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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

TDCOSMO VIII. A key test of systematics in the hierarchical method of time-delay cosmography

The largest source of systematic errors in the time-delay cosmography method likely arises from the lens model mass distribution, where an inaccurate choice of model could in principle bias the value of $H$ 0 . A Bayesian hierarchical framework has been proposed which combines lens systems with kinematic data, constraining the mass profile shape at a population level. The framework has been previously validated using a small sample of lensing galaxies drawn from hydro-simulations. The goal of this work is to expand the validation to a more general set of lenses consistent with observed systems, as well as confirm the capacity of the method to combine two lens populations: one which has time delay information and one which lacks time delays and has systematically different image radii. For this purpose, we generated samples of analytic lens mass distributions made of baryons+dark matter and fit the subsequent mock images with standard power-law models. Corresponding kinematics data were also emulated. The hierarchical framework applied to an ensemble of time-delay lenses allowed us to correct the $H$ 0 bias associated with model choice to find $H$ 0 within 1.5σ of the fiducial value. We then combined this set with a sample of corresponding lens systems which have no time delays and have a source at lower $z$, resulting in a systematically smaller image radius relative to their effective radius. The hierarchical framework has successfully accounted for this effect, recovering a value of $H$ 0 which is both more precise (σ ~ 2%) and more accurate (0.7% median offset) than the time-delay set alone. This result confirms that non-time-delay lenses can nonetheless contribute valuable constraining power to the determination of $H$ 0 via their kinematic constraints, assuming they come from the same global population as the time-delay set.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Limiting the number of quantisation levels of a harmonic lens as a method for improving the quality of the generated image

The characteristics (modulation transfer functions) of harmonic lenses made by direct laser patterning of resist are experimentally studied. The influence of technological errors in the manufacture of lenses on the formation of the point spread function is modelled for harmonic lenses with 32 and 256 quantisation levels. Direct laser writing is used to produce lenses with these numbers of levels. It is experimentally shown that the modulation transfer function of the harmonic lens with 32 quantisation levels is significantly greater at high spatial frequencies (50 mm{sup −1}). (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

The outer stellar mass of massive galaxies: a simple tracer of halo mass with scatter comparable to richness and reduced projection effects

ABSTRACT Using the weak gravitational lensing data from the Hyper Suprime-Cam Subaru Strategic Program (HSC survey), we study the potential of different stellar mass estimates in tracing halo mass. We consider galaxies with log10(M⋆/M⊙) > 11.5 at 0.2 < z < 0.5 with carefully measured light profiles, and clusters from the redMaPPer and CAMIRA richness-based algorithms. We devise a method (the ‘Top-N test’) to evaluate the scatter in the halo mass–observable relation for different tracers, and to inter-compare halo mass proxies in four number density bins using stacked galaxy–galaxy lensing profiles. This test reveals three key findings. Stellar masses based on CModel photometry and aperture luminosity within R <30 kpc are poor proxies of halo mass. In contrast, the stellar mass of the outer envelope is an excellent halo mass proxy. The stellar mass within R = [50, 100] kpc, M⋆, [50, 100], has performance comparable to the state-of-the-art richness-based cluster finders at log10Mvir ≳ 14.0 and could be a better halo mass tracer at lower halo masses. Finally, using N-body simulations, we find that the lensing profiles of massive haloes selected by M⋆, [50, 100] are consistent with the expectation for a sample without projection or mis-centring effects. Richness-selected clusters, on the other hand, display an excess at R ∼ 1 Mpc in their lensing profiles, which may suggest a more significant impact from selection biases. These results suggest that M⋆-based tracers have distinct advantages in identifying massive haloes, which could open up new avenues for cluster cosmology. The codes and data used in this work can be found here:

