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G. M. Bernstein

Publications and source records attributed to G. M. Bernstein.

At least 55 records · Page 3Linked to original sources
arXiv2023

Cosmology from Cross-Correlation of ACT-DR4 CMB Lensing and DES-Y3 Cosmic Shear

Cross-correlation between weak lensing of the Cosmic Microwave Background (CMB) and weak lensing of galaxies offers a way to place robust constraints on cosmological and astrophysical parameters with reduced sensitivity to certain systematic effects affecting individual surveys. We measure the angular cross-power spectrum between the Atacama Cosmology Telescope (ACT) DR4 CMB lensing and the galaxy weak lensing measured by the Dark Energy Survey (DES) Y3 data. Our baseline analysis uses the CMB convergence map derived from ACT-DR4 and $\textit{Planck}$ data, where most of the contamination due to the thermal Sunyaev Zel'dovich effect is removed, thus avoiding important systematics in the cross-correlation. In our modelling, we consider the nuisance parameters of the photometric uncertainty, multiplicative shear bias and intrinsic alignment of galaxies. The resulting cross-power spectrum has a signal-to-noise ratio $= 7.1$ and passes a set of null tests. We use it to infer the amplitude of the fluctuations in the matter distribution ($S_8 \equiv σ_8 (Ω_{\rm m}/0.3)^{0.5} = 0.782\pm 0.059$) with informative but well-motivated priors on the nuisance parameters. We also investigate the validity of these priors by significantly relaxing them and checking the consistency of the resulting posteriors, finding them consistent, albeit only with relatively weak constraints. This cross-correlation measurement will improve significantly with the new ACT-DR6 lensing map and form a key component of the joint 6x2pt analysis between DES and ACT.

astro-ph.CO↗
arXiv2023

Beyond the 3rd moment: A practical study of using lensing convergence CDFs for cosmology with DES Y3

Widefield surveys of the sky probe many clustered scalar fields -- such as galaxy counts, lensing potential, gas pressure, etc. -- that are sensitive to different cosmological and astrophysical processes. Our ability to constrain such processes from these fields depends crucially on the statistics chosen to summarize the field. In this work, we explore the cumulative distribution function (CDF) at multiple scales as a summary of the galaxy lensing convergence field. Using a suite of N-body lightcone simulations, we show the CDFs' constraining power is modestly better than that of the 2nd and 3rd moments of the field, as they approximately capture the information from all moments of the field in a concise data vector. We then study the practical aspects of applying the CDFs to observational data, using the first three years of the Dark Energy Survey (DES Y3) data as an example, and compute the impact of different systematics on the CDFs. The contributions from the point spread function are 2-3 orders of magnitude below the cosmological signal, while those from reduced shear approximation contribute $\lesssim 1\%$ to the signal. Source clustering effects and baryon imprints contribute $1-10\%$. Enforcing scale cuts to limit systematics-driven biases in parameter constraints degrades these constraints a noticeable amount, and this degradation is similar for the CDFs and the moments. We also detect correlations between the observed convergence field and the shape noise field at $13σ$. We find that the non-Gaussian correlations in the noise field must be modeled accurately to use the CDFs, or other statistics sensitive to all moments, as a rigorous cosmology tool.

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arXiv2023

A measurement of the mean central optical depth of galaxy clusters via the pairwise kinematic Sunyaev-Zel'dovich effect with SPT-3G and DES

We infer the mean optical depth of a sample of optically-selected galaxy clusters from the Dark Energy Survey (DES) via the pairwise kinematic Sunyaev-Zel'dovich (kSZ) effect. The pairwise kSZ signal between pairs of clusters drawn from the DES Year-3 cluster catalog is detected at $4.1 σ$ in cosmic microwave background (CMB) temperature maps from two years of observations with the SPT-3G camera on the South Pole Telescope. After cuts, there are 24,580 clusters in the $\sim 1,400$ deg$^2$ of the southern sky observed by both experiments. We infer the mean optical depth of the cluster sample with two techniques. The optical depth inferred from the pairwise kSZ signal is $\barτ_e = (2.97 \pm 0.73) \times 10^{-3}$, while that inferred from the thermal SZ signal is $\barτ_e = (2.51 \pm 0.55^{\text{stat}} \pm 0.15^{\rm syst}) \times 10^{-3}$. The two measures agree at $0.6 σ$. We perform a suite of systematic checks to test the robustness of the analysis.

