arXiv subjects

Alexandra Amon

Publications and source records attributed to Alexandra Amon.

At least 19 recordsLinked to original sources

arXiv2026

Evidence for a thermal pressure deficit in galaxy groups from the tSZ effect and weak lensing

Measurements of the thermal Sunyaev-Zel'dovich (tSZ) effect have yet to form a consistent picture of the thermodynamic state of the gas in the intracluster medium: their interpretation is complicated by foreground contamination and uncertain halo masses. We present new measurements of the tSZ effect around the Dark Energy Spectroscopic Instrument (DESI) Luminous Red Galaxy (LRG) sample, together with galaxy-galaxy lensing (GGL) measurements that enable a like-with-like comparison to state-of-the-art hydrodynamical simulations. We robustly isolate the tSZ signal by directly modeling the dust and radio emission of the target galaxies using the Atacama Cosmology Telescope (ACT) single-channel temperature maps, substantially reducing uncertainties from astrophysical foregrounds. Across halo masses $M_{500}=10^{13}-10^{14}~M_\odot$ and redshifts $0.4<z<1$, we find that the fiducial 1 Gpc$^3$ FLAMINGO simulation significantly overpredicts the observed tSZ signal at $\lesssim3'$ (i.e., $\lesssim 4\,R_{500}$ at $z=0.7$). Even the simulation with the strongest gas expulsion---which successfully reproduces the gas density inferred from kinetic SZ measurements of the same galaxy sample---overpredicts the thermal pressure. Because the strongest feedback model already reproduces the observed gas density, the remaining discrepancy is difficult to explain with additional gas depletion alone. Instead, current hydrodynamical simulations appear to overpredict the thermal pressure of galaxy groups by a factor of two, pointing toward missing non-thermal pressure support or significant departures from hydrostatic equilibrium.

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arXiv2026

Brightest Cluster Galaxy ellipticity as proxy for halo shape: Orientation bias, assembly bias, and potential selection effects in SZ-selected clusters

The orientation of triaxial galaxy clusters with respect to the line-of-sight is expected to be one of the prime sources of scatter and potential bias in optical observables (e.g., richness and weak-lensing signal) of galaxy clusters. In this work, we use the observed shape of the central Brightest Cluster Galaxy (BCG) as proxy for the orientation along the line-of-sight for clusters selected via the Sunyaev-Zel'dovich (SZ) effect from the South Pole Telescope (SPT) and Atacama Cosmology Telescope (ACT) surveys, matched to optically selected clusters from the Dark Energy Survey Year 3 (DES). We construct two samples of clusters that are designed to be identical in SZ mass estimate and redshift but with the roundest vs. the most elliptical BCGs, which we expect to correspond to BCGs (and clusters) with major axes aligned along the line-of-sight vs. in the plane of the sky, respectively. We find that the optical richness of round-BCG clusters is $\sim 10$\% larger than that of elliptical-BCG clusters, in agreement with the expectation from projection effects and presenting the first such detection in data. The density profiles, however, are not in agreement with the expectation from projection effects: the 1-halo term (below $6~h^{-1}\rm{Mpc}$) of both the weak-lensing and galaxy density profiles are the same for the subsamples, contrary to previous studies based on X-ray selected clusters. In the 2-halo regime (above $6~h^{-1}\rm{Mpc}$), we find a significant excess of the elliptical-BCG cluster profiles compared to the round-BCG cluster profiles, which is the opposite of the expectation from numerical simulations. We hypothesize that the intrinsic shape of the BCG reflects not just the orientation angle, but also intrinsic properties of the cluster which can affect both the SZ signal and the amplitude of the 2-halo term.

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arXiv2025

Confronting cosmic shear astrophysical uncertainties: DES Year 3 revisited

Cosmology from weak gravitational lensing has been limited by astrophysical uncertainties in baryonic feedback and intrinsic alignments. By calibrating these effects using external data, we recover non-linear information, achieving a 2% constraint on the clustering amplitude, $S_8$, resulting in a factor of two improvement on the $\Lambda$CDM constraints relative to the fiducial Dark Energy Survey Year 3 model. The posterior, $S_8=0.832^{+0.013}_{-0.017}$, shifts by $1.5\sigma$ to higher values, in closer agreement with the cosmic microwave background result for the standard six-parameter $\Lambda$CDM cosmology. Our approach uses a star-forming 'blue' galaxy sample with intrinsic alignment model parameters calibrated by direct spectroscopic measurements, together with a baryonic feedback model informed by observations of X-ray gas fractions and kinematic Sunyaev-Zel'dovich effect profiles that span a wide range in halo mass and redshift. Our results provide a blueprint for next-generation surveys: leveraging galaxy properties to control intrinsic alignments and external gas probes to calibrate feedback, unlocking a substantial improvement in the precision of weak lensing surveys.