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

STRIDES: automated uniform models for 30 quadruply imaged quasars

ABSTRACT Gravitational time delays provide a powerful one-step measurement of H0, independent of all other probes. One key ingredient in time-delay cosmography are high-accuracy lens models. Those are currently expensive to obtain, both, in terms of computing and investigator time (105–106 CPU hours and ∼0.5–1 yr, respectively). Major improvements in modelling speed are therefore necessary to exploit the large number of lenses that are forecast to be discovered over the current decade. In order to bypass this roadblock, we develop an automated modelling pipeline and apply it to a sample of 31 lens systems, observed by the Hubble Space Telescope in multiple bands. Our automated pipeline can derive models for 30/31 lenses with few hours of human time and <100 CPU hours of computing time for a typical system. For each lens, we provide measurements of key parameters and predictions of magnification as well as time delays for the multiple images. We characterize the cosmography-readiness of our models using the stability of differences in the Fermat potential (proportional to time delay) with respect to modelling choices. We find that for 10/30 lenses, our models are cosmography or nearly cosmography grade (<3 per cent and 3–5 per cent variations). For 6/30 lenses, the models are close to cosmography grade (5–10 per cent). These results utilize informative priors and will need to be confirmed by further analysis. However, they are also likely to improve by extending the pipeline modelling sequence and options. In conclusion, we show that uniform cosmography grade modelling of large strong lens samples is within reach.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Cluster cosmology with anisotropic boosts: validation of a novel forward modelling analysis and application on SDSS redMaPPer clusters

We present a novel analysis for cluster cosmology that fully forward models the abundances, weak lensing, and the clustering of galaxy clusters. Our analysis notably includes an empirical model for the anisotropic boosts impacting the lensing and clustering signals of optical clusters. These boosts arise from a preferential selection of clusters surrounded by anisotropic large-scale structure, a consequence of the limited discrimination between line-of-sight interlopers and true cluster members offered by photometric surveys. We validate our analysis via a blind cosmology challenge on mocks, and find that we can obtain tight and unbiased cosmological constraints without informative priors or external calibrations on any of our model parameters. We then apply our analysis on the SDSS redMaPPer clusters, and find results favoring low Ωm and high σ8, combining to yield the lensing strength constraint $S_8 = 0.715_{-0.021}^{+0.024}$. We investigate potential drivers behind these results through a series of post-unblinding tests, noting that our results are consistent with existing cluster cosmology constraints but clearly inconsistent with other CMB/LSS based cosmology results. From these tests, we find hints that a suppression in the cluster lensing signal may be driving our results.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Improving Dark Energy Constraints Using Low-Redshift Large-Scale Structures

The primary goal of this project was to improve constraints on dark energy measurements by improving our ability to extract cosmological information from low redshift large-scale structures. PI Clowe's project's primary aim was to reduce the bias in measurements of the masses of clusters of galaxies to a level where the evolution of the cluster mass function can be used in the Vera Rubin Observatory's Legacy Survey of Space and Time Dark Energy Science Collaboration survey to improve the accuracy of the measurement of dark energy and other cosmological parameters. Co-PI Seo's project studied observational systematics affecting large-scale clustering of galaxies, which will be used to improve dark energy constraints from the Dark Energy Spectroscopic Instrument (DESI). The cluster lensing project employed a series of simulations and observations of clusters of galaxies to test numerous potential systematic errors in cluster mass measurements using weak gravitational lensing as the accuracy of current weak lensing measurements are more than order of magnitude worse than what is required to use clusters of galaxies for accurate determination of dark energy parameters. PI Clowe and group developed and analyzed simulations to test for, and correct biases introduced in, the weak lensing measurement process. Finally, PI Clowe and group developed a method of detecting clusters using galaxy overdensities and applied the method to the BLISS and DES surveys. The success of spectroscopic dark energy mission such as the extended Baryon Oscillation Spectroscopic Survey (eBOSS) and the Dark Energy Spectroscopic Instrument (DESI) will depend on a thorough understanding of various observational systematics in the target density fluctuations that would give rise to spurious, non-cosmological signals. PI Seo and group developed a deep learning, artificial neural network (ANN) technique that modeled and mitigated such effects, aimed at deriving more robust galaxy clustering signals not only for the baryon acoustic oscillation feature and redshift-space distortions but also for primordial non-Gaussianity constraint.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

