arXiv subjects
Publications and source records attributed to Peter Schneider.
In the Lubin-Tate setting we compare different categories of $(φ_L,Γ_L)$-modules over various perfect or imperfect coefficient rings. Moreover, we study their associated Herr-complexes. Finally, we show that a Lubin Tate extension gives rise to a weakly decompleting, but not decompleting tower in the sense of Kedlaya and Liu.
Context. Weak lensing and clustering statistics beyond two-point functions can capture non-Gaussian information about the matter density field, thereby improving the constraints on cosmological parameters relative to the mainstream methods based on correlation functions and power spectra. Aims. This paper presents a cosmological analysis of the fourth data release of the Kilo Degree Survey based on the density split statistics, which measures the mean shear profiles around regions classified according to foreground densities. The latter is constructed from a bright galaxy sample, which we further split into red and blue samples, allowing us to probe their respective connection to the underlying dark matter density. Methods. We use the state-of-the-art model of the density splitting statistics and validate its robustness against mock data infused with known systematic effects such as intrinsic galaxy alignment and baryonic feedback. Results. After marginalising over the photometric redshift uncertainty and the residual shear calibration bias, we measure for the full KiDS-bright sample a structure growth parameter of $S_8 = σ_8 \sqrt{Ω_\mathrm{m}/0.3} = 0.74^{+0.03}_{-0.02}$ that is competitive to and consistent with two-point cosmic shear results, a matter density of $Ω_\mathrm{m} = 0.28 \pm 0.02$, and a constant galaxy bias of $b = 1.32^{+0.12}_{-0.10}$.
The center $Z(\mathcal{A})$ of an abelian category $\mathcal{A}$ is the endomorphism ring of the identity functor on that category. A localizing subcategory of a Grothendieck category $\mathcal{C}$ is said to be stable if it is stable under essential extensions. The set $\mathbf{L}^{st}(\mathcal{C})$ of stable localizing subcategories of $\mathcal{C}$ is partially ordered under reverse inclusion. We show $\mathcal{L} \mapsto Z(\mathcal{C}/\mathcal{L})$ defines a sheaf of commutative rings on $\mathbf{L}^{st}(\mathcal{C})$ with respect to finite coverings. When $\mathcal{C}$ is assumed to be locally noetherian, we also show that the sheaf condition holds for arbitrary coverings.
In this work, which is the first of a series to prepare a cosmological parameter analysis with third-order cosmic shear statistics, we model both the shear three-point correlation functions $Γ^{(i)}$ and the third-order aperture statistics $\langle\mathcal{M}_\mathrm{ap}^3\rangle$ from the BiHalofit bispectrum model and validate these statistics with a series of N-body simulations. We then investigate how to bin the shear three-point correlation functions to achieve an unbiased estimate for third-order aperture statistics in real data. Finally, we perform a cosmological parameter analysis on KiDS1000-like mock data with second- and third-order statistics. We recover all cosmological parameters with very little bias. Furthermore, we find that a joint analysis almost doubles the constraining power on $S_8$ and increases the figure-of-merit in the $Ω_\mathrm{m}$-$σ_8$ plane by a factor of 5.9 with respect to an analysis with only second-order shear statistics. Our modelling pipeline is publicly available at https://github.com/sheydenreich/threepoint/releases/.
Studying the statistical properties of the large-scale structure in the Universe with weak gravitational lensing is a prime goal of several current and forthcoming galaxy surveys. The power that weak lensing has to constrain cosmological parameters can be enhanced by considering statistics beyond second-order shear correlation functions or power spectra. One such higher-order probe that has proven successful in observational data is the density split statistics (DSS), in which one analyses the mean shear profiles around points that are classified according to their foreground galaxy density. In this paper, we generalise the most accurate DSS model to allow for a broad class of angular filter functions used for the classification of the different local density regions. This approach is motivated by earlier findings showing that an optimised filter can provide tighter constraints on model parameters compared to the standard top-hat case. We build on large deviation theory approaches and approximations thereof to model the matter density PDF, and on perturbative calculations of higher-order moments of the density field. The novel addition relies on the generalisation of these previously employed calculations to allow for general filter functions and is validated on several sets of numerical simulations. The revised model fits well the simulation measurements, with a residual systematic offset that is small compared to the statistical accuracy of current weak lensing surveys. The accuracy of the model is slightly lower for a compensated filter than for a non-negative filter function, and that it increases with the filter size. Using a Fisher matrix approach, we find constraints comparable to the commonly used two-point cosmic shear measures. Hence, our DSS model can be used in competitive analyses of current cosmic shear data, while it may need refinements for forthcoming lensing surveys.