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arXiv2025

The suppression of the matter power spectrum: strong feedback from X-ray gas mass fractions, kSZ effect profiles, and galaxy-galaxy lensing

Baryon feedback redistributes gas relative to the underlying dark matter distribution and suppresses the matter power spectrum on small scales, but the amplitude and scale dependence of this effect are uncertain. We constrain the impact of baryon feedback on the matter power spectrum by jointly analysing X-ray gas mass fractions from the eROSITA and HSC-XXL samples and SDSS/DESI+ACT kinetic Sunyaev-Zel'dovich (kSZ) effect profiles; the samples are characterised with galaxy-galaxy lensing and together span group and cluster masses at $0<z<1$. Using the baryonification framework, our joint eROSITA and kSZ model gives precise constraints on the suppression of the matter power spectrum: $10 \pm 2\%$ at $k=1~h~\mathrm{Mpc}^{-1}$. The inferred gas profiles are more extended and the power suppression is stronger than predicted by the fiducial models of recent hydrodynamical simulation suites, including FLAMINGO and BAHAMAS. The HSC-XXL gas mass fractions, which the fiducial simulations were calibrated to reproduce, prefer more moderate power suppression than the kSZ and eROSITA data: $5 \pm 4\%$ at $k=1~h~\mathrm{Mpc}^{-1}$. With a simulated LSST Year 1 weak lensing analysis, we demonstrate a framework for next-generation surveys: calibrating feedback models with multi-wavelength gas observables to recover the small-scale statistical power of cosmic shear.

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arXiv2025

The kinetic Sunyaev Zeldovich effect as a benchmark for AGN feedback models in hydrodynamical simulations: insights from DESI + ACT

Baryonic feedback remains one of the largest uncertainties in cosmological hydrodynamical simulations, with different prescriptions producing divergent predictions for the fraction of gas expelled from halos, the radial extent of the gas expulsion and the impact on large scale matter clustering. We present the first systematic study of the kinetic Sunyaev-Zel'dovich (kSZ) effect across a wide range of simulations (FLAMINGO, ANTILLES, BAHAMAS, SIMBA, FABLE and their variants), and compare them directly to DESI Year 1 + ACT kSZ measurements. We ensure a like-for-like comparison with observations by developing a robust methodology that accounts for the halo mass selection using galaxy-galaxy lensing, cosmic variance, miscentering and satellites, establishing the kSZ effect as a new benchmark for the simulations. We find that fiducial feedback models are disfavoured by >3 sigma, while simulations with more powerful AGN feedback within the FLAMINGO and BAHAMAS suites, as well as SIMBA, reproduce the observed kSZ signal within <2 sigma. We use the ANTILLES simulation suite to demonstrate that the amplitude of the kSZ effect is a strong predictor of matter power spectrum suppression, competitive with baryon fraction metrics. These results establish the kSZ as a critical probe for evaluating feedback physics and for advancing the fidelity of cosmological simulations.

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arXiv2025

Dwarf galaxy halo masses from spectroscopic and photometric lensing in DESI and DES

We present the most precise and lowest-mass weak lensing measurements of dwarf galaxies to date, enabled by spectroscopic lenses from the Dark Energy Spectroscopic Instrument (DESI) and photometric lenses from the Dark Energy Survey (DES) calibrated with DESI redshifts. Using DESI spectroscopy from the first data release, we construct clean samples of galaxies with median stellar masses $\log_{10}(M_*/M_{\odot})=8.3-10.1$ and measure their weak lensing signals with sources from DES, KiDS, and SDSS, achieving detections with $S/N$ up to 14 for dwarf galaxies ($\log_{10}(M_*/M_{\odot})<$9.25) -- opening up a new regime for lensing measurements of low-mass systems. Leveraging DES photometry calibrated with DESI, we extend to a photometric dwarf sample of over 700,000 galaxies, enabling robust lensing detections of dwarf galaxies with combined $S/N=38$ and a significant measurement down to $\log_{10}(M_*/M_{\odot})=8.0$. We show that the one-halo regime (scales $\lesssim 0.15h^{-1}\rm Mpc$) is insensitive to various systematic and sample selection effects, providing robust halo mass estimates, while the signal in the two-halo regime depends on galaxy color and environment. These results demonstrate that DESI already enables precise dwarf lensing measurements, and that calibrated photometric samples extend this capability. Together, they pave the way for novel constraints on dwarf galaxy formation and dark matter physics with upcoming surveys like the Vera C. Rubin Observatory's LSST.

