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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Dark Energy Survey Year 3 results: Simulation-based cosmological inference with wavelet harmonics, scattering transforms, and moments of weak lensing mass maps. II. cosmological results

Here, we present a simulation-based cosmological analysis using a combination of Gaussian and non-Gaussian statistics of the weak lensing mass (convergence) maps from the first three years of the Dark Energy Survey. We implement the following: (1) second and third moments; (2) wavelet phase harmonics; (3) the scattering transform. Our analysis is fully based on simulations, spans a space of seven 𝑤 Cold Dark Matter (𝑤⁢ CDM) cosmological parameters, and forward models the most relevant sources of systematics inherent in the data: masks, noise variations, clustering of the sources, intrinsic alignments, and shear and redshift calibration. We implement a neural network compression of the summary statistics, and we estimate the parameter posteriors using a simulation-based inference approach. Including and combining different non-Gaussian statistics is a powerful tool that strongly improves constraints over Gaussian statistics (in our case, the second moments); in particular, the figure of merit (𝑆 8 , Ω m ) is improved by 70% (Λ ⁢CDM) and 90% (𝑤 ⁢CDM). When all the summary statistics are combined, we achieve a 2% constraint on the amplitude of fluctuations parameter 𝑆 8 ≡ 𝜎 8 ⁢(Ω m /0.3) 0.5 , obtaining 𝑆 8 = 0.794 ±0.017 (Λ⁢ CDM) and 𝑆 8 = 0.817 ±0.021 (𝑤 ⁢CDM), and a ∼10% constraint on Ω m , obtaining Ω m =0.259 ±0.025 (Λ ⁢CDM) and Ω m = 0.273 ±0.029 (𝑤⁢ CDM). In the context of the 𝑤⁢ CDM scenario, these statistics also strengthen the constraints on the parameter 𝑤, obtaining 𝑤 <−0.72. The constraints from different statistics are shown to be internally consistent (with a 𝑝-value>0.1 for all combinations of statistics examined). We compare our results to other weak lensing results from the first three years of the Dark Energy Survey data, finding good consistency; we also compare with results from external datasets, such as planck constraints from the cosmic microwave background, finding statistical agreement, with discrepancies no greater than <2.2⁢𝜎.

79 ASTRONOMY AND ASTROPHYSICS↗
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 OSTI2020

Optimizing automatic morphological classification of galaxies with machine learning and deep learning using Dark Energy Survey imaging

There are several supervised machine learning methods used for the application of automated morphological classification of galaxies; however, there has not yet been a clear comparison of these different methods using imaging data, or an investigation for maximizing their effectiveness. We carry out a comparison between several common machine learning methods for galaxy classification [Convolutional Neural Network (CNN), K-nearest neighbour, logistic regression, Support Vector Machine, Random Forest, and Neural Networks] by using Dark Energy Survey (DES) data combined with visual classifications from the Galaxy Zoo 1 project (GZ1). Our goal is to determine the optimal machine learning methods when using imaging data for galaxy classification. We show that CNN is the most successful method of these ten methods in our study. Using a sample of ~2800 galaxies with visual classification from GZ1, we reach an accuracy of ~0.99 for the morphological classification of ellipticals and spirals. The further investigation of the galaxies that have a different ML and visual classification but with high predicted probabilities in our CNN usually reveals the incorrect classification provided by GZ1. We further find the galaxies having a low probability of being either spirals or ellipticals are visually lenticulars (S0), demonstrating that supervised learning is able to rediscover that this class of galaxy is distinct from both ellipticals and spirals. We confirm that ~2.5 percent galaxies are misclassified by GZ1 in our study. After correcting these galaxies’ labels, we improve our CNN performance to an average accuracy of over 0.99 (accuracy of 0.994 is our best result).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

The Dark Energy Survey Bright Arcs Survey: Candidate Strongly Lensed Galaxy Systems from the Dark Energy Survey 5000 Square Degree Footprint

We report the combined results of eight searches for strong gravitational lens systems in the full 5000 square degrees of Dark Energy Survey (DES) observations. The observations accumulated by the end of the third observing season fully covered the DES footprint in five filters (grizY), with an i-band limiting magnitude (at 10σ) of 23.44. In four searches, a list of potential candidates was identified using a color and magnitude selection from the object catalogs created from the first three observing seasons. Three other searches were conducted at the locations of previously identified galaxy clusters. Cutout images of potential candidates were then visually scanned using an object viewer. An additional set of candidates came from a data-quality check of a subset of the color–coadd tiles created from the full DES six-season data set. A short list of the most promising strong-lens candidates was then numerically ranked according to whether or not we judged them to be bona fide strong gravitational lens systems. These searches discovered a diverse set of 247 strong-lens candidate systems, of which 81 are identified for the first time. We provide the coordinates, magnitudes, and photometric properties of the lens and source objects, and an estimate of the Einstein radius for 81 new systems and 166 previously reported systems. This catalog will be of use for selecting interesting systems for detailed follow up, studies of galaxy cluster and group mass profiles, as well as a training/validation set for automated strong-lens searches.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Dark Energy Survey Year 3 results: calibration of lens sample redshift distributions using clustering redshifts with BOSS/eBOSS

