arXiv subjects

Maciej Bilicki

Publications and source records attributed to Maciej Bilicki.

At least 55 records · Page 3Linked to original sources

arXiv2023

KiDS-1000: Cosmology with improved cosmic shear measurements

We present refined cosmological parameter constraints derived from a cosmic shear analysis of the fourth data release of the Kilo-Degree Survey (KiDS-1000). Our main improvements include enhanced galaxy shape measurements made possible by an updated version of the lensfit code and improved shear calibration achieved with a newly developed suite of multi-band image simulations. Additionally, we incorporated recent advancements in cosmological inference from the joint Dark Energy Survey Year 3 and KiDS-1000 cosmic shear analysis. Assuming a spatially flat standard cosmological model, we constrain $S_8\equivσ_8(Ω_{\rm m}/0.3)^{0.5} = 0.776_{-0.027-0.003}^{+0.029+0.002}$, where the second set of uncertainties accounts for the systematic uncertainties within the shear calibration. These systematic uncertainties stem from minor deviations from realism in the image simulations and the sensitivity of the shear measurement algorithm to the morphology of the galaxy sample. Despite these changes, our results align with previous KiDS studies and other weak lensing surveys, and we find a ${\sim}2.3σ$ level of tension with the Planck cosmic microwave background constraints on $S_8$.

astro-ph.CO↗

arXiv2023

Impact of modelling galaxy redshift uncertainties on the gravitational-wave dark standard siren measurement of the Hubble constant

Gravitational wave science is a new and rapidly expanding field of observational astronomy. Multimessenger observations of the binary neutron star merger GW170817 have provided some iconic results including the first gravitational-wave standard-siren measurement of the Hubble constant, opening up a new way to probe cosmology. The majority of the compact binary sources observed in gravitational waves are however without bright electromagnetic counterparts. In these cases, one can fall back on the ``dark standard siren'' approach to include information statistically from potential host galaxies. For such a measurement, we need to be cautious about all possible sources of systematic errors. In this paper, we begin to study the possible errors coming from the galaxy catalogue sector, and in particular, look into the effect of galaxy redshift uncertainties for the cases where these are photometry-based. We recalculate the dark standard siren Hubble constant using the latest GWTC-3 events and associated galaxy catalogues, with different galaxy redshift uncertainty models, namely, the standard Gaussian, a modified Lorentzian, and no uncertainty at all. We find that not using redshift uncertainties at all can lead to a potential bias comparable with other potential systematic effects previously considered for the GWTC-3 $H_0$ measurement (however still small compared to the overall statistical error in this measurement). The difference between different uncertainty models leads to small differences in the results for the current data; their impact is much smaller than the current statistical errors and other potential sources of systematic errors which have been considered in previous robustness studies.

gr-qc↗

arXiv2023

ACT-DR5 Sunyaev-Zel'dovich Clusters: weak lensing mass calibration with KiDS

We present weak gravitational lensing measurements of a sample of 157 clusters within the Kilo Degree Survey (KiDS), detected with a $>5σ$ thermal Sunyaev-Zel'dovich (SZ) signal by the Atacama Cosmology Telescope (ACT). Using a halo-model approach we constrain the average total cluster mass, $M_{\rm WL}$, accounting for the ACT cluster selection function of the full sample. We find that the SZ cluster mass estimate $M_{\rm SZ}$, which was calibrated using X-ray observations, is biased with $M_{\rm SZ}/M_{\rm WL} = (1-b_{\rm SZ}) = 0.65\pm 0.05$. Separating the sample into six mass bins, we find no evidence of a strong mass-dependency for the mass bias, $(1-b_{\rm SZ})$. Adopting this ACT-KiDS SZ mass-calibration would bring the Planck SZ cluster count into agreement with the counts expected from the {\it Planck} cosmic microwave background $Λ$CDM cosmological model, although it should be noted that the cluster sample considered in this work has a lower average mass $M_{\rm SZ, uncor} = 3.64 \times 10^{14} M_{\odot}$ compared to the Planck cluster sample which has an average mass in the range $M_{\rm SZ, uncor} = (5.5-8.5) \times 10^{14} M_{\odot}$, depending on the sub-sample used.

