http://www.ita.uni-heidelberg.de/~jmerten/misc/bartelmann_weaklensing.pdf

Weak Gravitational Lensing

According to the theory of general relativity, masses deflect light in a way similar to convex glass lenses. This gravitational lensing effect is astigmatic, giving rise to image distortions. These distortions allow to quantify cosmic structures statistically on a broad range of scales, and to map the spatial distribution of dark and visible matter. We summarise the theory of weak gravitational lensing and review applications to galaxies, galaxy clusters and larger-scale structures in the Universe.

Weak gravitational lensing

http://inspirehep.net/record/1084324/files/arXiv:1201.2434.pdf

Observational probes of cosmic acceleration

Studies of galaxy clusters have proved crucial in helping to establish the standard model of cosmology, with a Universe dominated by dark matter and dark energy. A theoretical basis that describes clusters as massive, multicomponent, quasi-equilibrium systems is growing in its capability to interpret multiwavelength observations of expanding scope and sensitivity. We review current cosmological results, including contributions to fundamental physics, obtained from observations of galaxy clusters. These results are consistent with and complementary to those from other methods. We highlight several areas of opportunity for the next few years, and emphasize the need for accurate modeling of survey selection and sources of systematic error. Capitalizing on these opportunities will require a multiwavelength approach and the application of rigorous statistical frameworks, utilizing the combined strengths of observers, simulators, and theorists.

/pdf/cosmological-parameters-from-observations-of-galaxy-clusters-3cur3tnzpg.pdf

Cosmological Parameters from Observations of Galaxy Clusters

We present cosmological parameter constraints from a tomographic weak gravitational lensing analysis of ~450deg$^2$ of imaging data from the Kilo Degree Survey (KiDS). For a flat $\Lambda$CDM cosmology with a prior on $H_0$ that encompasses the most recent direct measurements, we find $S_8\equiv\sigma_8\sqrt{\Omega_{\rm m}/0.3}=0.745\pm0.039$. This result is in good agreement with other low redshift probes of large scale structure, including recent cosmic shear results, along with pre-Planck cosmic microwave background constraints. A $2.3$-$\sigma$ tension in $S_8$ and `substantial discordance' in the full parameter space is found with respect to the Planck 2015 results. We use shear measurements for nearly 15 million galaxies, determined with a new improved `self-calibrating' version of $lens$fit validated using an extensive suite of image simulations. Four-band $ugri$ photometric redshifts are calibrated directly with deep spectroscopic surveys. The redshift calibration is confirmed using two independent techniques based on angular cross-correlations and the properties of the photometric redshift probability distributions. Our covariance matrix is determined using an analytical approach, verified numerically with large mock galaxy catalogues. We account for uncertainties in the modelling of intrinsic galaxy alignments and the impact of baryon feedback on the shape of the non-linear matter power spectrum, in addition to the small residual uncertainties in the shear and redshift calibration. The cosmology analysis was performed blind. Our high-level data products, including shear correlation functions, covariance matrices, redshift distributions, and Monte Carlo Markov Chains are available at http://kids.strw.leidenuniv.nl.

/pdf/kids-450-cosmological-parameter-constraints-from-tomographic-4cs7kyczma.pdf

KiDS-450: cosmological parameter constraints from tomographic weak gravitational lensing

Cosmic shear constrains cosmology by exploiting the apparent alignments of pairs of galaxies due to gravitational lensing by intervening mass clumps. However, galaxies may become (intrinsically) aligned with each other, and with nearby mass clumps, during their formation. This effect needs to be disentangled from the cosmic shear signal to place constraints on cosmology. We use the linear intrinsic alignment model as a base and compare it to an alternative model and data. If intrinsic alignments are ignored then the dark energy equation of state is biased by ~50%. We examine how the number of tomographic redshift bins affects uncertainties on cosmological parameters and find that when intrinsic alignments are included two or more times as many bins are required to obtain 80% of the available information. We investigate how the degradation in the dark energy figure of merit depends on the photometric redshift scatter. Previous studies have shown that lensing does not place stringent requirements on the photometric redshift uncertainty, so long as the uncertainty is well known. However, if intrinsic alignments are included the requirements become a factor of three tighter. These results are quite insensitive to the fraction of catastrophic outliers, assuming that this fraction is well known. We show the effect of uncertainties in photometric redshift bias and scatter. Finally, we quantify how priors on the intrinsic alignment model would improve dark energy constraints.

http://iopscience.iop.org/article/10.1088/1367-2630/9/12/444/pdf

Dark energy constraints from cosmic shear power spectra: impact of intrinsic alignments on photometric redshift requirements