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arXiv2025

Joint X-ray, kinetic Sunyaev-Zeldovich, and weak lensing measurements: toward a consensus picture of efficient gas expulsion from groups and clusters

There is no consensus on how baryon feedback shapes the underlying matter distribution from either simulations or observations. We confront the uncertain landscape by jointly analyzing new measurements of the gas distribution around groups and clusters -- DESI+ACT kinetic Sunyaev-Zel'dovich (kSZ) effect profiles and eROSITA X-ray gas masses -- with mean halo masses characterized by galaxy-galaxy lensing. Across a wide range of halo masses ($M_{500}=10^{13-14}M_\odot$) and redshifts ($0 8 \sigma$ discrepant. The FLAMINGO simulation variant with the most gas expulsion, and therefore the most suppression of the matter power spectrum relative to a dark matter only simulation, provides a good description of how much gas is expelled and how far it extends; the enhanced gas depletion is achieved by more powerful but less frequent AGN outbursts. Joint kSZ, X-ray, and lensing measurements form a consistent picture of gas expulsion beyond several $R_{500}$, implying a more suppressed matter power spectrum than predicted by most recent simulations. Complementary observables and next-generation simulations are critical to understanding the physical mechanism behind this extreme gas expulsion and mapping its impact on the large-scale matter distribution.

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arXiv2025

Dimensional reduction for sampled priors and application to photometric redshift distributions

A typical Bayesian inference on the values of some parameters of interest $\bf q$ from some data $D$ involves running a Markov Chain (MC) to sample from the posterior $p({\bf q},{\bf n} | D) \propto \mathcal{L}(D | {\bf q},{\bf n}) p({\bf q}) p({\bf n}),$ where $\bf n$ are some nuisance parameters with separable prior. In some cases, the nuisance parameters are high-dimensional, and their prior $p({\bf n})$ is itself defined only by a set of samples that have been drawn from some other MC. The MC for the posterior will typically require evaluation of $p({\bf n})$ at arbitrary values of ${\bf n},$ i.e.\ one needs to provide a density estimator over the full $\bf n$ space from the provided samples. But the high dimensionality of $\bf n$ hinders both the density estimation and the efficiency of the MC for the posterior. We describe a solution to this problem: a linear compression of the $\bf n$ space into a much lower-dimensional space $\bf u$ which projects away directions in $\bf n$ space that cannot appreciably alter $\mathcal{L}.$ The algorithm for doing so is a slight modification to principal components analysis, and is less restrictive on $p(\bf n)$ than other proposed solutions to this issue. We demonstrate this ``mode projection'' technique using the analysis of 2-point correlation functions of weak lensing fields and galaxy density in the \textit{Dark Energy Survey}, where $\bf n$ is a binned representation of the redshift distribution $n(z)$ of the galaxies.

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arXiv2025

Disentangling the Halo: Joint Model for Measurements of the Kinetic Sunyaev-Zeldovich Effect and Galaxy-Galaxy Lensing

We present the first joint analysis of the kinetic Sunyaev-Zeldovich (kSZ) effect with galaxy-galaxy lensing (GGL) for CMASS galaxies in the Baryon Oscillation Spectroscopic Survey (BOSS). We show these complementary probes can disentangle baryons from dark matter in the outskirts of galactic halos by alleviating model degeneracies that are present when fitting to kSZ or GGL measurements alone. In our joint kSZ+GGL analysis we show that the baryon density profile is well constrained on scales from 0.3 to 50 Mpc/$h$. With our well constrained profile of the baryon density, we provide direct comparisons to simulations. For our model we find an outer slope of the baryon distribution that is shallower than predicted by some hydrodynamical simulations, consistent with enhanced baryonic feedback. We also show that not including baryons in a model for GGL can bias halo mass estimates low by $\sim 20\%$ compared to a model that includes baryons and is jointly fit to kSZ+GGL measurements. Our modelling code galaxy-galaxy lensing and kSZ (\texttt{glasz}) is publicly available at https://github.com/James11222/glasz.