astro-ph.CO↗

arXiv2023

KiDS-1000: cross-correlation with Planck cosmic microwave background lensing and intrinsic alignment removal with self-calibration

Galaxy shear - cosmic microwave background (CMB) lensing convergence cross-correlations contain additional information on cosmology to auto-correlations. While being immune to certain systematic effects, they are affected by the galaxy intrinsic alignments (IA). This may be responsible for the reported low lensing amplitude of the galaxy shear $\times$ CMB convergence cross-correlations, compared to the standard Planck $Λ$CDM (cosmological constant and cold dark matter) cosmology prediction. In this work, we investigate how IA affects the Kilo-Degree Survey (KiDS) galaxy lensing shear - Planck CMB lensing convergence cross-correlation and compare it to previous treatments with or without IA taken into consideration. More specifically, we compare marginalization over IA parameters and the IA self-calibration (SC) method (with additional observables defined only from the source galaxies) and prove that SC can efficiently break the degeneracy between the CMB lensing amplitude $A_{\rm lens}$ and the IA amplitude $A_{\rm IA}$. We further investigate how different systematics affect the resulting $A_{\rm IA}$ and $A_{\rm lens}$, and validate our results with the MICE2 simulation. We find that by including the SC method to constrain IA, the information loss due to the degeneracy between CMB lensing and IA is strongly reduced. The best-fit values are $A_{\rm lens}=0.84^{+0.22}_{-0.22}$ and $A_{\rm IA}=0.60^{+1.03}_{-1.03}$, while different angular scale cuts can affect $A_{\rm lens}$ by $\sim10\%$. We show that appropriate treatment of the boost factor, cosmic magnification, and photometric redshift modeling is important for obtaining the correct IA and cosmological results.

astro-ph.CO↗

arXiv2023

Constrained simulations of the local Universe with Modified Gravity

We present a methodology for constructing modified gravity (MG) constrained simulations of the local Universe using positions and peculiar velocities from the CosmicFlows data set. Our analysis focuses on the following MG models: the normal branch of the Dvali-Gabadadze-Porrati (nDGP) model and Hu-Sawicki $f(R)$ model. We develop a model independent methodology for constructing constrained simulations with any given power spectra and numerically calculated linear growth functions. Initial conditions (ICs) for a set of constrained simulations are constructed for the standard cosmological model $Λ$CDM and the MG models. Differences between the model's reconstructed Wiener filtered density and the resultant simulation density are presented showing the importance for the generation of MG constrained ICs to study the subtle effects of MG in the local Universe. These are the first MG constrained simulations ever produced. The current work paves the way to improved approximate methods for models with scale-dependent growth functions, such as $f(R)$, and for high-resolution hydrodynamical MG zoom-in simulations of the local Universe.

astro-ph.CO↗

arXiv2023

KiDS-Legacy calibration: unifying shear and redshift calibration with the SKiLLS multi-band image simulations

We present SKiLLS, a suite of multi-band image simulations for the weak lensing analysis of the complete Kilo-Degree Survey (KiDS), dubbed KiDS-Legacy analysis. The resulting catalogues enable joint shear and redshift calibration, enhancing the realism and hence accuracy over previous efforts. To create a large volume of simulated galaxies with faithful properties and to a sufficient depth, we integrated cosmological simulations with high-quality imaging observations. We also improved the realism of simulated images by allowing the point spread function (PSF) to differ between CCD images, including stellar density variations and varying noise levels between pointings. Using realistic variable shear fields, we accounted for the impact of blended systems at different redshifts. Although the overall correction is minor, we found a clear redshift-bias correlation in the blending-only variable shear simulations, indicating the non-trivial impact of this higher-order blending effect. We also explored the impact of the PSF modelling errors and found a small yet noticeable effect on the shear bias. Finally, we conducted a series of sensitivity tests, including changing the input galaxy properties. We conclude that our fiducial shape measurement algorithm, lensfit, is robust within the requirements of lensing analyses with KiDS. As for future weak lensing surveys with tighter requirements, we suggest further investments in understanding the impact of blends at different redshifts, improving the PSF modelling algorithm and developing the shape measurement method to be less sensitive to the galaxy properties.

