Forthcoming projects such as DES, LSST, WFIRST, and Euclid aim to measure weak lensing shear correlations with unprecedented precision, constraining the dark energy equation of state at the percent level. Reliance on photometrically-determined redshifts constitutes a major source of uncertainty for these surveys. Additionally, interpreting the weak lensing signal requires a detailed understanding of the nonlinear physics of gravitational collapse. We present a new analysis of the stringent calibration requirements for weak lensing analyses of future imaging surveys that addresses both photo-z uncertainty and errors in the calibration of the matter power spectrum. We find that when photo-z uncertainty is taken into account the requirements on the level of precision in the prediction for the matter power spectrum are more stringent than previously thought. Including degree-scale galaxy clustering statistics in a joint analysis with weak lensing not only strengthens the survey's constraining power by ~20%, but can also have a profound impact on the calibration demands, decreasing the degradation in dark energy constraints with matter power spectrum uncertainty by a factor of 2-5. Similarly, using galaxy clustering information significantly relaxes the demands on photo-z calibration. We compare these calibration requirements to the contemporary state-of-the-art in photometric redshift estimation and predictions of the power spectrum and suggest strategies to utilize forthcoming data optimally.
We estimate uncertainties of cosmological parameters for phenomenological interacting dark energy models using weak lensing convergence power spectrum and bispectrum. We focus on the bispectrum tomography and examine how well the weak lensing bispectrum with tomography can constrain the interactions between dark sectors, as well as other cosmological parameters. Employing the Fisher matrix analysis, we forecast parameter uncertainties derived from weak lensing bispectra with a two-bin tomography and place upper bounds on strength of the interactions between the dark sectors. The cosmic shear w…
Cosmic shear can only be measured where there are galaxies. This source-lens clustering (SLC) effect has two sources, intrinsic source clustering and cosmic magnification (magnification/size bias). Lensing tomography can suppress the former. However, this reduction is limited by the existence of photo-z error and nonzero redshift bin width. Furthermore, SLC induced by cosmic magnification cannot be reduced by lensing tomography. Through N-body simulations, we quantify the impact of SLC on the lensing power spectrum in the context of lensing tomography. We consider both the standard estimator a…
We present a novel, purely geometric probe of cosmology based on measurements of differential time delays between images of strongly lensed quasars due to finite source effects. Our approach is solely dependent on cosmology via a ratio of angular diameter distances, the image separation, and the source size. It thereby entirely avoids the challenges of lens modelling that conventionally limit time delay cosmography, and instead entails the lensed reverberation mapping of the quasar Broad Line Region. We demonstrate that differential time delays are measurable with short cadence spectroscopic m…
The shapes of distant galaxies are sheared by intervening galaxy clusters. We examine this effect in Stripe 82, a 275 square degree region observed multiple times in the Sloan Digital Sky Survey and coadded to achieve greater depth. We obtain a mass-richness calibration that is similar to other SDSS analyses, demonstrating that the coaddition process did not adversely affect the lensing signal. We also propose a new parameterization of the effect of tomography on the cluster lensing signal which does not require binning in redshift, and we show that using this parameterization we can detect to…
We investigate the abundance, small-scale clustering and galaxy-galaxy lensing signal of galaxies in the Baryon Oscillation Spectroscopic Survey (BOSS). To this end, we present new measurements of the redshift and stellar mass dependence of the lensing properties of the galaxy sample. We analyse to what extent models assuming the Planck18 cosmology fit to the number density and clustering can accurately predict the small-scale lensing signal. In qualitative agreement with previous BOSS studies at redshift $z \sim 0.5$ and with results from the Sloan Digital Sky Survey, we find that the expecte…
The weak lensing effect on the cosmic microwave background (CMB) induces distortions in spatial pattern of CMB anisotropies, and statistical properties of CMB anisotropies become a weakly non-Gaussian field. We first summarize the weak lensing effect on the CMB (CMB lensing) in the presence of scalar, vector and tensor perturbations. Then we focus on the lensing effect on CMB statistics and methods to estimate deflection angles and their power spectrum. We end by summarizing recent observational progress and future prospect.