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arXiv2025

Prospects for disentangling dark matter with weak lensing

We investigate the degeneracy between the effects of ultra-light axion dark matter and baryonic feedback in suppressing the matter power spectrum. We forecast that galaxy shear data from the Rubin Observatory's Legacy Survey of Space and Time (LSST) could limit an axion of mass $m = 10^{-25}\,\mathrm{eV}$ to be $\lesssim 5\%$ of the dark matter, stronger than any current bound, if the interplay between axions and feedback is accurately modelled. Using a halo model emulator to construct power spectra for mixed cold and axion dark matter cosmologies, including baryonic effects, we find that galaxy shear is sensitive to axions from $10^{-27}\,\mathrm{eV}$ to $10^{-21}\,\mathrm{eV}$, with the capacity to set competitive bounds across much of this range. For axions with $m \sim 10^{-25}\,\mathrm{eV}$, the scales at which axions and feedback impact structure formation are similar, introducing a parameter degeneracy. We find that, with an external feedback constraint, we can break the degeneracy and constrain the axion transfer function, such that LSST could detect a $10^{-25}\,\mathrm{eV}$ axion comprising 10\% of the dark matter at $\sim 3 \sigma$ significance. Direct reconstruction of the non-linear matter power spectrum provides an alternative way of analysing weak lensing surveys, with the advantage of identifying the scale-dependent features in the data that the dark matter model imposes. We advocate for dedicated cosmological hydrodynamical simulations with an axion dark matter component so that upcoming galaxy and cosmic microwave background lensing surveys can disentangle the dark matter-baryon transfer function.

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arXiv2025

The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics

The standard model of cosmology has provided a good phenomenological description of a wide range of observations both at astrophysical and cosmological scales for several decades. This concordance model is constructed by a universal cosmological constant and supported by a matter sector described by the standard model of particle physics and a cold dark matter contribution, as well as very early-time inflationary physics, and underpinned by gravitation through general relativity. There have always been open questions about the soundness of the foundations of the standard model. However, recent years have shown that there may also be questions from the observational sector with the emergence of differences between certain cosmological probes. In this White Paper, we identify the key objectives that need to be addressed over the coming decade together with the core science projects that aim to meet these challenges. These discordances primarily rest on the divergence in the measurement of core cosmological parameters with varying levels of statistical confidence. These possible statistical tensions may be partially accounted for by systematics in various measurements or cosmological probes but there is also a growing indication of potential new physics beyond the standard model. After reviewing the principal probes used in the measurement of cosmological parameters, as well as potential systematics, we discuss the most promising array of potential new physics that may be observable in upcoming surveys. We also discuss the growing set of novel data analysis approaches that go beyond traditional methods to test physical models. [Abridged]

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arXiv2025

The case for large-scale AGN feedback in galaxy formation simulations: insights from XFABLE

While cosmological simulations of galaxy formation have reached maturity, able to reproduce many fundamental galaxy and halo properties, no consensus has yet been reached on the impact of `baryonic feedback' on the non-linear matter power spectrum. This severely limits the precision of (and potentially biases) small-scale cosmological constraints obtained from weak lensing and galaxy surveys. Recent observational evidence indicates that `baryonic feedback' may be more extreme than commonly assumed in current cosmological hydrodynamical simulations. In this paper, we therefore explore a range of empirical AGN feedback models, within the FABLE simulation suite, with different parameterizations as a function of cosmic time, host halo properties, and/or spatial location where feedback energy is thermalized. We demonstrate that an AGN radio-mode feedback acting in a larger population of black holes, with jets thermalizing at relatively large cluster-centric distances, as exemplified by our XFABLE model, is in good agreement with the latest weak lensing + kSZ constraints across all k-scales. Furthermore, XFABLE maintains good agreement with the galaxy stellar mass function, gas fraction measurements, and all key galaxy group and cluster properties, including scaling relations and ICM radial profiles. Our work highlights the pressing need to model black hole accretion and feedback physics with a greater level of realism, including relativistic, magnetized jets in full cosmological simulations. Finally, we discuss how a range of complementary observational probes in the near future will enable us to constrain AGN feedback models, and therefore reduce `baryonic feedback' modelling uncertainty for the upcoming era of large cosmological surveys.