One probe for systematic effects in gravitational lensing surveys is the presence of so-called B-modes in the cosmic shear two-point correlation functions ξ_\pm(\vt), since lensing is expected to produce only E-mode shear. Furthermore, there exist ambiguous modes which can not uniquely be assigned to either E- or B-mode shear. We derive explicit equations for the pure-mode shear correlation functions ξ_\pm^E/B(\vt) and their ambiguous components ξ_\pm^amb(\vt), that can be derived from the measured ξ_\pm(\vt) on a finite angular interval \tmin\le\vt\le\tmax, such that the latter can be decomposed uniquely into pure-mode functions as ξ_+=ξ_+^E+ξ_+^B+ξ_+^amb and ξ_-=ξ_-^E-ξ_-^B+ξ_-^amb. The derivation is obtained by defining a new set of COSEBIs, for which explicit relations are obtained, and which yields a smaller covariance between COSEBI modes. We derive the relation between ξ_\pm^E/B/amb and the underlying E-/B-mode power spectra. The pure-mode correlation functions can provide a diagnostics of systematics in configuration space. We then apply our results to SLICS simulations and the KiDS-1000 cosmic shear data, calculate the new COSEBIs and the pure-mode correlation functions, as well as the corresponding covariances, and show that the new statistics fit equally well to the best-fitting cosmological model as the previous KiDS-1000 analysis and recovers the same level of (insignificant) B-modes. We also consider in some detail the ambiguous modes at first- and second-order level, finding some surprising results; for example, the shear field of a point mass, when cut along a line through the center, can not be ascribed uniquely to an E-mode shear and is thus ambiguous, and the shear correlation functions resulting from a random ensemble of point masses, when measured over a finite angular range, correspond to an ambiguous mode.
Halo models and halo occupation distributions (HODs) are important tools to model the galaxy and matter distribution. We present and assess a new method for constraining the parameters of HODs using the gravitational lensing shear around galaxy pairs, galaxy-galaxy-galaxy-lensing (G3L). In contrast to galaxy-galaxy-lensing, G3L is sensitive to correlations between the per-halo numbers of galaxies from different populations. We use G3L to probe these correlations and test the default hypothesis that they are negligible. We derive a halo model for G3L and validate it with realistic mock data from the Millennium Simulation and a semi-analytic galaxy model. Then, we analyse public data from the Kilo-Degree Survey (KiDS), the VISTA Infrared Kilo-Degree Galaxy Survey (VIKING) and data from the Galaxy And Mass Assembly Survey (GAMA) to infer the HODs of galaxies at $z<0.5$ in five different stellar mass bins between $10^{8.5}h^{-2} M_\odot$ and $10^{11.5}h^{-2} M_\odot$ and two colours (red and blue), as well as correlations between satellite numbers. The analysis recovers the true HODs in the simulated data within the $68\%$ credibility range. The inferred HODs vary significantly with colour and stellar mass. There is also strong evidence ($>3σ$) for correlations, increasing with halo mass, between the numbers of red and blue satellites and galaxies with stellar masses below $10^{10} \Msun. Possible causes of these correlations are the selection of similar galaxies in different samples, the survey flux limit, or physical mechanisms like a fixed ratio between the satellite numbers of distinct populations. The decorrelation for halos with smaller masses is probably an effect of shot noise by low-occupancy halos. The inferred HODs can be used to complement galaxy-galaxy-lensing or galaxy clustering HOD studies or as input to cosmological analyses and improved mock galaxy catalogues.
We conduct a pseudo-$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 background (CIB). We find our results to be insensitive to the CIB, while intrinsic alignment provides a small but significant contribution to the lensing--tSZ cross-correlation. The cosmological constraints are consistent with those of other low-redshift probes and prefer strong baryon feedback. The inferred amplitude of the lensing--tSZ cross-correlation signal, which scales as $σ_8(Ω_\mathrm{m}/0.3)^{0.2}$, is low by $\sim 2\,σ$ compared to the primary cosmic microwave background constraints by Planck. The lensing--tSZ measurements are then combined with pseudo-$C_\ell$ measurements of KiDS-1000 cosmic shear into a novel joint analysis, accounting for the full cross-covariance between the probes, providing tight cosmological constraints by breaking parameter degeneracies inherent to both probes. The joint analysis gives an improvement of 40% on the constraint of $S_8=σ_8\sqrt{Ω_\mathrm{m}/0.3}$ over cosmic shear alone, while providing constraints on baryon feedback consistent with hydrodynamical simulations, demonstrating the potential of such joint analyses with baryonic tracers such as the tSZ effect. We discuss remaining modelling challenges that need to be addressed if these baryonic probes are to be included in future precision-cosmology analyses.