The topic of this article is weak cosmic shear tomography where the line of sight-weighting is carried out with a set of specifically constructed orthogonal polynomials, dubbed TaRDiS (Tomography with orthogonAl Radial Distance polynomIal Systems). We investigate the properties of these polynomials and employ weak convergence spectra, which have been obtained by weighting with these polynomials, for the estimation of cosmological parameters. We quantify their power in constraining parameters in a Fisher-matrix technique and demonstrate how each polynomial projects out statistically independent…
CMB lensing tomography, or the cross-correlation between CMB lensing maps and large-scale structure tracers over a well-defined redshift range, has the potential to map the amplitude and growth of structure over cosmic time, provide some of the most stringent tests of gravity, and break important degeneracies between cosmological parameters. In this work, we use the unWISE galaxy catalog to provide three samples at median redshifts $z \sim 0.6, 1.1$ and 1.5, fully spanning the Dark Energy dominated era, together with the most recent Planck CMB lensing maps. We obtain a combined cross-correlati…
We describe a tomographic dissection of the Planck CMB lensing data, cross-correlating this map with galaxies in different ranges of photometric redshift. We use the nearly all-sky 2MPZ and WISExSCOS catalogues for z<0.35, extending to z<0.6 using SDSS. We describe checks for consistency between the different datasets, and perform a test for possible leakage of thermal Sunyaev--Zel'dovich signal into our cross-correlation measurements. The amplitude of the cross-correlation allows us to estimate the evolution of density fluctuations as a function of redshift, thus providing a test of theories …
We describe the first spectroscopic tomographic (spectrotomographic) weak lensing measurement for a galaxy cluster based only on background galaxies with spectroscopically determined redshifts. We use the massive cluster A2029 to demonstrate the power of combining spectroscopy and lensing to obtain accurate masses and to overcome biases from contamination and photometric redshift errors. We detect the shear signal from the cluster at $>3.9 σ$. The shear signal scales with source redshift in a way that is consistent with the angular diameter distance ratio variation in a $Λ$CDM Universe. Furthe…
With the availability of galaxy distance indicators in weak lensing surveys, lensing tomography can be harnessed to constrain the three-dimensional (3D) matter power spectrum over a range of redshift and physical scale. By combining galaxy-galaxy lensing and galaxy clustering, this can be extended to probe the 3D galaxy-matter and galaxy-galaxy power spectrum or, alternatively, galaxy biasing parameters. To achieve this aim, this paper introduces and discusses minimum variance estimators and a more general Bayesian approach to statistically invert a set of noisy tomography 2-point correlation …
We re-examine a genuine power of weak lensing bispectrum tomography for constraining cosmological parameters, when combined with the power spectrum tomography, based on the Fisher information matrix formalism. To account for the full information at two- and three-point levels, we include all the power spectrum and bispectrum information built from all-available combinations of tomographic redshift bins, multipole bins and different triangle configurations over a range of angular scales (up to lmax=2000 as our fiducial choice). For the parameter forecast, we use the halo model approach in Kayo,…
We present a new method for constructing three-dimensional mass maps from gravitational lensing shear data. We solve the lensing inversion problem using truncation of singular values (within the context of generalized least squares estimation) without a priori assumptions about the statistical nature of the signal. This singular value framework allows a quantitative comparison between different filtering methods: we evaluate our method beside the previously explored Wiener filter approaches. Our method yields near-optimal angular resolution of the lensing reconstruction and allows cluster size…
We measure the harmonic-space auto-power spectrum of the galaxy overdensity in the LOFAR Two-metre Sky Survey (LoTSS) First Data Release and its cross correlation with the map of the lensing convergence of the cosmic microwave background (CMB) from the Planck collaboration. We report a $\sim5σ$ detection of the cross-correlation. We show that the combination of the clustering power spectrum and CMB lensing cross-correlation allows us to place constraints on the high-redshift tail of the redshift distribution, one of the largest sources of uncertainty in the use of continuum surveys for cosmolo…
