arXiv subjects

Benjamin Joachimi

Publications and source records attributed to Benjamin Joachimi.

At least 73 records · Page 4Linked to original sources

arXiv2021

Organised Randoms: Learning and correcting for systematic galaxy clustering patterns in KiDS using self-organising maps

We present a new method for the mitigation of observational systematic effects in angular galaxy clustering via corrective random galaxy catalogues. Real and synthetic galaxy data, from the Kilo Degree Survey's (KiDS) 4$^{\rm{th}}$ Data Release (KiDS-$1000$) and the Full-sky Lognormal Astro-fields Simulation Kit (FLASK) package respectively, are used to train self-organising maps (SOMs) to learn the multivariate relationships between observed galaxy number density and up to six systematic-tracer variables, including seeing, Galactic dust extinction, and Galactic stellar density. We then create `organised' randoms, i.e. random galaxy catalogues with spatially variable number densities, mimicking the learnt systematic density modes in the data. Using realistically biased mock data, we show that these organised randoms consistently subtract spurious density modes from the two-point angular correlation function $w(\vartheta)$, correcting biases of up to $12σ$ in the mean clustering amplitude to as low as $0.1σ$, over a high signal-to-noise angular range of 7-100 arcmin. Their performance is also validated for angular clustering cross-correlations in a bright, flux-limited subset of KiDS-$1000$, comparing against an analogous sample constructed from highly-complete spectroscopic redshift data. Each organised random catalogue object is a `clone' carrying the properties of a real galaxy, and is distributed throughout the survey footprint according to the parent galaxy's position in systematics-space. Thus, sub-sample randoms are readily derived from a single master random catalogue via the same selection as applied to the real galaxies. Our method is expected to improve in performance with increased survey area, galaxy number density, and systematic contamination, making organised randoms extremely promising for current and future clustering analyses of faint samples.

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arXiv2021

The PAU Survey: narrowband photometric redshifts using Gaussian processes

We study the performance of the hybrid template-machine-learning photometric redshift (photo-$z$) algorithm Delight, which uses Gaussian processes, on a subset of the early data release of the Physics of the Accelerating Universe Survey (PAUS). We calibrate the fluxes of the $40$ PAUS narrow bands with $6$ broadband fluxes ($uBVriz$) in the COSMOS field using three different methods, including a new method which utilises the correlation between the apparent size and overall flux of the galaxy. We use a rich set of empirically derived galaxy spectral templates as guides to train the Gaussian process, and we show that our results are competitive with other standard photometric redshift algorithms. Delight achieves a photo-$z$ $68$th percentile error of $σ_{68}=0.0081(1+z)$ without any quality cut for galaxies with $i_\mathrm{auto}<22.5$ as compared to $0.0089(1+z)$ and $0.0202(1+z)$ for the BPz and ANNz2 codes, respectively. Delight is also shown to produce more accurate probability distribution functions for individual redshift estimates than BPz and ANNz2. Common photo-$z$ outliers of Delight and BCNz2 (previously applied to PAUS) are found to be primarily caused by outliers in the narrowband fluxes, with a small number of cases potentially indicating spectroscopic redshift failures in the reference sample. In the process, we introduce performance metrics derived from the results of BCNz2 and Delight, allowing us to achieve a photo-$z$ quality of $σ_{68}<0.0035(1+z)$ at a magnitude of $i_\mathrm{auto}<22.5$ while keeping $50$ per cent objects of the galaxy sample.