We introduce a derived smooth duality functor on the unbounded derived category of smooth mod p representations of a p-adic Lie group. Using this functor we relate various subcategories of admissible complexes.
Magnification changes the observed number counts of galaxies on the sky. This biases the observed tangential shear profiles around galaxies, the so-called galaxy-galaxy lensing (GGL) signal, and the related excess mass profile. Correspondingly, inference of physical quantities, such as the mean mass profile of halos around galaxies, are affected by magnification effects. We use simulated shear and galaxy data of the Millennium Simulation to quantify the effect on shear and mass estimates from magnified lens and source number counts. The former are due to the large-scale matter distribution in the foreground of the lenses, the latter are caused by magnification of the source population by the matter associated with the lenses. The GGL signal is calculated from the simulations by an efficient fast-Fourier transform that can also be applied to real data. The numerical treatment is complemented by a leading-order analytical description of the magnification effects, which is shown to fit the numerical shear data well. We find the magnification effect is strongest for steep galaxy luminosity functions and high redshifts. For a lens redshift of $z_\mathrm{d}=0.83$, a limiting magnitude of $22\,\mathrm{mag}$ in the $r$-band and a source redshift of $z_\mathrm{s}=0.99$, we find that a magnification correction changes the shear profile up to $45\%$ and the mass is biased by up to $55 \%$. For medium-redshift galaxies the relative change in shear and mass is typically a few percent. As expected, the sign of the bias depends on the local slope of the lens luminosity function $α_\mathrm{d}$, where the mass is biased low for $α_\mathrm{d}<1$ and biased high for $α_\mathrm{d}>1$. Whereas the magnification effect of sources is rarely than more $1\%$, the statistical power of future weak lensing surveys warrants correction for this effect.
Let $G$ be a locally profinite group and let $k$ be a field of positive characteristic $p$. Let $Z(G)$ denote the center of $G$ and let $\mathfrak{Z}(G)$ denote the Bernstein center of $G$, that is, the $k$-algebra of natural endomorphisms of the identity functor on the category of smooth $k$-linear representations of $G$. We show that if $G$ contains an open pro-$p$ subgroup but no proper open centralisers, then there is a natural isomorphism of $k$-algebras $\mathfrak{Z}(Z(G)) \xrightarrow{\cong} \mathfrak{Z}(G)$. We also describe $\mathfrak{Z}(Z(G))$ explicitly as a particular completion of the abstract group ring $k[Z(G)]$. Both conditions on $G$ are satisfied whenever $G$ is the group of points of any connected smooth algebraic group defined over a local field of residue characteristic $p$. In particular, when the algebraic group is semisimple, we show that $\mathfrak{Z}(G) = k[Z(G)]$.
We present measurements of $f_h$, the ratio of the aligned components of the projected halo and galaxy ellipticities, for a sample of central galaxies using weak gravitational lensing data from the Kilo-Degree Survey (KiDS). Using a lens galaxy shape estimation that is more sensitive to outer galaxy regions, we find $f_{\rm h}=0.50\pm0.20$ for our full sample and $f_{\rm h}=0.55\pm0.19$ for an intrinsically red (and therefore higher stellar-mass) sub-sample, rejecting the hypothesis of round halos and/or galaxies being un-aligned with their parent halo at $2.5σ$ and $2.9σ$, respectively. We quantify the 93.4% purity of our central galaxy sample using numerical simulations and overlapping spectroscopy from the Galaxy and Mass Assembly survey. This purity ensures that the interpretation of our measurements is not complicated by the presence of a significant fraction of satellite galaxies. Restricting our central galaxy ellipticity measurement to the inner isophotes, we find $f_{\rm h}=0.34\pm0.17$ for our red sub-sample, suggesting that the outer galaxy regions are more aligned with their dark matter halos compared to the inner regions. Our results are in agreement with previous studies and suggest that lower mass halos are rounder and/or less aligned with their host galaxy than samples of more massive galaxies, studied in galaxy groups and clusters.