Cosmological weak lensing is the powerful probe of cosmology. Here we address one of the most fundamental, statistical questions inherent in weak lensing cosmology: whether or not we can recover the initial Gaussian information content of large-scale structure by combining the weak lensing observables, here focused on the weak lensing power spectrum and bispectrum. To address this question we fully take into account correlations between the power spectra of different multipoles and the bispectra of different triangle configurations, measured from a finite area survey. In particular we show tha…
A number of recent, low-redshift, lensing measurements hint at a universe in which the amplitude of lensing is lower than that predicted from the $Λ$CDM model fit to the data of the Planck CMB mission. Here we use the auto- and cross-correlation signal of unWISE galaxies and Planck CMB lensing maps to infer cosmological parameters at low redshift. In particular, we consider three unWISE samples (denoted as "blue", "green" and "red") at median redshifts $z \sim 0.6$, $1.1$ and 1.5, which fully cover the Dark Energy dominated era. Our cross-correlation measurements, with combined significance $S…
Dark energy can be studied by its influence on the expansion of the Universe as well as on the growth history of the large-scale structure. In this paper, we follow the growth of the cosmic density field in early dark energy cosmologies by combining observations of the primary CMB temperature and polarisation power spectra at high redshift, of the CMB lensing deflection field at intermediate redshift and of weak cosmic shear at low redshifts for constraining the allowed amount of early dark energy. We present these forecasts using the Fisher-matrix formalism and consider the combination of Pla…
Doppler lensing is the apparent change in object size and magnitude due to peculiar velocities. Objects falling into an overdensity appear larger on its near side, and smaller on its far side, than typical objects at the same redshifts. This effect dominates over the usual gravitational lensing magnification at low redshift. Doppler lensing is a promising new probe of cosmology, and we explore in detail how to utilize the effect with forthcoming surveys. We present cosmological simulations of the Doppler and gravitational lensing effects based on the Millennium simulation. We show that Doppler…
We construct cosmic microwave background lensing mass maps using data from the 2014 and 2015 seasons of observations with the Atacama Cosmology Telescope (ACT). These maps cover 2100 square degrees of sky and overlap with a wide variety of optical surveys. The maps are signal dominated on large scales and have fidelity such that their correlation with the cosmic infrared background is clearly visible by eye. We also create lensing maps with thermal Sunyaev-Zel'dovich contamination removed using a novel cleaning procedure that only slightly degrades the lensing signal-to-noise ratio. The cross-…
This document was submitted as supporting material to an Engineering Change Proposal (ECP) for the Square Kilometre Array (SKA). This ECP requests gridded visibilities as an extra imaging data product from the SKA, in order to enable bespoke analysis techniques to measure source morphologies to the accuracy necessary for precision cosmology with radio weak lensing. We also discuss the properties of an SKA weak lensing data set and potential overlaps with other cosmology science goals.
We present high signal-to-noise galaxy-galaxy lensing measurements of the BOSS CMASS sample using 250 square degrees of weak lensing data from CFHTLenS and CS82. We compare this signal with predictions from mock catalogs trained to match observables including the stellar mass function and the projected and two dimensional clustering of CMASS. We show that the clustering of CMASS, together with standard models of the galaxy-halo connection, robustly predicts a lensing signal that is 20-40% larger than observed. Detailed tests show that our results are robust to a variety of systematic effects. …
Weak gravitational lensing is becoming a mature technique for constraining cosmological parameters, and future surveys will be able to constrain the dark energy equation of state $w$. When analyzing galaxy surveys, redshift information has proven to be a valuable addition to angular shear correlations. We forecast parameter constraints on the triplet $(Ω_m,w,σ_8)$ for an LSST-like photometric galaxy survey, using tomography of the shear-shear power spectrum, convergence peak counts and higher convergence moments. We find that redshift tomography with the power spectrum reduces the area of the …
We seek to prove the means, motive and opportunity of 2 < z < 5 dropout galaxies for large-scale structure. Together with low-z tracers, these samples would map practically every linear mode and facilitate a tomographic decomposition of the CMB lensing kernel over an unprecedented volume, thereby yielding a proxy for (the time evolution of) matter density fluctuations that provides compelling tests of horizon-scale General Relativity, neutrino masses and Inflation-- viz., curvature, running of the spectral index and a scale-dependent halo bias induced by (local) primordial non-Gaussianity. Foc…