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arXiv2023

Dark Energy Survey Year 3 results: Magnification modeling and impact on cosmological constraints from galaxy clustering and galaxy-galaxy lensing

We study the effect of magnification in the Dark Energy Survey Year 3 analysis of galaxy clustering and galaxy-galaxy lensing, using two different lens samples: a sample of Luminous red galaxies, redMaGiC, and a sample with a redshift-dependent magnitude limit, MagLim. We account for the effect of magnification on both the flux and size selection of galaxies, accounting for systematic effects using the Balrog image simulations. We estimate the impact of magnification on the galaxy clustering and galaxy-galaxy lensing cosmology analysis, finding it to be a significant systematic for the MagLim sample. We show cosmological constraints from the galaxy clustering auto-correlation and galaxy-galaxy lensing signal with different magnifications priors, finding broad consistency in cosmological parameters in $Λ$CDM and $w$CDM. However, when magnification bias amplitude is allowed to be free, we find the two-point correlations functions prefer a different amplitude to the fiducial input derived from the image simulations. We validate the magnification analysis by comparing the cross-clustering between lens bins with the prediction from the baseline analysis, which uses only the auto-correlation of the lens bins, indicating systematics other than magnification may be the cause of the discrepancy. We show adding the cross-clustering between lens redshift bins to the fit significantly improves the constraints on lens magnification parameters and allows uninformative priors to be used on magnification coefficients, without any loss of constraining power or prior volume concerns.

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arXiv2023

The Dark Energy Survey Six-Year Calibration Star Catalog

This Technical Note presents a catalog of calibrated reference stars that was generated by the Forward Calibration Method (FGCM) pipeline (arXiv:1706.01542) as part of the FGCM photometric calibration of the full Dark Energy Survey (DES) 6-Year data set (Y6). This catalog provides DES grizY magnitudes for 17 million stars with i-band magnitudes mostly in the range 16 < i < 21 spread over the full DES footprint covering 5000 square degrees over the Southern Galactic Cap at galactic latitudes b < -20 degrees (plus a few outlying fields disconnected from the main survey footprint). These stars are calibrated to a uniformity of better than 1.8 milli-mag (0.18%) RMS over the survey area. The absolute calibration of the catalog is computed with reference to the STISNIC.007 spectrum of the Hubble Space Telescope CalSpec standard star C26202; including systematic errors, the absolute flux system is known at the approximately 1% level. As such, these stars provide a useful reference catalog for calibrating grizY-band or grizY-like band photometry in the Southern Hemisphere, particularly for observations within the DES footprint.

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arXiv2023

Photometry of outer Solar System objects from the Dark Energy Survey I: photometric methods, light curve distributions and trans-Neptunian binaries

We report the methods of and initial scientific inferences from the extraction of precision photometric information for the $>800$ trans-Neptunian objects (TNOs) discovered in the images of the Dark Energy Survey (DES). Scene-modelling photometry is used to obtain shot-noise-limited flux measures for each exposure of each TNO, with background sources subtracted. Comparison of double-source fits to the pixel data with single-source fits are used to identify and characterize two binary TNO systems. A Markov Chain Monte Carlo method samples the joint likelihood of the intrinsic colors of each source as well as the amplitude of its flux variation, given the time series of multiband flux measurements and their uncertainties. A catalog of these colors and light curve amplitudes $A$ is included with this publication. We show how to assign a likelihood to the distribution $q(A)$ of light curve amplitudes in any subpopulation. Using this method, we find decisive evidence (i.e. evidence ratio $<0.01$) that cold classical (CC) TNOs with absolute magnitude $6<H_r<8.2$ are more variable than the hot classical (HC) population of the same $H_r$, reinforcing theories that the former form in situ and the latter arise from a different physical population. Resonant and scattering TNOs in this $H_r$ range have variability consistent with either the HC's or CC's. DES TNOs with $H_r<6$ are seen to be decisively less variable than higher-$H_r$ members of any dynamical group, as expected. More surprising is that detached TNOs are decisively less variable than scattering TNOs, which requires them to have distinct source regions or some subsequent differential processing.