The Optical Corrector for the Dark Energy Spectroscopic Instrument

The Dark Energy Spectroscopic Instrument (DESI) is currently measuring the spectra of 40 million galaxies and quasars, the largest such survey ever made to probe the nature of cosmological dark energy. The 4 m Mayall telescope at Kitt Peak National Observatory has been adapted for DESI, including the construction of a 3$_{.}^{°}$2 diameter prime focus corrector that focuses astronomical light onto a 0.8 m diameter focal surface with excellent image quality over the DESI bandpass of 360–980 nm. The wide-field corrector includes six lenses, as large as 1.1 m in diameter and as heavy as 237 kilograms, including two counterrotating wedged lenses that correct for atmospheric dispersion over zenith angles from 0° to 60°. The lenses, cells, and barrel assembly all meet precise alignment tolerances on the order of tens of microns. The barrel alignment is maintained throughout a range of observing angles and temperature excursions in the Mayall dome by use of a hexapod, which is itself supported by a new cage, ring, and truss structure. In this paper we describe the design, fabrication, and performance of the new corrector and associated structure, focusing on how they meet DESI requirements. In particular, we describe the prescription and specifications of the lenses, design choices and error budgeting of the barrel assembly, stray light mitigations, and integration and test at the Mayall telescope. We conclude with some validation highlights that demonstrate the successful corrector on-sky performance, and we list some lessons learned during the multiyear fabrication phase.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

RELICS: A Very Large ( θ E ~ 40") Cluster Lens—RXC J0032.1+1808

Extensive surveys with the Hubble Space Telescope over the past decade, targeting some of the most massive clusters in the sky, have uncovered dozens of galaxy cluster strong lenses. The massive cluster strong-lens scale is typically θ E ~ 10'' to ~30''–35'', with only a handful of clusters known with Einstein radii θ E ~ 40'' or above (for z source = 2, nominally). Here we report another very large cluster lens, RXC J0032.1+1808 (z = 0.3956), the second-richest cluster in the redMapper cluster catalog and the 85th most massive cluster in the Planck Sunyaev–Zel'dovich catalog. With our light-traces-mass and fully parametric approaches, we construct strong-lensing models based on 18 multiple images of five background galaxies newly identified in the Hubble data, mainly from the Reionization Lensing Cluster Survey (RELICS), in addition to a known sextuply imaged system in this cluster. Furthermore, we compare these models to Lenstool and GLAFIC models that were produced independently as part of the RELICS program. All models reveal a large effective Einstein radius of θ E ≃ 40'' (z source = 2), owing to the obvious concentration of substructures near the cluster center. Although RXC J0032.1+1808 has a very large critical area and high lensing strength, only three magnified high-redshift candidates are found within the field targeted by RELICS. Nevertheless, we expect many more high-redshift candidates will be seen in wider and deeper observations with Hubble or the James Webb Space Telescope. Finally, the comparison between several algorithms demonstrates that the total error budget is largely dominated by systematic uncertainties.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Large-scale Gravitational Lens Modeling with Bayesian Neural Networks for Accurate and Precise Inference of the Hubble Constant

We investigate the use of approximate Bayesian neural networks (BNNs) in modeling hundreds of time delay gravitational lenses for Hubble constant (H 0 ) determination. Here, our BNN was trained on synthetic Hubble Space Telescope quality images of strongly lensed active galactic nuclei with lens galaxy light included. The BNN can accurately characterize the posterior probability density functions (PDFs) of model parameters governing the elliptical power-law mass profile in an external shear field. We then propagate the BNN-inferred posterior PDFs into an ensemble H 0 inference, using simulated time delay measurements from a plausible dedicated monitoring campaign. Assuming well-measured time delays and a reasonable set of priors on the environment of the lens, we achieve a median precision of 9.3% per lens in the inferred H 0 . A simple combination of a set of 200 test lenses results in a precision of 0.5 km s –1 Mpc –1 (0.7%), with no detectable bias in this H 0 recovery test. The computation time for the entire pipeline—including the generation of the training set, BNN training and H0 inference—translates to 9 minutes per lens on average for 200 lenses and converges to 6 minutes per lens as the sample size is increased. Being fully automated and efficient, our pipeline is a promising tool for exploring ensemble-level systematics in lens modeling for H 0 inference.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Halo Properties and Mass Functions of Groups/Clusters from the DESI Legacy Imaging Surveys DR9