The subject of this paper is optimisation of weak lensing tomography: We carry out numerical minimisation of a measure of total statistical error as a function of the redshifts of the tomographic bin edges by means of a Nelder-Mead algorithm in order to optimise the sensitivity of weak lensing with respect to different optimisation targets. Working under the assumption of a Gaussian likelihood for the parameters of a $w_0 w_a$CDM-model and using Euclid's conservative survey specifications, we compare an equipopulated, equidistant and optimised bin setting and find that in general the equipopul…
We seek to clarify the origin of constraints on the dark energy equation of state parameter from CMB lensing tomography, that is the combination of galaxy clustering and the cross-correlation of galaxies with CMB lensing in a number of redshift bins. In particular, we consider the two-point correlation functions which can be formed with a catalog of galaxy locations and photometric redshifts from the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) and CMB lensing maps from the CMB-S4 experiment. We focus on the analytic understanding of the origin of the constraints. Dark ener…
Despite the impressive success of the standard cosmological model, several anomalies defy its triumph. Among them is the so-called lensing anomaly: the Planck satellite observes stronger CMB gravitational lensing than expected. The role of neutrinos in this anomaly has been mostly overlooked, despite their key role in CMB lensing, because in the standard scenario they tend to increase the tension. Here, we show that this strongly depends on the assumed neutrino equation of state. We demonstrate that if neutrinos have yet undiscovered long-range interactions, the lensing pattern is significantl…
In recent years cross correlation of lensing of the Cosmic Microwave Background (CMB) with other large scale structure (LSS) tracers has been used as a method to detect CMB lensing. Current experiments are also becoming sensitive enough to measure CMB lensing without the help of auxiliary tracers. As data quality improves rapidly, it has been suggested that the CMB lensing-LSS cross correlation may provide new insights into parameters describing cosmological structure growth. In this work we perform forecasts that combine the lensing potential auto power spectrum from various future CMB experi…
Likelihood-free inference provides a rigorous approach to preform Bayesian analysis using forward simulations only. The main advantage of likelihood-free methods is its ability to account for complex physical processes and observational effects in forward simulations. Here we explore the potential of likelihood-free forward modeling for Bayesian cosmological inference using the redshift evolution of the cluster abundance combined with weak-lensing mass calibration. We use two complementary likelihood-free methods, namely Approximate Bayesian Computation (ABC) and Density-Estimation Likelihood-…
Recently, it has been shown that cross-correlating CMB lensing and 3D cosmic shear allows to considerably tighten cosmological parameter constraints. We investigate whether similar improvement can be achieved in a conventional tomographic setup. We present Fisher parameter forecasts for a Euclid-like galaxy survey in combination with different ongoing and forthcoming CMB experiments. In contrast to a fully three-dimensional analysis we find only marginal improvement. Assuming Planck-like CMB data we show that including the full covariance of the combined CMB and cosmic shear data improves the …
The wealth of incoming and future cosmological observations will allow us to map out the structure and evolution of the observable universe to an unprecedented level of precision. Among these observations is the weak gravitational lensing of galaxies, e.g., cosmic shear that measures the minute distortions of background galaxy images by intervening cosmic structure. Weak lensing and cosmic shear promise to be a powerful probe of astrophysics and cosmology, constraining models of dark energy, measuring the evolution of structure in the universe, and testing theories of gravity on cosmic scales.…
We perform a combined analysis of cosmic shear tomography, galaxy-galaxy lensing tomography, and redshift-space multipole power spectra (monopole and quadrupole) using 450 deg$^2$ of imaging data by the Kilo Degree Survey (KiDS) overlapping with two spectroscopic surveys: the 2-degree Field Lensing Survey (2dFLenS) and the Baryon Oscillation Spectroscopic Survey (BOSS). We restrict the galaxy-galaxy lensing and multipole power spectrum measurements to the overlapping regions with KiDS, and self-consistently compute the full covariance between the different observables using a large suite of $N…