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arXiv2023

Non-local contribution from small scales in galaxy-galaxy lensing: Comparison of mitigation schemes

Recent cosmological analyses with large-scale structure and weak lensing measurements, usually referred to as 3$\times$2pt, had to discard a lot of signal-to-noise from small scales due to our inability to accurately model non-linearities and baryonic effects. Galaxy-galaxy lensing, or the position-shear correlation between lens and source galaxies, is one of the three two-point correlation functions that are included in such analyses, usually estimated with the mean tangential shear. However, tangential shear measurements at a given angular scale $θ$ or physical scale $R$ carry information from all scales below that, forcing the scale cuts applied in real data to be significantly larger than the scale at which theoretical uncertainties become problematic. Recently there have been a few independent efforts that aim to mitigate the non-locality of the galaxy-galaxy lensing signal. Here we perform a comparison of the different methods, including the Y-transformation, the Point-Mass marginalization methodology and the Annular Differential Surface Density statistic. We do the comparison at the cosmological constraints level in a combined galaxy clustering and galaxy-galaxy lensing analysis. We find that all the estimators yield equivalent cosmological results assuming a simulated Rubin Observatory Legacy Survey of Space and Time (LSST) Year 1 like setup and also when applied to DES Y3 data. With the LSST Y1 setup, we find that the mitigation schemes yield $\sim$1.3 times more constraining $S_8$ results than applying larger scale cuts without using any mitigation scheme.

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arXiv2023

Synchronous rotation in the (136199) Eris-Dysnomia system

We combine photometry of Eris from a 6-month campaign on the Palomar 60-inch telescope in 2015, a 1-month Hubble Space Telescope WFC3 campaign in 2018, and Dark Energy Survey data spanning 2013--2018 to determine a light curve of definitive period $15.771\pm 0.008$~days (1-$σ$ formal uncertainties), with nearly sinusoidal shape and peak-to-peak flux variation of 3\%. This is consistent at part-per-thousand precision with the $P=15.78590\pm0.00005$~day period of Dysnomia's orbit around Eris, strengthening the recent detection of synchronous rotation of Eris by Szakats et al (2022) with independent data. Photometry from Gaia is consistent with the same light curve. We detect a slope of $0.05\pm0.01$~mag per degree of Eris' brightness with respect to illumination phase, intermediate between Pluto's and Charon's values. Variations of $0.3$~mag are detected in Dysnomia's brightness, plausibly consistent with a double-peaked light curve at the synchronous period. The synchronous rotation of Eris is consistent with simple tidal models initiated with a giant-impact origin of the binary, but is difficult to reconcile with gravitational capture of Dysnomia by Eris.

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arXiv2023

Mapping Variations of Redshift Distributions with Probability Integral Transforms

We present a method for mapping variations between probability distribution functions and apply this method within the context of measuring galaxy redshift distributions from imaging survey data. This method, which we name PITPZ for the probability integral transformations it relies on, uses a difference in curves between distribution functions in an ensemble as a transformation to apply to another distribution function, thus transferring the variation in the ensemble to the latter distribution function. This procedure is broadly applicable to the problem of uncertainty propagation. In the context of redshift distributions, for example, the uncertainty contribution due to certain effects can be studied effectively only in simulations, thus necessitating a transfer of variation measured in simulations to the redshift distributions measured from data. We illustrate the use of PITPZ by using the method to propagate photometric calibration uncertainty to redshift distributions of the Dark Energy Survey Year 3 weak lensing source galaxies. For this test case, we find that PITPZ yields a lensing amplitude uncertainty estimate due to photometric calibration error within 1 per cent of the truth, compared to as much as a 30 per cent underestimate when using traditional methods.