astro-ph.CO↗

arXiv2023

KiDS-1000 Cosmology: Constraints from density split statistics

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 $b = 1.32^{+0.12}_{-0.10}$.

astro-ph.CO↗

arXiv2022

The Hitchhiker's guide to the galaxy catalog approach for gravitational wave cosmology

We outline the ``dark siren'' galaxy catalog method for cosmological inference using gravitational wave (GW) standard sirens, clarifying some common misconceptions in the implementation of this method. When a confident transient electromagnetic counterpart to a GW event is unavailable, the identification of a unique host galaxy is in general challenging. Instead, as originally proposed by Schutz (1986), one can consult a galaxy catalog and implement a dark siren statistical approach incorporating all potential host galaxies within the localization volume. Trott & Hunterer 2021 recently claimed that this approach results in a biased estimate of the Hubble constant, $H_0$, when implemented on mock data, even if optimistic assumptions are made. We demonstrate explicitly that, as previously shown by multiple independent groups, the dark siren statistical method leads to an unbiased posterior when the method is applied to the data correctly. We highlight common sources of error possible to make in the generation of mock data and implementation of the statistical framework, including the mismodeling of selection effects and inconsistent implementations of the Bayesian framework, which can lead to a spurious bias.

gr-qc↗

arXiv2022

Cosmic star formation history with tomographic cosmic infrared background-galaxy cross-correlation

In this work, we probe the star formation history of the Universe using tomographic cross-correlation between the cosmic infrared background (CIB) and galaxy samples. The galaxy samples are from the Kilo-Degree Survey (KiDS), while the CIB maps are made from \planck\, sky maps. We measure the cross-correlation in harmonic space with a significance of 43$σ$. We model the cross-correlation with a halo model, which links CIB anisotropies to star formation rates (SFR) and galaxy abundance. We assume that SFR has a lognormal dependence on halo mass, while galaxy abundance follows the halo occupation distribution (HOD) model. The cross-correlations give a best-fit maximum star formation efficiency of $η_{\mathrm{max}}= 0.41^{+0.09}_{-0.14}$ at a halo mass $\log_{10}(M_{\mathrm{peak}}/M_{\odot})= {12.14\pm 0.36}$. The derived star formation rate density (SFRD) is well constrained up to $z\sim 1.5$. The constraining power at high redshift is mainly limited by the KiDS survey depth. A combination with external SFRD measurements from previous studies gives $\log_{10}(M_{\mathrm{peak}}/M_{\odot})=12.42^{+0.35}_{-0.19}$. This tightens the SFRD constraint up to $z=4$, yielding a peak SFRD of $0.09_{-0.004}^{+0.003}\,M_{\odot} \mathrm { year }^{-1} \mathrm{Mpc}^{-3}$ at $z=1.74^{+0.06}_{-0.02}$, corresponding to a lookback time of $10.05^{+0.12}_{-0.03}$ Gyr. Both constraints are consistent, and the derived SFRD agrees with previous studies and simulations. Additionally, we estimate the galaxy bias $b$ of KiDS galaxies from the constrained HOD parameters and yield an increasing bias from $b=1.1_{-0.31}^{+0.17}$ at $z=0$ to $b=1.96_{-0.64}^{+0.18}$ at $z=1.5$. Finally, we provide a forecast for future galaxy surveys and conclude that, due to their considerable depth, future surveys will yield a much tighter constraint on the evolution of the SFRD.

astro-ph.GA↗

arXiv2022

Galaxy morphoto-Z with neural Networks (GaZNets). I. Optimized accuracy and outlier fraction from Imaging and Photometry