This is the fourth in a series of papers studying the astrophysics and cosmology of massive, dynamically relaxed galaxy clusters. Here, we use measurements of weak gravitational lensing from the Weighing the Giants project to calibrate Chandra X-ray measurements of total mass that rely on the assumption of hydrostatic equilibrium. This comparison of X-ray and lensing masses provides a measurement of the combined bias of X-ray hydrostatic masses due to both astrophysical and instrumental sources. Assuming a fixed cosmology, and within a characteristic radius (r_2500) determined from the X-ray d…
In this paper, we investigate whether galaxy assembly bias can reconcile the 20-40% disagreement between the observed galaxy projected clustering signal and the galaxy-galaxy lensing signal in the BOSS CMASS galaxy sample reported in Leauthaud et al. (2017). We use the suite of AbacusCosmos Lamda-CDM simulations at Planck best-fit cosmology and two flexible implementations of extended halo occupation distribution (HOD) models that incorporate galaxy assembly bias to build forward models and produce joint fits of the observed galaxy clustering signal and the galaxy-galaxy lensing signal. We fin…
Weak gravitational lensing, the deflection of light by mass, is one of the best tools to constrain the growth of cosmic structure with time and reveal the nature of dark energy. I discuss the sources of systematic uncertainty in weak lensing measurements and their theoretical interpretation, including our current understanding and other options for future improvement. These include long-standing concerns such as the estimation of coherent shears from galaxy images or redshift distributions of galaxies selected based on photometric redshifts, along with systematic uncertainties that have receiv…
We present a tomographic cosmological weak lensing analysis of the HST COSMOS Survey. Applying our lensing-optimized data reduction, principal component interpolation for the ACS PSF, and improved modelling of charge-transfer inefficiency, we measure a lensing signal which is consistent with pure gravitational modes and no significant shape systematics. We carefully estimate the statistical uncertainty from simulated COSMOS-like fields obtained from ray-tracing through the Millennium Simulation. We test our pipeline on simulated space-based data, recalibrate non-linear power spectrum correctio…
We present a Bayesian reconstruction algorithm that infers the three-dimensional large-scale matter distribution from the weak gravitational lensing effects measured in the image shapes of galaxies. The algorithm is designed to also work with non-Gaussian posterior distributions which arise, for example, from a non-Gaussian prior distribution. In this work, we use a lognormal prior and compare the reconstruction results to a Gaussian prior in a suite of increasingly realistic tests on mock data. We find that in cases of high noise levels (i.e. for low source galaxy densities and/or high shape …
It is usually assumed that the ellipticity power spectrum measured in weak lensing observations can be expressed as an integral over the underlying matter power spectrum. This is true at second order in the gravitational potential. We extend the standard calculation, constructing all corrections to fourth order in the gravitational potential. There are four types of corrections: corrections to the lensing shear due to multiple-deflections; corrections due to the fact that shape distortions probe the reduced shear $γ/(1-κ)$ rather than the shear itself; corrections associated with the non-linea…
We discuss detectability of the nonlinear growth of the large-scale structure in the cosmic microwave background (CMB) lensing. Lensing signals involved in CMB anisotropies have been measured from multiple CMB experiments, such as Atacama Cosmology Telescope (ACT), Planck, POLARBEAR, and South Pole Telescope (SPT). Reconstructed lensing signals are useful to constrain cosmology via their angular power spectrum, while detectability and cosmological application of their bispectrum induced by the nonlinear evolution are not well studied. Extending the analytic estimate of the galaxy lensing bispe…
We investigate the expected cosmological constraints from a combination of weak lensing and large-scale galaxy clustering using realistic redshift distributions. Introducing a systematic bias in the weak lensing redshift distributions (of 0.05 in redshift) produces a $>2σ$ bias in the recovered matter power spectrum amplitude and dark energy equation of state, for preliminary Stage III surveys. We demonstrate that these cosmological errors can be largely removed by marginalising over unknown biases in the assumed weak lensing redshift distributions, if we assume high quality redshift informati…