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arXiv2022

The Dark Energy Survey Year 3 and eBOSS: constraining galaxy intrinsic alignments across luminosity and colour space

We present direct constraints on galaxy intrinsic alignments using the Dark Energy Survey Year 3 (DES Y3), the Extended Baryon Oscillation Spectroscopic Survey (eBOSS) and its precursor, the Baryon Oscillation Spectroscopic Survey (BOSS). Our measurements incorporate photometric red sequence (redMaGiC) galaxies from DES with median redshift $z\sim0.2-1.0$, luminous red galaxies (LRGs) from eBOSS at $z\sim0.8$, and also a SDSS-III BOSS CMASS sample at $z\sim0.5$. We measure two point intrinsic alignment correlations, which we fit using a model that includes lensing, magnification and photometric redshift error. Fitting on scales $6<r_{\rm p} < 70$ Mpc$/h$, we make a detection of intrinsic alignments in each sample, at $5σ-22σ$ (assuming a simple one parameter model for IAs). Using these red samples, we measure the IA-luminosity relation. Our results are statistically consistent with previous results, but offer a significant improvement in constraining power, particularly at low luminosity. With this improved precision, we see detectable dependence on colour between broadly defined red samples. It is likely that a more sophisticated approach than a binary red/blue split, which jointly considers colour and luminosity dependence in the IA signal, will be needed in future. We also compare the various signal components at the best fitting point in parameter space for each sample, and find that magnification and lensing contribute $\sim2-18\%$ of the total signal. As precision continues to improve, it will certainly be necessary to account for these effects in future direct IA measurements. Finally, we make equivalent measurements on a sample of Emission Line Galaxies (ELGs) from eBOSS at $z\sim 0.8$. We report a null detection, constraining the IA amplitude (assuming the nonlinear alignment model) to be $A_1=0.07^{+0.32}_{-0.42}$ ($|A_1|<0.78$ at $95\%$ CL).

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arXiv2022

Dark Energy Survey Year 3 results: Cosmological constraints from galaxy clustering and galaxy-galaxy lensing using the MagLim lens sample

Two of the most sensitive probes of the large scale structure of the universe are the clustering of galaxies and the tangential shear of background galaxy shapes produced by those foreground galaxies, so-called galaxy-galaxy lensing. Combining the measurements of these two two-point functions leads to cosmological constraints that are independent of the galaxy bias factor. The optimal choice of foreground, or lens, galaxies is governed by the joint, but conflicting requirements to obtain accurate redshift information and large statistics. We present cosmological results from the full 5000 sq. deg. of the Dark Energy Survey first three years of observations (Y3) combining those two-point functions, using for the first time a magnitude-limited lens sample (MagLim) of 11 million galaxies especially selected to optimize such combination, and 100 million background shapes. We consider two cosmological models, flat $Λ$CDM and $w$CDM. In $Λ$CDM we obtain for the matter density $Ω_m = 0.320^{+0.041}_{-0.034}$ and for the clustering amplitude $S_8 = 0.778^{+0.037}_{-0.031}$, at 68% C.L. The latter is only 1$σ$ smaller than the prediction in this model informed by measurements of the cosmic microwave background by the Planck satellite. In $w$CDM we find $Ω_m = 0.32^{+0.044}_{-0.046}$, $S_8=0.777^{+0.049}_{-0.051}$, and dark energy equation of state $w=-1.031^{+0.218}_{-0.379}$. We find that including smaller scales while marginalizing over non-linear galaxy bias improves the constraining power in the $Ω_m-S_8$ plane by $31$% and in the $Ω_m-w$ plane by $41$% while yielding consistent cosmological parameters from those in the linear bias case. These results are combined with those from cosmic shear in a companion paper to present full DES-Y3 constraints from the three two-point functions (3x2pt).