Let $G={\rm SL}_2(\mathfrak F) $ where $\mathfrak F$ is a finite extension of $\mathbb Q_p$. We suppose that the pro-$p$ Iwahori subgroup $I$ of $G$ is a Poincaré group of dimension $d$. Let $k$ be a field containing the residue field of $\mathfrak F$. In this article, we study the graded Ext-algebra $E^*={\operatorname{Ext}}_{\operatorname{Mod}(G)}^*(k[G/I], k[G/I])$. Its degree zero piece $E^0$ is the usual pro-$p$ Iwahori-Hecke algebra $H$. We study $E^d$ as an $H$-bimodule and deduce that for an irreducible admissible smooth representation of $G$, we have $H^d(I,V)=0$ unless $V$ is the trivial representation. When $\mathfrak F=\mathbb Q_p$ with $p\geq 5$, we have $d=3$. In that case we describe $E^*$ as an $H$-bimodule and give the structure as an algebra of the centralizer in $E^*$ of the center of $H$. We deduce results on the values of the functor $H^*(I, {}_-)$ which attaches to a (finite length) smooth $k$-representation $V$ of $G$ its cohomology with respect to $I$. We prove that $H^*(I,V)$ is always finite dimensional. Furthermore, if $V$ is irreducible, then $V$ is supersingular if and only if $H^*(I,V)$ is a supersingular $H$-module.
We forecast and optimize the cosmological power of various weak-lensing aperture mass ($M_{\rm ap}$) map statistics for future cosmic shear surveys, including peaks, voids, and the full distribution of pixels (1D $M_{\rm ap}$). These alternative methods probe the non-Gaussian regime of the matter distribution, adding complementary cosmological information to the classical two-point estimators. Based on the SLICS and cosmo-SLICS $N$-body simulations, we build Euclid-like mocks to explore the $S_8 - Ω_{\rm m} - w_0$ parameter space. We develop a new tomographic formalism which exploits the cross-information between redshift slices (cross-$M_{\rm ap}$) in addition to the information from individual slices (auto-$M_{\rm ap}$) probed in the standard approach. Our auto-$M_{\rm ap}$ forecast precision is in good agreement with the recent literature on weak-lensing peak statistics, and is improved by $\sim 50$% when including cross-$M_{\rm ap}$. It is further boosted by the use of 1D $M_{\rm ap}$ that outperforms all other estimators, including the shear two-point correlation function ($γ$-2PCF). When considering all tomographic terms, our uncertainty range on the structure growth parameter $S_8$ is enhanced by $\sim 45$% (almost twice better) when combining 1D $M_{\rm ap}$ and the $γ$-2PCF compared to the $γ$-2PCF alone. We additionally measure the first combined forecasts on the dark energy equation of state $w_0$, finding a factor of three reduction of the statistical error compared to the $γ$-2PCF alone. This demonstrates that the complementary cosmological information explored by non-Gaussian $M_{\rm ap}$ map statistics not only offers the potential to improve the constraints on the recent $σ_8$ - $Ω_{\rm m}$ tension, but also constitutes an avenue to understand the accelerated expansion of our Universe.
We present weak lensing shear catalogues from the fourth data release of the Kilo-Degree Survey, KiDS-1000, spanning 1006 square degrees of deep and high-resolution imaging. Our `gold-sample' of galaxies, with well-calibrated photometric redshift distributions, consists of 21 million galaxies with an effective number density of $6.17$ galaxies per square arcminute. We quantify the accuracy of the spatial, temporal, and flux-dependent point-spread function (PSF) model, verifying that the model meets our requirements to induce less than a $0.1σ$ change in the inferred cosmic shear constraints on the clustering cosmological parameter $S_8 = σ_8\sqrt{Ω_{\rm m}/0.3}$. Through a series of two-point null-tests, we validate the shear estimates, finding no evidence for significant non-lensing B-mode distortions in the data. The PSF residuals are detected in the highest-redshift bins, originating from object selection and/or weight bias. The amplitude is, however, shown to be sufficiently low and within our stringent requirements. With a shear-ratio null-test, we verify the expected redshift scaling of the galaxy-galaxy lensing signal around luminous red galaxies. We conclude that the joint KiDS-1000 shear and photometric redshift calibration is sufficiently robust for combined-probe gravitational lensing and spectroscopic clustering analyses.