During the past few years, secure detections of cosmic shear have been obtained, manifest in the correlation of the observed ellipticities of galaxies. Constraints have already been placed on cosmological parameters, such as the normalisation of the matter power spectrum σ8. One possible systematic contaminant of the lensing correlation signal arises from intrinsic galaxy alignment, which is still poorly constrained. Unlike lensing, intrinsic correlations only pertain to galaxies with small physical separations, the correlation length being a few Mpc. We present a new method that harnesses this property, and isolates the lensing and intrinsic components of the galaxy ellipticitycorrelation function using measurements between different redshift slices. The observed signal is approximated by a set of template functions, making no strong assumptions about the amplitude or correlation length of any intrinsic alignment. We also show that the near-degeneracy between the matter density parameter Ωm and σ8 can be lifted using correlation function tomography, even in the presence of an intrinsic alignment signal.

https://www.aanda.org/articles/aa/pdf/2003/04/aa3114.pdf

Separating cosmic shear from intrinsic galaxy alignments: Correlation function tomography

Cosmological weak lensing gives rise to correlations in the ellipticities of faint galaxies. This cosmic shear signal depends upon the matter power spectrum, thus providing a means to constrain cosmological parameters. It has recently been proposed that intrinsic alignments arising at the epoch of galaxy formation can also contribute significantly to the observed correlations, the amplitude increasing with decreasing survey depth. Here we consider the two-point shear correlation function, and demonstrate that photometric redshift information can be used to suppress the intrinsic signal; at the same time Poisson noise is increased, due to a decrease in the effective number of galaxy pairs. The choice to apply such a redshift-depending weighting will depend on the characteristics of the survey in question. In surveys with $\left\langle z \right\rangle \sim 1$, although the lensing signal dominates, the measurement error bars may soon become smaller than the intrinsic alignment signal; hence, in order not to be dominated by systematics, redshift information in cosmic shear statistics will become a necessity. We discuss various aspects of this.

/pdf/suppressing-the-contribution-of-intrinsic-galaxy-alignments-43oyj73h7t.pdf

Suppressing the contribution of intrinsic galaxy alignments to the shear two-point correlation function

Weak gravitational lensing can be used to directly measure the mass along a line-of-sight without any dependence on the dynamical state of the mass, and thus can be used to measure the masses of clusters even if they are not relaxed. One common technique used to measure cluster masses is fitting azimuthally-averaged gravitational s hear profiles with a spherical mass model. In this paper we quantify how asphericity and projected substructure in clusters can affect the virial mass and concentration measured with this technique by simulating weak lensing observations on 30 independent lines-of-sights th rough each of four high-resolution N-body cluster simulations. We find that the variations in th e measured virial mass and concentration are of a size similar to the error expected in idea l weak lensing observations and are correlated, but that the virial mass and concentration o f the mean shear profile agree well with that measured in three dimensional models of the clusters. The dominant effect causing the variations is the proximity of the line-of-sight to the m ajor axis of the 3-D cluster mass distribution, with projected substructure only causing mi nor perturbations in the measured concentration. Finally we find that the best-fit “universal” CDM models used to fit the shear profiles over-predict the surface density of the clusters du e to the cluster mass density falling off faster than the r 3 model assumption.

/pdf/effects-of-asphericity-and-substructure-on-the-determination-c4su59vf3c.pdf

Effects of asphericity and substructure on the determination of cluster mass with weak gravitational lensing

Cosmic shear leads to a correlation of the observed ellipticities of galaxies, an effect which is used to place constraints on cosmological parameters, and to explore the evolution of dark matter and dark energy in the universe. However, a possible systematic contaminant of the lensing signal is intrinsic galaxy alignment, with a correlation length of a few Mpc. Hirata & Seljak (2004, Phys. Rev. D, 70, 063526) have recently demonstrated that for some models of intrinsic distortions, there may also be a cross-correlation between the intrinsic and lensing signals, which may dominate the intrinsic signal, and suppress the lensing power spectrum by several tens of percent. Unlike the pure intrinsic signal, this new term cannot be accounted for by neglecting or down-weighting pairs of galaxies which are physically close. Extending the correlation function tomography method of King & Schneider (2003, A&A, 398, 23) we illustrate how the impact of both intrinsic and cross-correlations can be significantly reduced, in the context of surveys with photometric redshift information. For a ground-based cosmic shear survey of ∼ 100 sq. degrees with photometric redshifts, even in the presence of systematic contaminants at the level considered here, cosmological models degenerate in the Ω m - σ 8 plane can be distinguished well in excess of the 3-σ level.

/pdf/cosmic-shear-as-a-tool-for-precision-cosmology-minimising-4dfyyds80b.pdf

Lindsay J. King

Papers

Dark energy constraints from cosmic shear power spectra: impact of intrinsic alignments on photometric redshift requirements

Separating cosmic shear from intrinsic galaxy alignments: Correlation function tomography

Suppressing the contribution of intrinsic galaxy alignments to the shear two-point correlation function

Effects of asphericity and substructure on the determination of cluster mass with weak gravitational lensing

Cosmic shear as a tool for precision cosmology: Minimising intrinsic galaxy alignment-lensing interference