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arXiv2021

KiDS-1000 Cosmology: constraints beyond flat $Λ$CDM

We present constraints on extensions to the flat $Λ$CDM cosmological model by varying the spatial curvature $Ω_K$, the sum of the neutrino masses $\sum m_ν$, the dark energy equation of state parameter $w$, and the Hu-Sawicki $f(R)$ gravity $f_{R0}$ parameter. With the combined $3\times2$pt measurements of cosmic shear from the Kilo-Degree Survey (KiDS-1000), galaxy clustering from the Baryon Oscillation Spectroscopic Survey (BOSS), and galaxy-galaxy lensing from the overlap between KiDS-1000, BOSS, and the spectroscopic 2-degree Field Lensing Survey (2dFLenS), we find results that are fully consistent with a flat $Λ$CDM model with $Ω_K=0.011^{+0.054}_{-0.057}$, $\sum m_ν<1.76$ eV (95% CL), and $w=-0.99^{+0.11}_{-0.13}$. The $f_{R0}$ parameter is unconstrained in our fully non-linear $f(R)$ cosmic shear analysis. Considering three different model selection criteria, we find no clear preference for either the fiducial flat $Λ$CDM model or any of the considered extensions. Besides extensions to the flat $Λ$CDM parameter space, we also explore restrictions to common subsets of the flat $Λ$CDM parameter space by fixing the amplitude of the primordial power spectrum to the Planck best-fit value, as well as adding external data from supernovae and lensing of the CMB. Neither the beyond-$Λ$CDM models nor the imposed restrictions explored in this analysis are able to resolve the $\sim 3σ$ tension in $S_8$ between the $3\times2$pt constraints and Planck, with the exception of $w$CDM, where the $S_8$ tension is resolved. The tension in the $w$CDM case persists, however, when considering the joint $S_8$-$w$ parameter space. The joint flat $Λ$CDM CMB lensing and $3\times2$pt analysis is found to yield tight constraints on $Ω_{\rm m}=0.307^{+0.008}_{-0.013}$, $σ_8=0.769^{+0.022}_{-0.010}$, and $S_8=0.779^{+0.013}_{-0.013}$.

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arXiv2021

The PAU Survey: Intrinsic alignments and clustering of narrow-band photometric galaxies

We present the first measurements of the projected clustering and intrinsic alignments (IA) of galaxies observed by the Physics of the Accelerating Universe Survey (PAUS). With photometry in 40 narrow optical passbands ($450\rm{nm}-850\rm{nm}$), the quality of photometric redshift estimation is $σ_{z} \sim 0.01(1 + z)$ for galaxies in the $19\,\rm{deg}^{2}$ Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) W3 field, allowing us to measure the projected 3D clustering and IA for flux-limited, faint galaxies ($i < 22.5$) out to $z\sim0.8$. To measure two-point statistics, we developed, and tested with mock photometric redshift samples, `cloned' random galaxy catalogues which can reproduce data selection functions in 3D and account for photometric redshift errors. In our fiducial colour-split analysis, we made robust null detections of IA for blue galaxies and tentative detections of radial alignments for red galaxies ($\sim1-3σ$), over scales of $0.1-18\,h^{-1}\rm{Mpc}$. The galaxy clustering correlation functions in the PAUS samples are comparable to their counterparts in a spectroscopic population from the Galaxy and Mass Assembly survey, modulo the impact of photometric redshift uncertainty which tends to flatten the blue galaxy correlation function, whilst steepening that of red galaxies. We investigate the sensitivity of our correlation function measurements to choices in the random catalogue creation and the galaxy pair-binning along the line of sight, in preparation for an optimised analysis over the full PAUS area.

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arXiv2021

Self-calibration of weak lensing systematic effects using combined two- and three-point statistics

We investigate the prospects for using the weak lensing bispectrum alongside the power spectrum to control systematic uncertainties in a Euclid-like survey. Three systematic effects are considered: the intrinsic alignment of galaxies, uncertainties in the means of tomographic redshift distributions, and multiplicative bias in the measurement of the shear signal. We find that the bispectrum is very effective in mitigating these systematic errors. Varying all three systematics simultaneously, a joint power spectrum and bispectrum analysis reduces the area of credible regions for the cosmological parameters $Ω_\mathrm{m}$ and $σ_8$ by a factor of 90 and for the two parameters of a time-varying dark energy equation of state by a factor of almost 20, compared with the baseline approach of using the power spectrum alone and of imposing priors consistent with the accuracy requirements specified for Euclid. We also demonstrate that including the bispectrum self-calibrates all three systematic effects to the stringent levels required by the forthcoming generation of weak lensing surveys, thereby reducing the need for external calibration data.

