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 information for the galaxy clustering sample. Furthermore the cosmological constraining power is mostly retained despite removing much of the information on the weak lensing redshift distribution biases. We show that this comes from complementary degeneracy directions between cosmic shear and the combination of galaxy clustering with cross-correlation between shear and galaxy number density. Finally we examine how the self-calibration performs when the assumed distributions differ from the true distributions by more than a simple uniform bias. We find that the effectiveness of this self-calibration method will depend on the details of a given experiment and the nature of the uncertainties on the estimated redshift distributions.
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.
I present an estimator for the angular cross-correlation of two tracers of the cosmological large-scale structure that utilizes redshift information to isolate separate physical contributions. The estimator is derived by solving the Limber equation for a re-weighting of the foreground tracer that nulls either clustering or lensing contributions to the cross-correlation function. Applied to future photometric surveys, the estimator can enhance the measurement of gravitational lensing magnification effects to provide a competitive independent constraint on the dark energy equation of state.
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…
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 investigate the spectro-photometric variability of quasars due to lensing of small mass substructure (from several tens to several hundreds solar masses). The aim of this paper is to explore the milli/microlensing influence on the flux anomaly observed between images of a lensed quasar in different spectral bands and possible influence of small mass structure lensing of non-macrolensed quasars.We find that spectro-photometric variability may be also caused by lensing of small mass diffuse structure and can produce the flux anomaly which is sometimes seen in different images of a lensed quas…
Accurate weak-lensing analysis requires not only accurate measurement of galaxy shapes but also precise and unbiased measurement of galaxy redshifts. The photometric redshift technique appears as the only possibility to determine the redshift of the background galaxies used in the weak-lensing analysis. Using the photometric redshift quality, simple shape measurement requirements, and a proper sky model, we explore what could be an optimal weak-lensing dark energy mission based on FoM calculation. We found that photometric redshifts reach their best accuracy for the bulk of the faint galaxy po…
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…
This article introduces a family of analytical functions of the form x^ν K_ν(x), where K_ν is the incomplete Bessel function of the third kind. This family of functions can describe the density profile, projected and integrated light profiles and the gravitational potentials of galaxies. For the proper choice of parameters, these functions accurately approximate Sersic functions over a range of indices and are good fits to galaxy light profiles. With an additional parameter corresponding to a galaxy core radius, these functions can fit galaxy like M87 over a factor of 100,000 in radius. Unlike…
We present a new measurement of structure growth at $z \simeq 0.08$ obtained by correlating the cosmic microwave background (CMB) lensing potential map from the \textit{Planck} satellite with the angular distribution of the 2MASS Photometric Redshift galaxies. After testing for, and finding no evidence for systematic effects, we calculate the angular auto- and cross-power spectra. We combine these spectra to estimate the amplitude of structure growth using the bias-independent $D_G$ estimator introduced by Giannantonio et al. 2016. We find that the relative amplitude of $D_G$ with respect to t…
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…
Exploring Cosmological Constraints of the Void-Lensing Cross-Correlation in the CSST Photometric Survey
National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；School of Astronomy and Space Sciences, University of Chinese Academy of Sciences(UCAS)（中国科学院大学天文与空间科学学院）；Science Center for China Space Station Telescope, National Astronomical Observatories, Chinese Academy of Science（中国科学院国家天文台中国空间站望远镜科学中心）
We study the importance of gravitational lensing in the modelling of the number counts of galaxies. We confirm previous results for photometric surveys, showing that lensing cannot be neglected in a survey like LSST since it would infer a significant shift of cosmological parameters. For a spectroscopic survey like SKA2, we find that neglecting lensing in the monopole, quadrupole and hexadecapole of the correlation function also induces an important shift of parameters. For $Λ$CDM parameters, the shift is moderate, of the order of 0.6$σ$ or less. However, for a model-independent analysis, that…
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…
Weak gravitational lensing is a valuable probe of galaxy formation and cosmology. Here we quantify the effects of using photometric redshifts (photo-z) in galaxy-galaxy lensing, for both sources and lenses, both for the immediate goal of using galaxies with photo-z as lenses in the Sloan Digital Sky Survey (SDSS) and as a demonstration of methodology for large, upcoming weak lensing surveys that will by necessity be dominated by lens samples with photo-z. We calculate the bias in the lensing mass calibration as well as consequences for absolute magnitude (i.e., k-corrections) and stellar mass …
We study the sensitivity of weak lensing surveys to the effects of catastrophic redshift errors - cases where the true redshift is misestimated by a significant amount. To compute the biases in cosmological parameters, we adopt an efficient linearized analysis where the redshift errors are directly related to shifts in the weak lensing convergence power spectra. We estimate the number Nspec of unbiased spectroscopic redshifts needed to determine the catastrophic error rate well enough that biases in cosmological parameters are below statistical errors of weak lensing tomography. While the stra…
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.