Abstract Based on a large group/cluster catalog recently constructed from the DESI Legacy Imaging Surveys DR9 using an extended halo-based group finder, we measure and model the group–galaxy weak-lensing signals for groups/clusters in a few redshift bins within redshift range 0.1 ≤ z < 0.6. Here, the background shear signals are obtained based on the DECaLS survey shape catalog, derived with the F ourier _Q uad method. We divide the lens samples into five equispaced redshift bins and seven mass bins, which allow us to probe the redshift and mass dependence of the lensing signals, and hence the resulting halo properties. In addition to these sample selections, we also check the signals around different group centers, e.g., the brightest central galaxy, the luminosity-weighted center, and the number-weighted center. We use a lensing model that includes off-centering to describe the lensing signals that we measure for all mass and redshift bins. The results demonstrate that our model predictions for the halo masses, biases, and concentrations are stable and self-consistent among different samples for different group centers. Taking advantage of the very large and complete sample of groups/clusters, as well as the reliable estimations of their halo masses, we provide measurements of the cumulative halo mass functions up to redshift z = 0.6, with a mass precision at 0.03 ∼ 0.09 dex.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

It is not σ 8 : constraining the non-linear matter power spectrum with the Dark Energy Survey Year-5 supernova sample

The weak gravitational lensing magnification of Type Ia supernovae (SNe Ia) is sensitive to the matter power spectrum on scales $k\gt 1 h$ Mpc$^{-1}$, making it unwise to interpret SNe Ia lensing in terms of power on linear scales. We compute the probability density function of SNe Ia magnification as a function of standard cosmological parameters, plus an empirical parameter $A_{\rm mod}$ which describes the suppression or enhancement of matter power on non-linear scales compared to a cold dark matter only model. While baryons are expected to enhance power on the scales relevant to SN Ia lensing, other physics such as neutrino masses or non-standard dark matter may suppress power. Using the Dark Energy Survey Year-5 sample, we find $A_{\rm mod} = 0.77^{+0.69}_{-0.40}$ (68 per cent credible interval around the median). Although the median is consistent with unity there are hints of power suppression, with $A_{\rm mod} \lt 1.09$ at 68 per cent credibility.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Redox Heterogeneities Promote Thioarsenate Formation and Release into Groundwater from Low Arsenic Sediments

Groundwater contamination by As from natural and anthropogenic sources is a worldwide concern. Redox heterogeneities over space and time are common and can influence the molecular-level speciation of As, and thus, As release/retention but are largely unexplored. Here, we present results from a dual-domain column experiment, with natural organic-rich, fine-grained, and sulfidic sediments embedded as lenses (referred to as “reducing lenses”) within natural aquifer sand. We show that redox interfaces in sulfur-rich, alkaline aquifers may release concerning levels of As, even when sediment As concentration is low (<2 mg/kg), due to the formation of mobile thioarsenates at aqueous sulfide/Fe molar ratios <1. In our experiments, this behavior occurred in the aquifer sand between reducing lenses and was attributed to the spreading of sulfidic conditions and subsequent Fe reductive dissolution. In contrast, inside reducing lenses (and some locations in the aquifer) the aqueous sulfide/Fe molar ratios exceeded 1 and aqueous sulfide/As molar ratios exceeded 100, which partitioned As(III)–S to the solid phase (associated with organics or as realgar (As 4 S 4 )). These results highlight the importance of thioarsenates in natural sediments and indicate that redox interfaces and sediment heterogeneities could locally degrade groundwater quality, even in aquifers with unconcerning solid-phase As concentrations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