In the era of large sky surveys, photometric redshifts (photo-z) represent crucial information for galaxy evolution and cosmology studies. In this work, we propose a new Machine Learning (ML) tool called Galaxy morphoto-Z with neural Networks (GaZNet-1), which uses both images and multi-band photometry measurements to predict galaxy redshifts, with accuracy, precision and outlier fraction superior to standard methods based on photometry only. As a first application of this tool, we estimate photo-z of a sample of galaxies in the Kilo-Degree Survey (KiDS). GaZNet-1 is trained and tested on $\sim140 000$ galaxies collected from KiDS Data Release 4 (DR4), for which spectroscopic redshifts are available from different surveys. This sample is dominated by bright (MAG$\_$AUTO$<21$) and low redshift ($z < 0.8$) systems, however, we could use $\sim$ 6500 galaxies in the range $0.8 < z < 3$ to effectively extend the training to higher redshift. The inputs are the r-band galaxy images plus the 9-band magnitudes and colours, from the combined catalogs of optical photometry from KiDS and near-infrared photometry from the VISTA Kilo-degree Infrared survey. By combining the images and catalogs, GaZNet-1 can achieve extremely high precision in normalized median absolute deviation (NMAD=0.014 for lower redshift and NMAD=0.041 for higher redshift galaxies) and low fraction of outliers ($0.4$\% for lower and $1.27$\% for higher redshift galaxies). Compared to ML codes using only photometry as input, GaZNet-1 also shows a $\sim 10-35$% improvement in precision at different redshifts and a $\sim$ 45% reduction in the fraction of outliers. We finally discuss that, by correctly separating galaxies from stars and active galactic nuclei, the overall photo-z outlier fraction of galaxies can be cut down to $0.3$\%.

astro-ph.GA↗

arXiv2022

The dark matter halo masses of elliptical galaxies as a function of observationally robust quantities

Context. The assembly history of the stellar component of a massive elliptical galaxy is closely related to that of its dark matter halo. Measuring how the properties of galaxies correlate with their halo mass can help understand their evolution. Aims. We investigate how the dark matter halo mass of elliptical galaxies varies as a function of their properties, using weak gravitational lensing observations. To minimise the chances of biases, we focus on galaxy properties that can be determined robustly: the surface brightness profile and the colour. Methods. We selected 2409 central massive elliptical galaxies from the SDSS spectroscopic sample. We first measured their surface brightness profile and colours by fitting Sersic models to photometric data from the Kilo-Degree Survey (KiDS). We fitted their halo mass distribution as a function of redshift, rest-frame $r-$band luminosity, half-light radius and rest-frame $u-g$ colour, using KiDS weak lensing data and a Bayesian hierarchical approach. For the sake of robustness to assumptions on the large-radii behaviour of the surface brightness, we repeated the analysis replacing total luminosity and half-light radius with the luminosity within a 10~kpc aperture, $L_{r,10}$, and the light-weighted surface brightness slope, $Γ_{10}$. Results. We did not detect any correlation between halo mass and either half-light radius or colour, at fixed redshift and luminosity. Conclusions. Our results indicate that the average star formation efficiency of massive elliptical galaxies has little dependence on their final size or colour. This suggests that the origin of the diversity in the size and colour distribution of these objects lies with properties other than halo mass.

astro-ph.GA↗

arXiv2022

Galaxy And Mass Assembly (GAMA): Self-Organizing Map Application on Nearby Galaxies

Galaxy populations show bimodality in a variety of properties: stellar mass, colour, specific star-formation rate, size, and Sérsic index. These parameters are our feature space. We use an existing sample of 7556 galaxies from the Galaxy and Mass Assembly (GAMA) survey, represented using five features and the K-means clustering technique, showed that the bimodalities are the manifestation of a more complex population structure, represented by between 2 and 6 clusters. Here we use Self Organizing Maps (SOM), an unsupervised learning technique which can be used to visualize similarity in a higher dimensional space using a 2D representation, to map these five-dimensional clusters in the feature space onto two-dimensional projections. To further analyze these clusters, using the SOM information, we agree with previous results that the sub-populations found in the feature space can be reasonably mapped onto three or five clusters. We explore where the "green valley" galaxies are mapped onto the SOM, indicating multiple interstitial populations within the green valley population. Finally, we use the projection of the SOM to verify whether morphological information provided by GalaxyZoo users, for example, if features are visible, can be mapped onto the SOM-generated map. Voting on whether galaxies are smooth, likely ellipticals, or "featured" can reasonably be separated but smaller morphological features (bar, spiral arms) can not. SOMs promise to be a useful tool to map and identify instructive sub-populations in multidimensional galaxy survey feature space, provided they are large enough.