astro-ph.CO↗
arXiv2022

The Dark Energy Survey Year 3 high redshift sample: Selection, characterization and analysis of galaxy clustering

The fiducial cosmological analyses of imaging galaxy surveys like the Dark Energy Survey (DES) typically probe the Universe at redshifts $z < 1$. This is mainly because of the limited depth of these surveys, and also because such analyses rely heavily on galaxy lensing, which is more efficient at low redshifts. In this work we present the selection and characterization of high-redshift galaxy samples using DES Year 3 data, and the analysis of their galaxy clustering measurements. In particular, we use galaxies that are fainter than those used in the previous DES Year 3 analyses and a Bayesian redshift scheme to define three tomographic bins with mean redshifts around $z \sim 0.9$, $1.2$ and $1.5$, which significantly extend the redshift coverage of the fiducial DES Year 3 analysis. These samples contain a total of about 9 million galaxies, and their galaxy density is more than 2 times higher than those in the DES Year 3 fiducial case. We characterize the redshift uncertainties of the samples, including the usage of various spectroscopic and high-quality redshift samples, and we develop a machine-learning method to correct for correlations between galaxy density and survey observing conditions. The analysis of galaxy clustering measurements, with a total signal-to-noise $S/N \sim 70$ after scale cuts, yields robust cosmological constraints on a combination of the fraction of matter in the Universe $Ω_m$ and the Hubble parameter $h$, $Ω_m h = 0.195^{+0.023}_{-0.018}$, and 2-3% measurements of the amplitude of the galaxy clustering signals, probing galaxy bias and the amplitude of matter fluctuations, $b σ_8$. A companion paper $\textit{(in preparation)}$ will present the cross-correlations of these high-$z$ samples with CMB lensing from Planck and SPT, and the cosmological analysis of those measurements in combination with the galaxy clustering presented in this work.

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arXiv2022

Cross-correlation of DES Y3 lensing and ACT/${\it Planck}$ thermal Sunyaev Zel'dovich Effect II: Modeling and constraints on halo pressure profiles

Hot, ionized gas leaves an imprint on the cosmic microwave background via the thermal Sunyaev Zel'dovich (tSZ) effect. The cross-correlation of gravitational lensing (which traces the projected mass) with the tSZ effect (which traces the projected gas pressure) is a powerful probe of the thermal state of ionized baryons throughout the Universe, and is sensitive to effects such as baryonic feedback. In a companion paper (Gatti et al. 2021), we present tomographic measurements and validation tests of the cross-correlation between galaxy shear measurements from the first three years of observations of the Dark Energy Survey, and tSZ measurements from a combination of Atacama Cosmology Telescope and ${\it Planck}$ observations. In this work, we use the same measurements to constrain models for the pressure profiles of halos across a wide range of halo mass and redshift. We find evidence for reduced pressure in low mass halos, consistent with predictions for the effects of feedback from active galactic nuclei. We infer the hydrostatic mass bias ($B \equiv M_{500c}/M_{\rm SZ}$) from our measurements, finding $B = 1.8\pm0.1$ when adopting the ${\it Planck}$-preferred cosmological parameters. We additionally find that our measurements are consistent with a non-zero redshift evolution of $B$, with the correct sign and sufficient magnitude to explain the mass bias necessary to reconcile cluster count measurements with the ${\it Planck}$-preferred cosmology. Our analysis introduces a model for the impact of intrinsic alignments (IA) of galaxy shapes on the shear-tSZ correlation. We show that IA can have a significant impact on these correlations at current noise levels.