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…
Accurate weak lensing mass estimates of clusters are needed in order to calibrate mass proxies for the cosmological exploitation of galaxy cluster surveys. Such measurements require accurate knowledge of the redshift distribution of the weak lensing source galaxies. In this context, we investigate the accuracy of photometric redshifts (photo-$z$s) computed by the 3D-HST team for the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey fields, which provide a relevant photometric reference data set for deep weak lensing studies. Through the comparison to spectroscopic redshifts and ph…
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）
We present a method that accurately propagates residual uncertainties in photometric redshift distributions into the cosmological inference from weak lensing measurements. The redshift distributions of tomographic redshift bins are parameterised using a flexible modified Gaussian mixture model. We fit this model to pre-calibrated redshift distributions and implement an analytic marginalisation over the potentially several hundred redshift nuisance parameters in the weak lensing likelihood, which is demonstrated to accurately recover the cosmological posterior. By iteratively fitting cosmologic…
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 …
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 …
Double source lensing, with two sources lensed by the same foreground galaxy, involves the distance between each source and the lens and hence is a probe of the universe away from the observer. The double source distance ratio also reduces sensitivity to the lens model and has good complementarity with standard distance probes. We show that using this technique at high redshifts $z>1$, to be enabled by data from the Euclid satellite and other surveys, can give insights on dark energy, both in terms of $w_0$-$w_a$ and redshift binned density. We find a dark energy figure of merit of 245 from co…
Effect of gravitational magnification on the measurement of distance modulus of type Ia supernovae is presented. We investigate a correlation between magnification and Hubble residual to explore how the magnification affects the estimation of cosmological parameters. We estimate magnification of type Ia supernovae in two distinct methods: one is based on convergence mass reconstruction under the weak lensing limit and the other is based on the direct measurement from galaxies distribution. Both magnification measurements are measured from Subaru Hyper Suprime-Cam survey catalogue. For both mea…
Pinning down the total neutrino mass and the dark energy equation of state is a key aim for upcoming galaxy surveys. Weak lensing is a unique probe of the total matter distribution whose non-Gaussian statistics can be quantified by the one-point probability distribution function (PDF) of the lensing convergence. We calculate the convergence PDF on mildly non-linear scales from first principles using large-deviation statistics, accounting for dark energy and the total neutrino mass. For the first time, we comprehensively validate the cosmology-dependence of the convergence PDF model against lar…
Mass calibration uncertainty is the largest systematic effect for using clusters of galaxies to constrain cosmological parameters. We present weak lensing mass measurements from the Canada-France-Hawaii Telescope Stripe 82 Survey for galaxy clusters selected through their high signal-to-noise thermal Sunyaev-Zeldovich (tSZ) signal measured with the Atacama Cosmology Telescope (ACT). For a sample of 9 ACT clusters with a tSZ signal-to-noise greater than five the average weak lensing mass is $\left(4.8\pm0.8\right)\,\times10^{14}\,\mathrm{M}_\odot$, consistent with the tSZ mass estimate of $\lef…
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…
We explore synergies between the Nancy Grace Roman Space Telescope and CMB lensing data to constrain dark energy and modified gravity scenarios. A simulated likelihood analysis of the galaxy clustering and weak lensing data from the Roman Space Telescope High Latitude Survey combined with CMB lensing data from the Simons Observatory is undertaken, marginalizing over important astrophysical effects and calibration uncertainties. Included in the modeling are the effects of baryons on small-scale clustering, scale-dependent growth suppression by neutrinos, as well as uncertainties in the galaxy c…
Cosmology and Source Redshift Constraints from Galaxy Clustering and Tomographic Weak Lensing with HSC Y3 and SDSS using the Point-Mass Correction Model
Recent detections of the cross-correlation of the thermal Sunyaev-Zel'dovich (tSZ) effect and weak gravitational lensing (WL) enable unique studies of cluster astrophysics and cosmology. In this work, we present constraints on the amplitude of the non-thermal pressure fraction in galaxy clusters, $α_0$, and the amplitude of the matter power spectrum, $σ_8$, using measurements of the tSZ power spectrum from Planck, and the tSZ-WL cross-correlation from Planck and the Red Cluster Sequence Lensing Survey. We fit the data to a semi-analytic model with the covariance matrix using $N$-body simulatio…
We derive an estimator for the lensing potential from galaxy number counts which contains a linear and a quadratic term. We show that this estimator has a much larger signal-to-noise ratio than the corresponding estimator from intensity mapping. This is due to the additional lensing term in the number count angular power spectrum which is present already at linear order. We estimate the signal-to-noise ratio for future photometric surveys. Particularly at high redshifts, $z\gtrsim 1.5$, the signal to noise ratio can become of order 30. Therefore, the number counts in photometric surveys would …