astro-ph.GA↗

arXiv2022

Universality of the halo mass function in modified gravity cosmologies

We study the halo mass function (HMF) in modified gravity (MG) models using a set of large $N$-body simulations -- the ELEPHANT suite. We consider two popular beyond-general relativity scenarios: the Hu-Sawicki chameleon $f(R)$ model and the normal branch of the Dvali-Gabadadze-Porrati braneworld (nDGP). We show that in MG, analytic formulation based on the Press-Schechter framework offers a grossly inaccurate description of the HMF. We find, however, that once the HMF is expressed in terms of the dimensionless multiplicity function, it approximately assumes a redshift-independent universal character for all the models. Exploiting this property, we propose universal fits for the MG HMF in terms of their fractional departures from the $\mathrm{Λ\text{CDM}}$ case. We find two enclosed formulas, one for $f(R)$ and another for nDGP, that provide a reliable description of the HMF over the mass range covered by the simulations. These are accurate to a few percent with respect to the $N$-body data. We test the extrapolation potential of our fits against separate simulations with a different cosmological background and mass resolution, and find very good accuracy, within $\sim 10\%$. A particularly interesting finding from our analysis is a Gaussian-like shape of the HMF deviation that seems to appear universally across the whole $f(R)$ family, peaking at a mass variance scale characteristic for each $f(R)$ variant. We attribute this behavior to the specific physics of the environmentally-dependent chameleon screening models.

astro-ph.CO↗

arXiv2022

Galaxy And Mass Assembly (GAMA): Data Release 4 and the z < 0.1 total and z < 0.08 morphological galaxy stellar mass functions

In Galaxy And Mass Assembly Data Release 4 (GAMA DR4), we make available our full spectroscopic redshift sample. This includes 248682 galaxy spectra, and, in combination with earlier surveys, results in 330542 redshifts across five sky regions covering ~250deg^2. The redshift density, is the highest available over such a sustained area, has exceptionally high completeness (95 per cent to r_KIDS=19.65mag), and is well suited for the study of galaxy mergers, galaxy groups, and the low redshift (z<0.25) galaxy population. DR4 includes 32 value-added tables or Data Management Units (DMUs) that provide a number of measured and derived data products including GALEX, ESO KiDS, ESO VIKING, WISE and Herschel Space Observatory imaging. Within this release, we provide visual morphologies for 15330 galaxies to z<0.08, photometric redshift estimates for all 18million objects to r_KIDS~25mag, and stellar velocity dispersions for 111830 galaxies. We conclude by deriving the total galaxy stellar mass function (GSMF) and its sub-division by morphological class (elliptical, compact-bulge and disc, diffuse-bulge and disc, and disc only). This extends our previous measurement of the total GSMF down to 10^6.75 M_sol h^-2_70 and we find a total stellar mass density of rho_*=(2.97+/-0.04)x10^8 M_sol h_70 Mpc^-3 or Omega_*=(2.17+/-0.03)x10^-3 h^-1_70. We conclude that at z<0.1, the Universe has converted 4.9+/-0.1 per cent of the baryonic mass implied by Big Bang Nucleosynthesis into stars that are gravitationally bound within the galaxy population.

astro-ph.GA↗

arXiv2022

Joint constraints on cosmology and the impact of baryon feedback: combining KiDS-1000 lensing with the thermal Sunyaev-Zeldovich effect from Planck and ACT

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.