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arXiv2022

Photometric Properties of Jupiter Trojans detected by the Dark Energy Survey

The Jupiter Trojans are a large group of asteroids that are co-orbiting with Jupiter near its L4 and L5 Lagrange points. The study of Jupiter Trojans is crucial for testing different models of planet formation that are directly related to our understanding of solar system evolution. In this work, we select known Jupiter Trojans listed by the Minor Planet Center (MPC) from the full six years dataset (Y6) of the Dark Energy Survey (DES) to analyze their photometric properties. The DES data allow us to study Jupiter Trojans with a fainter magnitude limit than previous studies in a homogeneous survey with $griz$ band measurements. We extract a final catalog of 573 unique Jupiter Trojans. Our sample include 547 asteroids belonging to L5. This is one of the largest analyzed samples for this group. By comparing with the data reported by other surveys we found that the color distribution of L5 Trojans is similar to that of L4 Trojans. We find that L5 Trojans' $g - i$ and $g - r$ colors become less red with fainter absolute magnitudes, a trend also seen in L4 Trojans. Both the L4 and L5 clouds consistently show such a color-size correlation over an absolute magnitude range $11 < H < 18$. We also use DES colors to perform taxonomic classifications. C and P-type asteroids outnumber D-type asteroids in the L5 Trojans DES sample, which have diameters in the 5 - 20 km range. This is consistent with the color-size correlation.

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arXiv2022

Mapping gas around massive galaxies: cross-correlation of DES Y3 galaxies and Compton-$y$-maps from SPT and Planck

We cross-correlate positions of galaxies measured in data from the first three years of the Dark Energy Survey with Compton-$y$-maps generated using data from the South Pole Telescope (SPT) and the {\it Planck} mission. We model this cross-correlation measurement together with the galaxy auto-correlation to constrain the distribution of gas in the Universe. We measure the hydrostatic mass bias or, equivalently, the mean halo bias-weighted electron pressure $\langle b_{h}P_{e}\rangle$, using large-scale information. We find $\langle b_{h}P_{e}\rangle$ to be $[0.16^{+0.03}_{-0.04},0.28^{+0.04}_{-0.05},0.45^{+0.06}_{-0.10},0.54^{+0.08}_{-0.07},0.61^{+0.08}_{-0.06},0.63^{+0.07}_{-0.08}]$ meV cm$^{-3}$ at redshifts $z \sim [0.30, 0.46, 0.62,0.77, 0.89, 0.97]$. These values are consistent with previous work where measurements exist in the redshift range. We also constrain the mean gas profile using small-scale information, enabled by the high-resolution of the SPT data. We compare our measurements to different parametrized profiles based on the cosmo-OWLS hydrodynamical simulations. We find that our data are consistent with the simulation that assumes an AGN heating temperature of $10^{8.5}$K but are incompatible with the model that assumes an AGN heating temperature of $10^{8.0}$K. These comparisons indicate that the data prefer a higher value of electron pressure than the simulations within $r_{500c}$ of the galaxies' halos.

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arXiv2022

Cosmic Shear in Harmonic Space from the Dark Energy Survey Year 1 Data: Compatibility with Configuration Space Results

We perform a cosmic shear analysis in harmonic space using the first year of data collected by the Dark Energy Survey (DES-Y1). We measure the cosmic weak lensing shear power spectra using the Metacalibration catalogue and perform a likelihood analysis within the framework of CosmoSIS. We set scale cuts based on baryonic effects contamination and model redshift and shear calibration uncertainties as well as intrinsic alignments. We adopt as fiducial covariance matrix an analytical computation accounting for the mask geometry in the Gaussian term, including non-Gaussian contributions. A suite of 1200 lognormal simulations is used to validate the harmonic space pipeline and the covariance matrix. We perform a series of stress tests to gauge the robustness of the harmonic space analysis. Finally, we use the DES-Y1 pipeline in configuration space to perform a similar likelihood analysis and compare both results, demonstrating their compatibility in estimating the cosmological parameters $S_8$, $σ_8$ and $Ω_m$. The methods implemented and validated in this paper will allow us to perform a consistent harmonic space analysis in the upcoming DES data.