A large field-of-view high-resolution hard x-ray microscope using polymer optics

Here, we present an effective approach using a matched pair of polymer-based condenser-objective lenses to build a compact full-field X-ray microscope with a high spatial resolution. A unique condenser comprising arrays of high-aspect-ratio prisms with equilateral cross-section is used for uniformly illuminating samples over a large field of view (FoV) from all angles, which match the acceptance of an objective made of interdigitated orthogonal rows of one-dimensional lenses. State-of-the-art Talbot grating interferometry used to characterize these lenses for the first time revealed excellent focusing properties and minimal wave-front distortions. Using a specific lens-pair designed for 20 keV X-rays, short-exposure times, and image registration with a cross-correlation technique, we circumvent vibrational instabilities to obtain distortion-free images with a uniform resolution of 240 nm (smallest resolvable line pair) over a large FoV, 80 × 80 µm 2 in extent. The results were contrasted with those collected under illumination using commercial two-dimensional parabolic lenses with a smaller FoV. This approach implemented on a diffractometer would enable diffraction-contrast or dark-field microscopy for fast observations of ‘mesoscopic’ phenomena in real space complementing reciprocal-space studies using diffraction on the same instrument.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Combination of cluster number counts and two-point correlations: validation on mock Dark Energy Survey

ABSTRACT We present a method of combining cluster abundances and large-scale two-point correlations, namely galaxy clustering, galaxy–cluster cross-correlations, cluster autocorrelations, and cluster lensing. This data vector yields comparable cosmological constraints to traditional analyses that rely on small-scale cluster lensing for mass calibration. We use cosmological survey simulations designed to resemble the Dark Energy Survey Year 1 (DES-Y1) data to validate the analytical covariance matrix and the parameter inferences. The posterior distribution from the analysis of simulations is statistically consistent with the absence of systematic biases detectable at the precision of the DES-Y1 experiment. We compare the χ2 values in simulations to their expectation and find no significant difference. The robustness of our results against a variety of systematic effects is verified using a simulated likelihood analysis of DES-Y1-like data vectors. This work presents the first-ever end-to-end validation of a cluster abundance cosmological analysis on galaxy catalogue level simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Self-calibrating optical galaxy cluster selection bias using cluster, galaxy, and shear cross-correlations

ABSTRACT The clustering signals of galaxy clusters are powerful tools for self-calibrating the mass–observable relation and are complementary to cluster abundance and lensing. In this work, we explore the possibility of combining three correlation functions – cluster lensing, the cluster–galaxy cross-correlation function, and the galaxy autocorrelation function – to self-calibrate optical cluster selection bias, the boosted clustering and lensing signals in a richness-selected sample mainly caused by projection effects. We develop mock catalogues of redMaGiC-like galaxies and redMaPPer-like clusters by applying halo occupation distribution models to N-body simulations and using counts-in-cylinders around massive haloes as a richness proxy. In addition to the previously known small-scale boost in projected correlation functions, we find that the projection effects also significantly boost three-dimensional correlation functions to scales of 100 $h^{-1} \, \rm Mpc$. We perform a likelihood analysis assuming survey conditions similar to the Dark Energy Survey and show that the selection bias can be self-consistently constrained at the 10 per cent level. We discuss strategies for applying this approach to real data. We expect that expanding the analysis to smaller scales and using deeper lensing data would further improve the constraints on cluster selection bias.

Astronomy & Astrophysics↗
DOE OSTI2026

SPT-3G D1: CMB temperature and polarization power spectra and cosmology from 2019 and 2020 observations of the SPT-3G main field

Here, we present measurements of the temperature and E-mode polarization angular power spectra of the cosmic microwave background (CMB) from observations of 4% of the sky with SPT-3G, the current camera on the South Pole Telescope (SPT). The maps used in this analysis are the deepest used in a CMB TT / TE / EE analysis to date. The maps and resulting power spectra have been validated through blind and unblind tests. The measurements of the lensed EE and TE spectra are the most precise to date at ℓ = 1800 – 4000 and ℓ = 2200 – 4000 , respectively. Combining our TT / TE / EE spectra with previously published SPT-3G CMB lensing results, we find parameters for the standard Λ cold dark matter ( Λ CDM ) model consistent with Planck and ACT DR6 with comparable constraining power. We report a Hubble constant of H 0 = 66.66 ± 0.60 km s - 1 Mpc - 1 from SPT-3G alone, 6.2 σ away from local measurements from SH0ES. For the first time, combined ground-based ( SPT + ACT ) CMB primary and lensing data have reached Planck’s constraining power on some parameters, a milestone for CMB cosmology. The combination of these three CMB experiments yields the tightest CMB constraints to date, with H 0 = 67.19 ± 0.38 km s - 1 Mpc - 1 , and the amplitude of clustering σ 8 = 0.8137 ± 0.0037 . CMB data alone show no evidence for physics beyond Λ CDM , however, we observe a 2.8 σ difference in Λ CDM between CMB and baryon acoustic oscillation (BAO) results from DESI-DR2, which is relaxed in extended models. The combination of CMB and BAO yields 2 − 3 σ shifts from Λ CDM in the curvature of the Universe, the amplitude of CMB lensing, or the dark energy equation of state. It also drives mild preferences for models that address the Hubble tension through modified recombination or variations in the electron mass in a nonflat Universe. This work highlights the growing power of ground-based CMB experiments and lays a foundation for further cosmological analyses with SPT-3G.