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arXiv2021

Group-scale intrinsic galaxy alignments in the Illustris-TNG and MassiveBlack-II simulations

We study the alignments of satellite galaxies, and their anisotropic distribution, with respect to location and orientation of their host central galaxy in MassiveBlack-II and IllustrisTNG simulations. We find that: the shape of the satellite system in halos of mass ($> 10^{13}h^{-1}M_{\odot}$) is well aligned with the shape of the central galaxy at $z=0.06$ with the mean alignment between the major axes being $\sim Δθ= 12^{\circ}$ when compared to a uniform random distribution; that satellite galaxies tend to be anisotropically distributed along the major axis of the central galaxy with a stronger alignment in halos of higher mass or luminosity; and that the satellite distribution is more anisotropic for central galaxies with lower star formation rate, which are spheroidal, and for red central galaxies.Radially we find that satellites tend to be distributed along the major axis of the shape of the stellar component of central galaxies at smaller scales and the dark matter component on larger scales. We find that the dependence of satellite anisotropy on central galaxy properties and the radial distance is similar in both the simulations with a larger amplitude in MassiveBlack-II. The orientation of satellite galaxies tends to point toward the location of the central galaxy at small scales and this correlation decreases with increasing distance, and the amplitude of satellite alignment is higher in high mass halos. However, the projected ellipticities do not exhibit a scale-dependent radial alignment, as has been seen in some observational measurements.

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arXiv2021

KiDS+VIKING-450: An internal-consistency test for cosmic shear tomography with a colour-based split of source galaxies

We performed an internal-consistency test of the KiDS+VIKING-450 (KV450) cosmic shear analysis with a colour-based split of source galaxies. Utilising the same measurements and calibrations for both sub-samples, we inspected the characteristics of the shear measurements and the performance of the calibration pipelines. On the modelling side, we examined the observational nuisance parameters, specifically those for the redshift calibration and intrinsic alignments, using a Bayesian analysis with dedicated test parameters. We verified that the current nuisance parameters are sufficient for the KV450 data to capture residual systematics, with slight deviations seen in the second and the third redshift tomographic bins. Our test also showcases the degeneracy between the inferred amplitude of intrinsic alignments and the redshift uncertainties in low redshift tomographic bins. The test is rather insensitive to the background cosmology and, therefore, can be implemented before any cosmological inference is made.

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arXiv2020

The halo model as a versatile tool to predict intrinsic alignments

Intrinsic alignments (IAs) of galaxies are an important contaminant for cosmic shear studies, but the modelling is complicated by the dependence of the signal on the source galaxy sample. In this paper, we use the halo model formalism to capture this diversity and examine its implications for Stage-III and Stage-IV cosmic shear surveys. We account for the different IA signatures at large and small scales, as well for the different contributions from central/satellite and red/blue galaxies, and we use realistic mocks to account for the characteristics of the galaxy populations as a function of redshift. We inform our model using the most recent observational findings: we include a luminosity dependence at both large and small scales and a radial dependence of the signal within the halo. We predict the impact of the total IA signal on the lensing angular power spectra, including the current uncertainties from the IA best-fits to illustrate the range of possible impact on the lensing signal: the lack of constraints for fainter galaxies is the main source of uncertainty for our predictions of the IA signal. We investigate how well effective models with limited degrees of freedom can account for the complexity of the IA signal. Although these lead to negligible biases for Stage-III surveys, we find that, for Stage-IV surveys, it is essential to at least include an additional parameter to capture the redshift dependence.

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arXiv2020

KiDS-1000 catalogue: Weak gravitational lensing shear measurements

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.

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arXiv2020

KiDS-1000 Cosmology: Multi-probe weak gravitational lensing and spectroscopic galaxy clustering constraints

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.

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arXiv2020

Minimising the impact of scale-dependent galaxy bias on the joint cosmological analysis of large scale structures

We present a mitigation strategy to reduce the impact of non-linear galaxy bias on the joint `$3 \times 2 $pt' cosmological analysis of weak lensing and galaxy surveys. The $Ψ$-statistics that we adopt are based on Complete Orthogonal Sets of E/B Integrals (COSEBIs). As such they are designed to minimise the contributions to the observable from the smallest physical scales where models are highly uncertain. We demonstrate that $Ψ$-statistics carry the same constraining power as the standard two-point galaxy clustering and galaxy-galaxy lensing statistics, but are significantly less sensitive to scale-dependent galaxy bias. Using two galaxy bias models, motivated by halo-model fits to data and simulations, we quantify the error in a standard $3 \times 2$pt analysis where constant galaxy bias is assumed. Even when adopting conservative angular scale cuts, that degrade the overall cosmological parameter constraints, we find of order $1 σ$ biases for Stage III surveys on the cosmological parameter $S_8 = σ_8(Ω_{\rm m}/0.3)^α$. This arises from a leakage of the smallest physical scales to all angular scales in the standard two-point correlation functions. In contrast, when analysing $Ψ$-statistics under the same approximation of constant galaxy bias, we show that the bias on the recovered value for $S_8$ can be decreased by a factor of $\sim 2$, with less conservative scale cuts. Given the challenges in determining accurate galaxy bias models in the highly non-linear regime, we argue that $3 \times 2$pt analyses should move towards new statistics that are less sensitive to the smallest physical scales.

