Motivated by a theorem in the K-theoretic setting relating the localization of K_0(X/T) over a closed point z \in Spec(K_0(BT)) to the Borel-Moore homology of the fixed points H.^{BM}(X^z; C), we prove an equivariant localization theorem for smooth quotient stacks by reductive groups G in the setting of derived loop spaces and periodic cyclic homology, realizing a Jordan decomposition of loops described by Ben-Zvi and Nadler. We show that the derived loop space L(X/G) is a family of twisted unipotent loop spaces over Aff(L(BG)) = G//G; more precisely, the fiber over a formal neighborhood of a semisimple orbit [z] \in G//G is the unipotent loop space of the classical fixed points with a twisted S^1-action. We further study the relationship between unipotent loop spaces and formal loop spaces, and prove that their Tate S^1-invariant functions are isomorphic. Applying a theorem of Bhatt identifying derived de Rham cohomology with Betti cohomology, we obtain an equivariant localization theorem for periodic cyclic homology in the smooth case, identifying the completion of HP(Perf(X/G)) at z \in G//G with the 2-periodic equivariant singular cohomology of the z-fixed points H*(X^z/G^z; k)((u)).

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## Scholarly Works (15 results)

LBL Publications (2024)

Context. The determination of accurate photometric redshifts (photo-zs) in large imaging galaxy surveys is key for cosmological studies. One of the most common approaches is machine learning techniques. These methods require a spectroscopic or reference sample to train the algorithms. Attention has to be paid to the quality and properties of these samples since they are key factors in the estimation of reliable photo-zs.
Aims. The goal of this work is to calculate the photo-zs for the Year 3 (Y3) Dark Energy Survey (DES) Deep Fields catalogue using the Directional Neighborhood Fitting (DNF) machine learning algorithm. Moreover, we want to develop techniques to assess the incompleteness of the training sample and metrics to study how incompleteness affects the quality of photometric redshifts. Finally, we are interested in comparing the performance obtained by DNF on the Y3 DES Deep Fields catalogue with that of the EAzY template fitting approach.
Methods. We emulated – at a brighter magnitude – the training incompleteness with a spectroscopic sample whose redshifts are known to have a measurable view of the problem. We used a principal component analysis to graphically assess the incompleteness and relate it with the performance parameters provided by DNF. Finally, we applied the results on the incompleteness to the photo-z computation on the Y3 DES Deep Fields with DNF and estimated its performance.
Results. The photo-zs of the galaxies in the DES deep fields were computed with the DNF algorithm and added to the Y3 DES Deep Fields catalogue. We have developed some techniques to evaluate the performance in the absence of “true” redshift and to assess the completeness. We have studied the tradeoff in the training sample between the highest spectroscopic redshift quality versus completeness. We found some advantages in relaxing the highest-quality spectroscopic redshift requirements at fainter magnitudes in favour of completeness. The results achieved by DNF on the Y3 Deep Fields are competitive with the ones provided by EAzY, showing notable stability at high redshifts. It should be noted that the good results obtained by DNF in the estimation of photo-zs in deep field catalogues make DNF suitable for the future Legacy Survey of Space and Time (LSST) and Euclid data, which will have similar depths to the Y3 DES Deep Fields.

LBL Publications (2022)

ABSTRACT:
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.

The fiducial cosmological analyses of imaging surveys like DES typically probe the Universe at redshifts z < 1. 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 ∼0.9, 1.2, and 1.5, which 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 ∼70 after scale cuts, yields robust cosmological constraints on a combination of the fraction of matter in the Universe

LBL Publications (2022)

We present high signal-to-noise measurements of three-point shear correlations and the third moment of the mass aperture statistic using the first 3 years of data from the Dark Energy Survey. We additionally obtain the first measurements of the configuration and scale dependence of the four three-point shear correlations which carry cosmological information. With the third-order mass aperture statistic, we present tomographic measurements over angular scales of 4 to 60 arcminutes with a combined statistical significance of 15.0σ. Using the tomographic information and measuring also the second-order mass aperture, we additionally obtain a skewness parameter and its redshift evolution. We find that the amplitudes and scale-dependence of these shear 3pt functions are in qualitative agreement with measurements in a mock galaxy catalog based on N-body simulations, indicating promise for including them in future cosmological analyses. We validate our measurements by showing that B-modes, parity-violating contributions and PSF modeling uncertainties are negligible, and determine that the measured signals are likely to be of astrophysical and gravitational origin.