Weak lensing surveys are reaching sensitivities at which uncertainties in the galaxy redshift distributions n(z) from photo-z errors degrade cosmological constraints. We use ray-tracing simulations and a simple treatment of photo-z errors to assess cosmological parameter biases from uncertainties in n(z) in an LSST-like survey. We use the power spectrum and the abundance of lensing peaks to infer cosmological parameters, and find that the former is somewhat more resilient to photo-z errors. We place conservative lower limits on the survey size at which different types of photo-z errors degrade…
Weak gravitational lensing causes subtle changes in the apparent shapes of galaxies due to the bending of light by the gravity of foreground masses. By measuring the shapes of large numbers of galaxies (millions in recent surveys, up to tens of billions in future surveys) we can infer the parameters that determine cosmology. Imperfections in the detectors used to record images of the sky can introduce changes in the apparent shape of galaxies, which in turn can bias the inferred cosmological parameters. In this paper we consider the effect of two widely discussed sensor imperfections: tree-rin…
We explore a variety of statistics of clusters selected with cosmic shear measurement by utilizing both analytic models and large numerical simulations. We first develop a halo model to predict the abundance and the clustering of weak lensing selected clusters. Observational effects such as galaxy shape noise are included in our model. We then generate realistic mock weak lensing catalogs to test the accuracy of our analytic model. To this end, we perform full-sky ray-tracing simulations that allow us to have multiple realizations of a large continuous area. We model the masked regions on the …
We describe a methodology to probe gravity with the cosmic microwave background (CMB) lensing convergence $κ$, specifically by measuring $E_G$, the ratio of the Laplacian of the gravitational scalar potential difference with the velocity divergence. Using CMB lensing instead of galaxy-galaxy lensing avoids intrinsic alignments while also lacking a hard limit on the lens redshift and significant uncertainties in the source plane. We model $E_G$ for general relativity and modified gravity, finding that $E_G$ for $f(R)$ gravity should be scale-dependent due to the scale-dependence of the growth r…
Weak gravitational lensing (WL) causes distortions of galaxy images and probes massive structures on large scales, allowing us to understand the late-time evolution of the Universe. One way to extract the cosmological information from WL is to use peak statistics. Peaks are tracers of massive halos and therefore probe the mass function. They retain non-Gaussian information and have already been shown as a promising tool to constrain cosmology. In this work, we develop a new model to predict WL peak counts. The model generates fast simulations based on halo sampling and selects peaks from the d…
We report the first detection of the gravitational lensing of the cosmic microwave background through a measurement of the four-point correlation function in the temperature maps made by the Atacama Cosmology Telescope. We verify our detection by calculating the levels of potential contaminants and performing a number of null tests. The resulting convergence power spectrum at 2-degree angular scales measures the amplitude of matter density fluctuations on comoving length scales of around 100 Mpc at redshifts around 0.5 to 3. The measured amplitude of the signal agrees with Lambda Cold Dark Mat…
Accurate measurement of the cluster mass function is a crucial element in efforts to constrain structure formation models, the normalisation of the matter power spectrum and the cosmological matter density, and the nature and evolution of dark energy. Large weak lensing surveys of ~20,000 galaxy clusters and groups will be key tools in the observational pursuit of that goal. These weak lensing studies often proceed by stacking the lensing signals of many clusters and groups binned by mass-correlated observables such as richness and luminosity; typically such analyses ignore the triaxial struct…
In the near future, the overlap of the Rubin Observatory Legacy Survey of Space and Time (LSST) and the Simons Observatory (SO) will present an ideal opportunity for joint cosmological dataset analyses. In this paper we simulate the joint likelihood analysis of these two experiments using six two-point functions derived from galaxy position, galaxy shear, and CMB lensing convergence fields. Our analysis focuses on realistic noise and systematics models and we find that the dark energy Figure-of-Merit (FoM) increases by 53% (92%) from LSST-only to LSST+SO in Year 1 (Year 6). We also investigate…
We conduct a pseudo-$C_\ell$ analysis of the tomographic cross-correlation between 1000 deg$^2$ of weak lensing data from the Kilo-Degree Survey (KiDS-1000) and the thermal Sunyaev-Zeldovich (tSZ) effect measured by Planck and the Atacama Cosmology Telescope (ACT). Using HMx, a halo-model-based approach that consistently models the gas, star, and dark matter components, we are able to derive constraints on both cosmology and baryon feedback for the first time from these data, marginalising over redshift uncertainties, intrinsic alignment of galaxies, and contamination by the cosmic infrared ba…
Kinematic lensing with high-resolution spectroscopic surveys. A unique opportunity for transformative cosmology at high redshifts in the 2040s
Università degli Studi di Torino（都灵大学）；INFN – Istituto Nazionale di Fisica Nucleare, Sezione di Torino（意大利国家核物理研究所都灵分部）；INAF – Istituto Nazionale di Astrofisica, Osservatorio Astrofisico di Torino（意大利国家天体物理研究所都灵天文台）