Camphuis, Etienne [Sorbonne Université; CNRS; Inst↗
DOE OSTI2025

The Dark Energy Camera All Data Everywhere cosmic shear project V: Constraints on cosmology and astrophysics from 270 million galaxies across 13,000 deg$^2$ of the sky

We present constraints on models of cosmology and astrophysics using cosmic shear data vectors from three datasets: the northern and southern Galactic cap of the Dark Energy Camera All Data Everywhere (DECADE) project, and the Dark Energy Survey (DES) Year 3. These data vectors combined consist of 270 million galaxies spread across 13,000 ${\rm deg}^2$ of the sky. We first extract constraints for $Λ$CDM cosmology and find $S_8= 0.805^{+0.019}_{-0.019}$ and $Ω_{\rm m} = 0.262^{+0.023}_{-0.036}$, which is consistent within $1.9 σ$ of constraints from the Planck satellite. Extending our analysis to dynamical dark energy models shows that lensing provides some (but still minor) improvements to existing constraints from supernovae and baryon acoustic oscillations. Finally, we study six different models for the impact of baryons on the matter power spectrum. We show the different models provide consistent constraints on baryon suppression, and associated cosmology, once the astrophysical priors are sufficiently wide. Current scale-cut approaches for mitigating baryon contamination result in a residual bias of $\approx 0.3σ$ in the $S_8, Ω_{\rm m}$ posterior. Using all scales with dedicated baryon modeling leads to negligible improvement as the new information is used solely to self-calibrate the baryon model on small scales. Additional non-lensing datasets, and/or calibrations of the baryon model, will be required to access the full statistical power of the lensing measurements. The combined dataset in this work represents the largest lensing dataset to date (most galaxies, largest area) and provides an apt testing ground for analyses of upcoming datasets from Stage IV surveys. The DECADE shear catalogs, data vectors, and likelihoods are made publicly available.

Anbajagane, D. [Chicago U., Astron. Astrophys. Ctr↗
DOE OSTI2021

A demonstration of improved constraints on primordial gravitational waves with delensing

We present a constraint on the tensor-to-scalar ratio, $r$, derived from measurements of cosmic microwave background (CMB) polarization $B$-modes with "delensing,'' whereby the uncertainty on $r$ contributed by the sample variance of the gravitational lensing $B$-modes is reduced by cross-correlating against a lensing $B$-mode template. This template is constructed by combining an estimate of the polarized CMB with a tracer of the projected large-scale structure. The large-scale-structure tracer used is a map of the cosmic infrared background derived from Planck satellite data, while the polarized CMB map comes from a combination of South Pole Telescope, BICEP/Keck, and Planck data. We expand the BICEP/Keck likelihood analysis framework to accept a lensing template and apply it to the BICEP/Keck data set collected through 2014 using the same parametric foreground modelling as in the previous analysis. From simulations, we find that the uncertainty on $r$ is reduced by $\sim10\%$, from $\sigma(r)$= 0.024 to 0.022, which can be compared with a $\sim26\%$ reduction obtained when using a perfect lensing template. Applying the technique to the real data, the constraint on $r$ is improved from $r_{0.05} < 0.090$ to $r_{0.05} < 0.082$ (95% C.L.). Furthermore, this is the first demonstration of improvement in an $r$ constraint through delensing.

79 ASTRONOMY AND ASTROPHYSICS↗