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. Phys. Rev. D 105, 123525 (2022)PRVDAQ2470-0010), 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 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 (BM500c/MSZ) from our measurements, finding B=1.8±0.1 when adopting the Planck-preferred cosmological parameters. We additionally find that our measurements are consistent with a nonzero redshift evolution of B, with the correct sign and sufficient magnitude to explain the mass bias necessary to reconcile cluster count measurements with the Planck-preferred cosmology. Our analysis introduces a model for the impact of intrinsic alignments (IAs) of galaxy shapes on the shear-tSZ correlation. We show that IA can have a significant impact on these correlations at current noise levels.

We present a validation of the Dark Energy Survey Year 3 (DES Y3) 3×2-point analysis choices by testing them on Buzzard2.0, a new suite of cosmological simulations that is tailored for the testing and validation of combined galaxy clustering and weak-lensing analyses. We show that the buzzard2.0 simulations accurately reproduce many important aspects of the DES Y3 data, including photometric redshift and magnitude distributions, and the relevant set of two-point clustering and weak-lensing statistics. We then show that our model for the 3×2-point data vector is accurate enough to recover the true cosmology in simulated surveys assuming the true redshift distributions for our source and lens samples, demonstrating robustness to uncertainties in the modeling of the nonlinear matter power spectrum, nonlinear galaxy bias, and higher-order lensing corrections. Additionally, we demonstrate for the first time that our photometric redshift calibration methodology, including information from photometry, spectroscopy, clustering cross-correlations, and galaxy-galaxy lensing ratios, is accurate enough to recover the true cosmology in simulated surveys in the presence of realistic photometric redshift uncertainties.

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 autocorrelation and galaxy-galaxy lensing signal with different magnifications priors, finding broad consistency in cosmological parameters in ΛCDM and wCDM. However, when magnification bias amplitude is allowed to be free, we find the two-point correlation 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 autocorrelation of the lens bins, indicating that systematics other than magnification may be the cause of the discrepancy. We show that 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.

LBL Publications (2021)

Galaxy-galaxy lensing is a powerful probe of the connection between galaxies and their host dark matter haloes, which is important both for galaxy evolution and cosmology. We extend the measurement and modelling of the galaxy-galaxy lensing signal in the recent Dark Energy Survey Year 3 cosmology analysis to the highly non-linear scales (100 kpc). This extension enables us to study the galaxy-halo connection via a Halo Occupation Distribution (HOD) framework for the two lens samples used in the cosmology analysis: a luminous red galaxy sample (redmagic) and a magnitude-limited galaxy sample (maglim). We find that redmagic (maglim) galaxies typically live in dark matter haloes of mass log10(Mh/M) ≈ 13.7 which is roughly constant over redshift (13.3-13.5 depending on redshift). We constrain these masses to 15 per cent, approximately 1.5 times improvement over the previous work. We also constrain the linear galaxy bias more than five times better than what is inferred by the cosmological scales only. We find the satellite fraction for redmagic (maglim) to be 0.1-0.2 (0.1-0.3) with no clear trend in redshift. Our constraints on these halo properties are broadly consistent with other available estimates from previous work, large-scale constraints, and simulations. The framework built in this paper will be used for future HOD studies with other galaxy samples and extensions for cosmological analyses.

Recent cosmological analyses with large-scale structure and weak lensing measurements, usually referred to as 3 × 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 set-up and also when applied to DES Y3 data. With the LSST Y1 set-up, we find that the mitigation schemes yield ∼1.3 times more constraining S8 results than applying larger scale cuts without using any mitigation scheme.