astro-ph.CO↗

arXiv2022

COWS: A filament finder for Hessian cosmic web identifiers

The large scale galaxy and matter distribution is often described by means of the cosmic web made up of voids, sheets, filaments and knots. Many different recipes exist for identifying this cosmic web. Here we focus on a sub-class of cosmic web identifiers, based on the analysis of the Hessian matrix, and proposed a method, called COsmic Web Skeleton (COWS), of separating a set of filaments cells into an ensemble of individual discreet filaments. Specifically, a thinning algorithm is applied to velocity shear tensor based cosmic web (V-web) to identify the spine of the filaments. This results in a set of filaments with well defined end-point and length. It is confirmed that these sit at local density ridges and align with the appropriate direction defined by the underlying velocity field. The radial density profile of these curved cylindrical filaments, as well as the distribution of their lengths is also examined. The robustness of all results is checked against resolution and the V-web threshold. The code for the COWS method has been made publicly available.

astro-ph.CO↗

arXiv2021

Galaxy And Mass Assembly (GAMA): $\mathbf{z \sim 0}$ Galaxy Luminosity Function down to $\mathbf{L \sim 10^{6}~L_\odot}$ via Clustering Based Redshift Inference

In this study we present a new experimental design using clustering-based redshift inference to measure the evolving galaxy luminosity function (GLF) spanning 5.5 decades from $L \sim 10^{11.5}$ to $ 10^6 ~ \mathrm{L}_\odot$. We use data from the Galaxy And Mass Assembly (GAMA) survey and the Kilo-Degree Survey (KiDS). We derive redshift distributions in bins of apparent magnitude to the limits of the GAMA-KiDS photometric catalogue: $m_r \lesssim 23$; more than a decade in luminosity beyond the limits of the GAMA spectroscopic redshift sample via clustering-based redshift inference. This technique uses spatial cross-correlation statistics for a reference set with known redshifts (in our case, the main GAMA sample) to derive the redshift distribution for the target ensemble. For the calibration of the redshift distribution we use a simple parametrisation with an adaptive normalisation factor over the interval $0.005 < z < 0.48$ to derive the clustering redshift results. We find that the GLF has a relatively constant power-law slope $α\approx -1.2$ for $-17 \lesssim M_r \lesssim -13$, and then appears to steepen sharply for $-13 \lesssim M_r \lesssim -10$. This upturn appears to be where Globular Clusters (GCs) take over to dominate the source counts as a function of luminosity. Thus we have mapped the GLF across the full range of the $z \sim 0$ field galaxy population from the most luminous galaxies down to the GC scale.

astro-ph.GA↗

arXiv2021

Geometry vs growth: Internal consistency of the flat ΛCDM model with KiDS-1000

We carry out a multi-probe self-consistency test of the flat $Λ$CDM model with the aim of exploring potential causes of the reported tensions between high- and low-redshift cosmological observations. We divide the model into two theory regimes determined by the smooth background (geometry) and the evolution of matter density fluctuations (growth), each governed by an independent set of Lambda Cold Dark Matter ($Λ$CDM) cosmological parameters. This extended model is constrained by a combination of weak gravitational lensing measurements from the Kilo-Degree Survey, galaxy clustering signatures extracted from Sloan Digital Sky Survey campaigns and the Six-Degree Field Galaxy Survey, and the angular baryon acoustic scale and the primordial scalar fluctuation power spectrum measured in $\textit{Planck}$ cosmic microwave background (CMB) data. We find strong consistency between the geometry and growth parameters, and with the posterior of standard $Λ$CDM analysis. Tension in the amplitude of matter density fluctuations as measured by the parameter $S_8$ persists at around 3$σ$, with a $1.5\,\%$ constraint of $S_8 = 0.776_{-0.008}^{+0.016}$ for the combined probes. We also observe a less significant preference (at least $2σ$) for higher values of the Hubble constant, $H_0 = 70.5^{+0.7}_{-1.5}\,{\rm km\, s^{-1} Mpc^{-1}}$, as well as for lower values of the total matter density parameter $Ω_{\rm{m}} = 0.289^{+0.007}_{-0.005}$ compared to the full $\textit{Planck}$ analysis. Including the subset of the CMB information in the probe combination enhances these differences rather than alleviate them, which we link to the discrepancy between low and high multipoles in $\textit{Planck}$ data.

astro-ph.CO↗