due to very little overhead, the wall-clock time required for sampling scales approximately with the number of CPUs. The CosmoPMC package contains post-processing and plotting programs, and in addition a Monte-Carlo Markov chain (MCMC) algorithm. The sampling engine is implemented in the library pmclib, and can be used independently. The software is available for download at http://www.cosmopmc.info.
Context. Weak gravitational lensing is a powerful probe of large-scale structure and cosmology. Most commonly, second-order correlations of observed galaxy ellipticities are expressed as a projection of the matter power spectrum, corresponding to the
lowest-order approximation between the projected and 3d power spectrum. Aims. The dominant lensing-only contribution beyond the zero-order approximation is the reduced shear, which takes into account not only lensing-induced distortions but also isotropic magnification of galaxy images. This involves an integral over the matter bispectrum. We provide a fast and general way to calculate this correction term. Methods. Using a model for the matter bispectrum, we fit elementary functions to the reduced-shear contribution and its derivatives with respect to cosmological parameters. The dependence on cosmology is encompassed in a Taylor-expansion around a fiducial model. Results. Within a region in parameter space comprising the WMAP7 68% error ellipsoid, the total reduced-shear power spectrum (shear plus fitted reduced-shear correction) is accurate to 1% (2%) for l<10^4 (l<2x10^5). This corresponds to a factor of four reduction of the bias compared to the case where no correction is used. This precision is necessary to match the accuracy of current non-linear power spectrum predictions from numerical simulations.
We use Bayesian model selection techniques to test extensions of the standard flat LambdaCDM paradigm. Dark-energy and curvature scenarios, and primordial perturbation models are considered. To that end, we calculate the Bayesian evidence in favour o
f each model using Population Monte Carlo (PMC), a new adaptive sampling technique which was recently applied in a cosmological context. The Bayesian evidence is immediately available from the PMC sample used for parameter estimation without further computational effort, and it comes with an associated error evaluation. Besides, it provides an unbiased estimator of the evidence after any fixed number of iterations and it is naturally parallelizable, in contrast with MCMC and nested sampling methods. By comparison with analytical predictions for simulated data, we show that our results obtained with PMC are reliable and robust. The variability in the evidence evaluation and the stability for various cases are estimated both from simulations and from data. For the cases we consider, the log-evidence is calculated with a precision of better than 0.08. Using a combined set of recent CMB, SNIa and BAO data, we find inconclusive evidence between flat LambdaCDM and simple dark-energy models. A curved Universe is moderately to strongly disfavoured with respect to a flat cosmology. Using physically well-motivated priors within the slow-roll approximation of inflation, we find a weak preference for a running spectral index. A Harrison-Zeldovich spectrum is weakly disfavoured. With the current data, tensor modes are not detected; the large prior volume on the tensor-to-scalar ratio r results in moderate evidence in favour of r=0. [Abridged]