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arXiv2020

Strong detection of the CMB lensingxgalaxy weak lensingcross-correlation from ACT-DR4,PlanckLegacy and KiDS-1000

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.

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arXiv2020

The PAU Survey: An improved photo-$z$ sample in the COSMOS field

We present -- and make publicly available -- accurate and precise photometric redshifts in the ACS footprint from the COSMOS field for objects with $i_{\mathrm{AB}}\leq 23$. The redshifts are computed using a combination of narrow band photometry from PAUS, a survey with 40 narrow bands spaced at $100Å$ intervals covering the range from $4500Å$ to $8500Å$, and 26 broad, intermediate, and narrow bands covering the UV, visible and near infrared spectrum from the COSMOS2015 catalogue. We introduce a new method that models the spectral energy distributions (SEDs) as a linear combination of continuum and emission line templates and computes its Bayes evidence, integrating over the linear combinations. The correlation between the UV luminosity and the OII line is measured using the 66 available bands with the zCOSMOS spectroscopic sample, and used as a prior which constrains the relative flux between continuum and emission line templates. The flux ratios between the OII line and $\mathrm{H}_α$, $\mathrm{H}_β$ and $\mathrm{OIII}$ are similarly measured and used to generate the emission line templates. Comparing to public spectroscopic surveys via the quantity $Δ_z\equiv(z_{\mathrm{photo}}-z_{\mathrm{spec}})/(1+z_{\mathrm{spec}})$, we find the photometric redshifts to be more precise than previous estimates, with $σ_{68}(Δ_z) \approx (0.003, 0.009)$ for galaxies at magnitude $i_{\mathrm{AB}}\sim18$ and $i_{\mathrm{AB}}\sim23$, respectively, which is $3\times$ and $1.66\times$ tighter than COSMOS2015. Additionally, we find the redshifts to be very accurate on average, yielding a median of the $Δ_z$ distribution compatible with $|\mathrm{median}(Δ_z)|\leq0.001$ at all redshifts and magnitudes considered. Both the added PAUS data and new methodology contribute significantly to the improved results.

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arXiv2020

KiDS-1000 Cosmology: Cosmic shear constraints and comparison between two point statistics

We present cosmological constraints from a cosmic shear analysis of the fourth data release of the Kilo-Degree Survey (KiDS-1000), doubling the survey area with nine-band optical and near-infrared photometry with respect to previous KiDS analyses. Adopting a spatially flat $Λ$CDM model, we find $S_8 = σ_8 (Ω_{\rm m}/0.3)^{0.5} = 0.759^{+0.024}_{-0.021}$ for our fiducial analysis, which is in $3σ$ tension with the prediction of the Planck Legacy analysis of the cosmic microwave background. We compare our fiducial COSEBIs (Complete Orthogonal Sets of E/B-Integrals) analysis with complementary analyses of the two-point shear correlation function and band power spectra, finding results to be in excellent agreement. We investigate the sensitivity of all three statistics to a number of measurement, astrophysical, and modelling systematics, finding our $S_8$ constraints to be robust and dominated by statistical errors. Our cosmological analysis of different divisions of the data pass the Bayesian internal consistency tests, with the exception of the second tomographic bin. As this bin encompasses low redshift galaxies, carrying insignificant levels of cosmological information, we find that our results are unchanged by the inclusion or exclusion of this sample.

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arXiv2020

Testing gravity using galaxy-galaxy lensing and clustering amplitudes in KiDS-1000, BOSS and 2dFLenS

The physics of gravity on cosmological scales affects both the rate of assembly of large-scale structure, and the gravitational lensing of background light through this cosmic web. By comparing the amplitude of these different observational signatures, we can construct tests that can distinguish general relativity from its potential modifications. We used the latest weak gravitational lensing dataset from the Kilo-Degree Survey, KiDS-1000, in conjunction with overlapping galaxy spectroscopic redshift surveys BOSS and 2dFLenS, to perform the most precise existing amplitude-ratio test. We measured the associated E_G statistic with 15-20% errors, in five dz = 0.1 tomographic redshift bins in the range 0.2 < z < 0.7, on projected scales up to 100 Mpc/h. The scale-independence and redshift-dependence of these measurements are consistent with the theoretical expectation of general relativity in a Universe with matter density Omega_m = 0.27 +/- 0.04. We demonstrate that our results are robust against different analysis choices, including schemes for correcting the effects of source photometric redshift errors, and compare the performance of angular and projected galaxy-galaxy lensing statistics.