We present a joint cosmological analysis of weak gravitational lensing observations from the Kilo-Degree Survey (KiDS-1000), with redshift-space galaxy clustering observations from the Baryon Oscillation Spectroscopic Survey (BOSS), and galaxy-galaxy lensing observations from the overlap between KiDS-1000, BOSS and the spectroscopic 2-degree Field Lensing Survey (2dFLenS). This combination of large-scale structure probes breaks the degeneracies between cosmological parameters for individual observables, resulting in a constraint on the structure growth parameter $S_8=σ_8 \sqrt{Ω_{\rm m}/0.3} = 0.766^{+0.020}_{-0.014}$, that has the same overall precision as that reported by the full-sky cosmic microwave background observations from Planck. The recovered $S_8$ amplitude is low, however, by $8.3 \pm 2.6$ % relative to Planck. This result builds from a series of KiDS-1000 analyses where we validate our methodology with variable depth mock galaxy surveys, our lensing calibration with image simulations and null-tests, and our optical-to-near-infrared redshift calibration with multi-band mock catalogues and a spectroscopic-photometric clustering analysis. The systematic uncertainties identified by these analyses are folded through as nuisance parameters in our cosmological analysis. Inspecting the offset between the marginalised posterior distributions, we find that the $S_8$-difference with Planck is driven by a tension in the matter fluctuation amplitude parameter, $σ_8$. We quantify the level of agreement between the CMB and our large-scale structure constraints using a series of different metrics, finding differences with a significance ranging between $\sim\! 3\,σ$, when considering the offset in $S_{8}$, and $\sim\! 2\,σ$, when considering the full multi-dimensional parameter space.
We measure the cross-correlation between galaxy weak lensing data from the Kilo Degree Survey (KiDS-1000, DR4) and cosmic microwave background (CMB) lensing data from the Atacama Cosmology Telescope (ACT, DR4) and the Planck Legacy survey. We use two samples of source galaxies, selected with photometric redshifts, $(0.1<z_{\rm B}<1.2)$ and $(1.2<z_{\rm B}<2)$, which produce a combined detection significance of the CMB lensing/weak galaxy lensing cross-spectrum of $7.7σ$. With the lower redshift galaxy sample, for which the cross-correlation is detected at a significance of $5.3σ$, we present joint cosmological constraints on the matter density parameter, $Ω_{\rm m}$, and the matter fluctuation amplitude parameter, $σ_8$, marginalising over three nuisance parameters that model our uncertainty in the redshift and shear calibration, and the intrinsic alignment of galaxies. We find our measurement to be consistent with the best-fitting flat $Λ$CDM cosmological models from both Planck and KiDS-1000. We demonstrate the capacity of CMB-weak lensing cross-correlations to set constraints on either the redshift or shear calibration, by analysing a previously unused high-redshift KiDS galaxy sample $(1.2<z_{\rm B}<2)$, with the cross-correlation detected at a significance of $7σ$. This analysis provides an independent assessment for the accuracy of redshift measurements in a regime that is challenging to calibrate directly owing to known incompleteness in spectroscopic surveys.
Cosmological simulations predict that galaxies are embedded into triaxial dark matter haloes, which appear approximately elliptical in projection. Weak gravitational lensing allows us to constrain these halo shapes and thereby test the nature of dark matter. Weak lensing has already provided robust detections of the signature of halo flattening at the mass scales of groups and clusters, whereas results for galaxies have been somewhat inconclusive. Here we combine data from five surveys (NGVSLenS, KiDS/KV450, CFHTLenS, CS82, and RCSLenS) in order to tighten observational constraints on galaxy-scale halo ellipticity for photometrically selected lens samples. We constrain $f_\rm{h}$, the average ratio between the aligned component of the halo ellipticity and the ellipticity of the light distribution, finding $f_\rm{h}=0.303^{+0.080}_{-0.079}$ for red lenses and $f_\rm{h}=0.217^{+0.160}_{-0.159}$ for blue lenses when assuming elliptical NFW density profiles and a linear scaling between halo ellipticity and galaxy ellipticity. Our constraints for red galaxies constitute the currently most significant ($3.8σ$) systematics-corrected detection of the signature of halo flattening at the mass scale of galaxies. Our results are in good agreement with expectations from the Millennium Simulation that apply the same analysis scheme and incorporate models for galaxy-halo misalignment. Assuming these misalignment models and the analysis assumptions stated above are correct, our measurements imply an average dark matter halo ellipticity for the studied red galaxy samples of $\langle|ε_\rm{h}|\rangle=0.174\pm 0.046$, where $|ε_{h}|=(1-q)/(1+q)$ relates to the ratio $q=b/a$ of the minor and major axes of the projected mass distribution. Similar measurements based on larger upcoming weak lensing data sets can help to calibrate models for intrinsic galaxy alignments. [abridged]