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arXiv2024

FLAMINGO: combining kinetic SZ effect and galaxy-galaxy lensing measurements to gauge the impact of feedback on large-scale structure

Energetic feedback processes associated with accreting supermassive black holes can expel gas from massive haloes and significantly alter various measures of clustering on ~Mpc scales, potentially biasing the values of cosmological parameters inferred from analyses of large-scale structure (LSS) if not modelled accurately. Here we use the state-of-the-art FLAMINGO suite of cosmological hydrodynamical simulations to gauge the impact of feedback on large-scale structure by comparing to Planck + ACT stacking measurements of the kinetic Sunyaev-Zel'dovich (kSZ) effect of SDSS BOSS galaxies. We make careful like-with-like comparisons to the observations, aided by high precision KiDS and DES galaxy-galaxy lensing measurements of the BOSS galaxies to inform the selection of the simulated galaxies. In qualitative agreement with several recent studies using dark matter only simulations corrected for baryonic effects, we find that the kSZ effect measurements prefer stronger feedback than predicted by simulations which have been calibrated to reproduce the gas fractions of low redshift X-ray-selected groups and clusters. We find that the increased feedback can help to reduce the so-called S8 tension between the observed and CMB-predicted clustering on small scales as probed by cosmic shear (although at the expense of agreement with the X-ray group measurements). However, the increased feedback is only marginally effective at reducing the reported offsets between the predicted and observed clustering as probed by the thermal SZ (tSZ) effect power spectrum and tSZ effect--weak lensing cross-spectrum, both of which are sensitive to higher halo masses than cosmic shear.

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arXiv2024

Reconstructing the matter power spectrum with future cosmic shear surveys

Analyses of cosmic shear typically condense weak lensing information over a range of scales to a single cosmological parameter, $S_8$. This paper presents a method to extract more information from Stage-IV cosmic shear measurements by directly reconstructing the matter power spectrum from linear to non-linear scales. We demonstrate that cosmic shear surveys will be sensitive to the shape of the matter power spectrum on non-linear scales. We show that it should be possible to distinguish between different models of baryonic feedback and we investigate the impact of intrinsic alignments and observational systematics on forecasted constraints. In addition to providing important information on galaxy formation, power spectrum reconstruction should provide a definitive answer to the question of whether weak lensing measurements of $S_8$ on linear scales are consistent with the $\textit{Planck}$ $\Lambda$CDM cosmology. In addition, power spectrum reconstruction may lead to new discoveries on the composition of the dark sector.

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arXiv2023

The mass profiles of dwarf galaxies from Dark Energy Survey lensing

We present a novel approach to extracting dwarf galaxies from photometric data to measure their average halo mass profile with weak lensing. We characterise their stellar mass and redshift distributions with a spectroscopic calibration sample. Using the ${\sim}5000\mathrm{deg}^2$ multi-band photometry from Dark Energy Survey and redshifts from the Satellites Around Galactic Analogs (SAGA) survey with an unsupervised machine learning method, we select a low-mass galaxy sample spanning redshifts $z{<}0.3$ and divide it into three mass bins. From low to high median mass, the bins contain [146 420, 330 146, 275 028] galaxies and have median stellar masses of $\log_{10}(M_*/M_{\odot})= [8.52^{+0.57}_{-0.76}, 9.02^{+0.50}_ {-0.64}, 9.49^{+0.50}_{-0.58}]$. We measure the stacked excess surface mass density profiles, $\Delta\Sigma(R)$, of these galaxies using galaxy--galaxy lensing with a signal-to-noise of [14, 23, 28]. Through a simulation-based forward-modelling approach, we fit the measurements to constrain the stellar-to-halo mass relation and find the median halo mass of these samples to be $\log_{10}(M_{\rm halo}/M_{\odot})$ = [$10.67\substack{+0.2\\-0.4}$, $11.01\substack{+0.14 \\ -0.27}$,$11.40\substack{+0.08\\-0.15}$]. The CDM profiles are consistent with NFW profiles over scales ${\lesssim}0.15 \rm{h}^{-1}$Mpc. We find that ${\sim}20$ per cent of the dwarf galaxy sample are satellites. This is the first measurement of the halo profiles and masses of such a comprehensive, low-mass galaxy sample. The techniques presented here pave the way for extracting and analysing even lower-mass dwarf galaxies and for more finely splitting galaxies by their properties with future photometric and spectroscopic survey data.