We investigate the origin of $Λ$CDM parameter constraints in weak lensing, with a focus on the Hubble constant. We explain why current cosmic shear data are sensitive to the parameter combination $S_8 \propto σ_8 Ω_m^{0.5}$, improving upon previous studies through use of the halo model. Motivated by the ongoing discrepancy in measurements of the Hubble constant from high and low redshift, we explain why cosmic shear provides almost no constraint on $H_0$ by showing how the lensing angular power spectrum depends on physical length scales in the dark matter distribution. We derive parameter cons…
In this paper, we assemble a catalog of 118 strong gravitational lensing systems from SLACS, BELLS, LSD and SL2S surveys and use them to constrain the cosmic equation of state. In particular we consider two cases of dark energy phenomenology: $XCDM$ model where dark energy is modeled by a fluid with constant $w$ equation of state parameter and in Chevalier - Polarski - Linder (CPL) parametrization where $w$ is allowed to evolve with redshift: $w(z) = w_0 + w_1 \frac{z}{1+z}$. We assume spherically symmetric mass distribution in lensing galaxies, but relax the rigid assumption of SIS model in f…
For the first time, measurements of the cosmic microwave background radiation (CMB) alone favor cosmologies with $w=-1$ dark energy over models without dark energy at a 3.2-sigma level. We demonstrate this by combining the CMB lensing deflection power spectrum from the Atacama Cosmology Telescope with temperature and polarization power spectra from the Wilkinson Microwave Anisotropy Probe. The lensing data break the geometric degeneracy of different cosmological models with similar CMB temperature power spectra. Our CMB-only measurement of the dark energy density $Ω_Λ$ confirms other measureme…
We measure the cross-correlation of Atacama Cosmology Telescope CMB lensing convergence maps with quasar maps made from the Sloan Digital Sky Survey DR8 SDSS-XDQSO photometric catalog. The CMB lensing-quasar cross-power spectrum is detected for the first time at a significance of 3.8 sigma, which directly confirms that the quasar distribution traces the mass distribution at high redshifts z>1. Our detection passes a number of null tests and systematic checks. Using this cross-power spectrum, we measure the amplitude of the linear quasar bias assuming a template for its redshift dependence, and…
Galaxy-scale strong gravitational lenses with measured stellar velocity dispersions allow a test of the weak-field metric on kiloparsec scales and a geometric measurement of the cosmological distance-redshift relation, provided that the mass-dynamical structure of the lensing galaxies can be independently constrained to a sufficient degree. We combine data on 53 galaxy-scale strong lenses from the Sloan Lens ACS Survey with a well-motivated fiducial set of lens-galaxy parameters to find (1) a constraint on the post-Newtonian parameter gamma = 1.01 +/- 0.05 and (2) a determination of Omega_Lamb…
On the cosmology dependence of the cluster weak-lensing mass bias
LMU Munich（慕尼黑大学）；INAF-Osservatorio Astronomico di Trieste（意大利天文学研究所的里雅斯特天文台）；Max-Planck-Institut für Astrophysik（马克斯·普朗克天体物理研究所）；Universität Innsbruck（因斯布鲁克大学）
Ongoing and future wide-field galaxy surveys can be used to locate a number of clusters of galaxies with cosmic shear measurement alone. We study constraints on cosmological models using statistics of weak lensing selected galaxy clusters. We extend our previous theoretical framework to model the statistical properties of clusters in variants of cosmological models as well as in the standard $Λ$CDM model. Weak lensing selection of clusters does not rely on the conventional assumption such as the relation between luminosity and mass and/or hydrostatic equilibrium, but a number of observational …
Redshift space distortion (RSD) is a powerful way of measuring the growth of structure and testing General Relativity, but it is limited by cosmic variance and the degeneracy between galaxy bias b and the growth rate factor f. The cross-correlation of lensing shear with the galaxy density field can in principle measure b in a manner free from cosmic variance limits, breaking the f-b degeneracy and allowing inference of the matter power spectrum from the galaxy survey. We analyze the growth constraints from a realistic tomographic weak lensing photo-z survey combined with a spectroscopic galaxy…
We report a measurement of the power spectrum of cosmic microwave background (CMB) lensing from two seasons of Atacama Cosmology Telescope Polarimeter (ACTPol) CMB data. The CMB lensing power spectrum is extracted from both temperature and polarization data using quadratic estimators. We obtain results that are consistent with the expectation from the best-fit Planck LCDM model over a range of multipoles L=80-2100, with an amplitude of lensing A_lens = 1.06 +/- 0.15 (stat.) +/- 0.06 (sys.) relative to Planck. Our measurement of the CMB lensing power spectrum gives sigma_8 Omega_m^0.25 = 0.643 …