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arXiv2020

Bayesian methods for fitting Baryon Acoustic Oscillations in the Lyman-$α$ forest

We study and compare fitting methods for the Lyman-$α$ (Ly$α$) forest 3D correlation function. We use the nested sampler PolyChord and the community code picca to perform a Bayesian analysis which we compare with previous frequentist analyses. By studying synthetic correlation functions, we find that the frequentist profile likelihood produces results in good agreement with a full Bayesian analysis. On the other hand, Maximum Likelihood Estimation with the Gaussian approximation for the uncertainties is inadequate for current data sets. We compute for the first time the full posterior distribution from the Ly$α$ forest correlation functions measured by the extended Baryon Oscillation Spectroscopic Survey (eBOSS). We highlight the benefits of sampling the full posterior distribution by expanding the baseline analysis to better understand the contamination by Damped Ly$α$ systems (DLAs). We make our improvements and results publicly available as part of the picca package.

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arXiv2020

KiDS+VIKING-450: Improved cosmological parameter constraints from redshift calibration with self-organising maps

We present updated cosmological constraints for the KiDS+VIKING-450 cosmic shear data set (KV450), estimated using redshift distributions and photometric samples defined using self-organising maps (SOMs). Our fiducial analysis finds marginal posterior constraints of $S_8\equivσ_8\sqrt{Ω_{\rm m}/0.3}=0.716^{+0.043}_{-0.038}$; smaller than, but otherwise consistent with, previous work using this data set ($|ΔS_8| = 0.023$). We analyse additional samples and redshift distributions constructed in three ways: excluding certain spectroscopic surveys during redshift calibration, excluding lower-confidence spectroscopic redshifts in redshift calibration, and considering only photometric sources which are jointly calibrated by at least three spectroscopic surveys. In all cases, the method utilised here proves robust: we find a maximal deviation from our fiducial analysis of $|ΔS_8| \leq 0.011$ for all samples defined and analysed using our SOM. To demonstrate the reduction in systematic biases found within our analysis, we highlight our results when performing redshift calibration without the DEEP2 spectroscopic data set. In this case we find marginal posterior constraints of $S_8=0.707_{-0.042}^{+0.046}$; a difference with respect to the fiducial that is both significantly smaller than, and in the opposite direction to, the equivalent shift from previous work. These results suggest that our improved cosmological parameter estimates are insensitive to pathological misrepresentation of photometric sources by the spectroscopy used for direct redshift calibration, and therefore that this systematic effect cannot be responsible for the observed difference between $S_8$ estimates made with KV450 and Planck CMB probes.

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arXiv2020

GEOMAX: beyond linear compression for 3pt galaxy clustering statistics

We present the GEOMAX algorithm and its Python implementation for a two-step compression of bispectrum measurements. The first step groups bispectra by the geometric properties of their arguments; the second step then maximises the Fisher information with respect to a chosen set of model parameters in each group. The algorithm only requires the derivatives of the data vector with respect to the parameters and a small number of mock data, producing an effective, non-linear compression. By applying GEOMAX to bispectrum monopole measurements from BOSS DR12 CMASS redshift-space galaxy clustering data, we reduce the $68\%$ credible intervals for the inferred parameters $\left(b_1,b_2,f,σ_8\right)$ by $\left(50.4\%,56.1\%,33.2\%,38.3\%\right)$ with respect to standard MCMC on the full data vector. We run the analysis and comparison between compression methods over one hundred galaxy mocks to test the statistical significance of the improvements. On average GEOMAX performs $\sim15\%$ better than geometrical or maximal linear compression alone and is consistent with being lossless. Given its flexibility, the GEOMAX approach has the potential to optimally exploit three-point statistics of various cosmological probes like weak lensing or line-intensity maps from current and future cosmological data-sets such as DESI, Euclid, PFS and SKA.

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