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arXiv2023

A non-linear solution to the $S_8$ tension II: Analysis of DES Year 3 cosmic shear

Weak galaxy lensing surveys have consistently reported low values of the $S_8$ parameter compared to the $\textit{Planck}\ \Lambda\rm{CDM}$ cosmology. Amon & Efstathiou (2022) used KiDS-1000 cosmic shear measurements to propose that this tension can be reconciled if the matter fluctuation spectrum is suppressed more strongly on non-linear scales than assumed in state-of-the-art hydrodynamical simulations. In this paper, we investigate cosmic shear data from the Dark Energy Survey (DES) Year 3. The non-linear suppression of the matter power spectrum required to resolve the $S_8$ tension between DES and the $\textit{Planck}\ \Lambda\rm{CDM}$ model is not as strong as inferred using KiDS data, but is still more extreme than predictions from recent numerical simulations. An alternative possibility is that non-standard dark matter contributes to the required suppression. We investigate the redshift and scale dependence of the suppression of the matter power spectrum. If our proposed explanation of the $S_8$ tension is correct, the required suppression must extend into the mildly non-linear regime to wavenumbers $k\sim 0.2 h {\rm Mpc}^{-1}$. In addition, all measures of $S_8$ using linear scales should agree with the $\textit{Planck}\ \Lambda\rm{CDM}$ cosmology, an expectation that will be testable to high precision in the near future.

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arXiv2022

A non-linear solution to the $S_8$ tension?

Weak galaxy lensing surveys have consistently reported a lower amplitude for the matter fluctuation spectrum, as measured by the $S_8$ parameter, than expected in the $\Lambda{\rm CDM}$ cosmology favoured by $Planck$. However, the expansion history follows the predictions of the $Planck$ $\Lambda{\rm CDM}$ cosmology to high accuracy, as do measurements of lensing of the cosmic microwave background anisotropies. Redshift space distortion measurements also appear to be consistent with $Planck$ $\Lambda{\rm CDM}$. In this paper, we argue that these observations can be reconciled with the $Planck$ $\Lambda{\rm CDM}$ cosmology if the matter power spectrum is suppressed more strongly on non-linear scales than assumed in analyses of weak galaxy lensing. We demonstrate this point by fitting a one-parameter model, characterising a suppression of the non-linear power spectrum, to the KiDS-1000 weak lensing measurements. Such a suppression could be attributed to new properties of the dark matter that affect non-linear scales, or to a response of the matter fluctuations to baryonic feedback processes that are stronger than expected from recent cosmological simulations. Our proposed explanation can be tested using measurements of the amplitude of the matter fluctuation spectrum on linear scales, in particular via high precision redshift space distortion measurements from forthcoming galaxy and quasar redshift surveys.

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arXiv2022

Minkowski Functionals in Joint Galaxy Clustering & Weak Lensing Analyses

We investigate the inclusion of clustering maps in a weak lensing Minkowski functional (MF) analysis of DES-like and LSST-like simulations to constrain cosmological parameters. The standard 3x2pt approach to lensing and clustering data uses two-point correlations as its primary statistic; MFs, morphological statistics describing the shape of matter fields, provide additional information for non-Gaussian fields. Previous analyses have studied MFs of lensing convergence maps; in this project we explore their simultaneous application to clustering maps. We employ a simplified linear galaxy bias model, and using a lognormal curved sky measurement and Monte Carlo Markov Chain (MCMC) sampling process for parameter inference, we find that MFs do not yield any information in the $\Omega_{\rm m}$ -- $\sigma_8$ plane not already generated by a 3x2pt analysis. However, we expect that MFs should improve constraining power when nonlinear baryonic and other small-scale effects are taken into account. As with a 3x2pt analysis, we find a significant improvement to constraints when adding clustering data to MF-only and MF$+C_\ell$ shear measurements, and strongly recommend future higher order statistics be measured from both convergence and clustering maps.

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