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arXiv2022

Dark Energy Survey Year 3 Results: Cosmology from Cosmic Shear and Robustness to Data Calibration

This work, together with its companion paper, Secco and Samuroff et al. (2021), presents the Dark Energy Survey Year 3 cosmic shear measurements and cosmological constraints based on an analysis of over 100 million source galaxies. With the data spanning 4143 deg$^2$ on the sky, divided into four redshift bins, we produce the highest significance measurement of cosmic shear to date, with a signal-to-noise of 40. We conduct a blind analysis in the context of the $Λ$CDM model and find a 3% constraint of the clustering amplitude, $S_8\equiv σ_8 (Ω_{\rm m}/0.3)^{0.5} = 0.759^{+0.025}_{-0.023}$. A $Λ$CDM-Optimized analysis, which safely includes smaller scale information, yields a 2% precision measurement of $S_8= 0.772^{+0.018}_{-0.017}$ that is consistent with the fiducial case. The two low-redshift measurements are statistically consistent with the Planck Cosmic Microwave Background result, however, both recovered $S_8$ values are lower than the high-redshift prediction by $2.3σ$ and $2.1σ$ ($p$-values of 0.02 and 0.05), respectively. The measurements are shown to be internally consistent across redshift bins, angular scales and correlation functions. The analysis is demonstrated to be robust to calibration systematics, with the $S_8$ posterior consistent when varying the choice of redshift calibration sample, the modeling of redshift uncertainty and methodology. Similarly, we find that the corrections included to account for the blending of galaxies shifts our best-fit $S_8$ by $0.5σ$ without incurring a substantial increase in uncertainty. We examine the limiting factors for the precision of the cosmological constraints and find observational systematics to be subdominant to the modeling of astrophysics. Specifically, we identify the uncertainties in modeling baryonic effects and intrinsic alignments as the limiting systematics.

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arXiv2022

Dark Energy Survey Year 3 Results: Constraints on cosmological parameters and galaxy bias models from galaxy clustering and galaxy-galaxy lensing using the redMaGiC sample

We constrain cosmological and galaxy-bias parameters using the combination of galaxy clustering and galaxy-galaxy lensing measurements from the Dark Energy Survey Year-3 data. We describe our modeling framework, and choice of scales analyzed, validating their robustness to theoretical uncertainties in small-scale clustering by analyzing simulated data. Using a linear galaxy bias model and redMaGiC galaxy sample, we obtain constraints on the matter density to be $Ω_{\rm m} = 0.325^{+0.033}_{-0.034}$. We also implement a non-linear galaxy bias model to probe smaller scales that includes parameterization based on hybrid perturbation theory and find that it leads to a 17% gain in cosmological constraining power. We perform robustness tests of our methodology pipeline and demonstrate the stability of the constraints to changes in the theoretical model. Using the redMaGiC galaxy sample as foreground lens galaxies, we find the galaxy clustering and galaxy-galaxy lensing measurements to exhibit significant signals akin to de-correlation between galaxies and mass on large scales, which is not expected in any current models. This likely systematic measurement error biases our constraints on galaxy bias and the $S_8$ parameter. We find that a scale-, redshift- and sky-area-independent phenomenological de-correlation parameter can effectively capture the impact of this systematic error. We trace the source of this de-correlation to a color-dependent photometric issue and minimize its impact on our result by changing the selection criteria of redMaGiC galaxies. Using this new sample, our constraints on the $S_8$ parameter are consistent with previous studies, and we find a small shift in the $Ω_{\rm m}$ constraints compared to the fiducial redMaGiC sample. We constrain the mean host halo mass of the redMaGiC galaxies in this new sample to be approximately $1.6 \times 10^{13} M_{\odot}/h$.

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