ABSTRACT We present clustering redshift measurements for Dark Energy Survey (DES) lens sample galaxies used in weak gravitational lensing and galaxy clustering studies. To perform these measurements, we cross-correlate with spectroscopic galaxies from the Baryon Acoustic Oscillation Survey (BOSS) and its extension, eBOSS. We validate our methodology in simulations, including a new technique to calibrate systematic errors that result from the galaxy clustering bias, and we find that our method is generally unbiased in calibrating the mean redshift. We apply our method to the data, and estimate the redshift distribution for 11 different photometrically selected bins. We find general agreement between clustering redshift and photometric redshift estimates, with differences on the inferred mean redshift found to be below |Δz| = 0.01 in most of the bins. We also test a method to calibrate a width parameter for redshift distributions, which we found necessary to use for some of our samples. Our typical uncertainties on the mean redshift ranged from 0.003 to 0.008, while our uncertainties on the width ranged from 4 to 9 per cent. We discuss how these results calibrate the photometric redshift distributions used in companion papers for DES Year 3 results.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Cross-correlation of Dark Energy Survey Year 3 lensing data with ACT and Planck thermal Sunyaev-Zel’dovich effect observations. I. Measurements, systematics tests, and feedback model constraints

Here we present a tomographic measurement of the cross-correlation between thermal Sunyaev-Zel’dovich (TSZ) maps from Planck and the Atacama Cosmology Telescope and weak galaxy lensing shears measured during the first three years of observations of the Dark Energy Survey. This correlation is sensitive to the thermal energy in baryons over a wide redshift range and is therefore a powerful probe of astrophysical feedback. We detect the correlation at a statistical significance of 21σ, the highest significance to date. We examine the TSZ maps for potential contaminants, including cosmic infrared background and radio sources, finding that cosmic infrared background has a substantial impact on our measurements and must be taken into account in our analysis. We use the cross-correlation measurements to test different feedback models. In particular, we model the TSZ using several different pressure profile models calibrated against hydrodynamical simulations. Our analysis marginalizes over redshift uncertainties, shear calibration biases, and intrinsic alignment effects. We also marginalize over Ω m and σ 8 using Planck or DES priors. We find that the data prefer the model with a low amplitude of the pressure profile at small scales, compatible with a scenario with strong active galactic nuclei feedback and ejection of gas from the inner part of the halos. When using a more flexible model for the shear profile, constraints are weaker, and the data cannot discriminate between different baryonic prescriptions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Dark Energy Survey Year 3 results: Simulation-based cosmological inference with wavelet harmonics, scattering transforms, and moments of weak lensing mass maps. Validation on simulations

Beyond-two-point statistics contain additional information on cosmological as well as astrophysical and observational (systematics) parameters. In this methodology paper we provide an end-to-end simulationbased analysis of a set of Gaussian and non-Gaussian weak lensing statistics using detailed mock catalogs of the Dark Energy Survey (DES). Here, we implement: 1) second and third moments; 2) wavelet phase harmonics (WPH); 3) the scattering transform (ST). Our analysis is fully based on simulations, it spans a space of seven $νw$CDM cosmological parameters, and it forward models the most relevant sources of systematics of the data (masks, noise variations, clustering of the sources, intrinsic alignments, and shear and redshift calibration). We implement a neural network compression of the summary statistics, and we estimate the parameter posteriors using a likelihood-free-inference approach. We validate the pipeline extensively, and we find that WPH exhibits the strongest performance when combined with second moments, followed by ST, and then by third moments. The combination of all the different statistics further enhances constraints with respect to second moments, up to 25 percent, 15 percent, and 90 percent for S 8 , Ω m , and the figure-of-merit FoM S8;Ωm , respectively. We further find that non-Gaussian statistics improve constraints on w and on the amplitude of intrinsic alignment with respect to second moments constraints. The methodological advances presented here are suitable for application to Stage IV surveys from Euclid, Rubin-LSST, and Roman with additional validation on mock catalogs for each survey. In a companion paper we present an application to DES Year 3 data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Joint analysis of Dark Energy Survey Year 3 data and CMB lensing from SPT and Planck . I. Construction of CMB lensing maps and modeling choices

Joint analyses of cross-correlations between measurements of galaxy positions, galaxy lensing, and lensing of the cosmic microwave background (CMB) offer powerful constraints on the large-scale structure of the Universe. In a forthcoming analysis, we will present cosmological constraints from the analysis of such cross-correlations measured using Year 3 data from the Dark Energy Survey (DES), and CMB data from the South Pole Telescope (SPT) and Planck. Here we present two key ingredients of this analysis: (1) an improved CMB lensing map in the SPT-SZ survey footprint and (2) the analysis methodology that will be used to extract cosmological information from the cross-correlation measurements. Relative to previous lensing maps made from the same CMB observations, we have implemented techniques to remove contamination from the thermal Sunyaev Zel’dovich effect, enabling the extraction of cosmological information from smaller angular scales of the cross-correlation measurements than in previous analyses with DES Year 1 data. We describe our model for the cross-correlations between these maps and DES data, and validate our modeling choices to demonstrate the robustness of our analysis. We then forecast the expected cosmological constraints from the galaxy survey-CMB lensing auto and cross-correlations. We find that the galaxy-CMB lensing and galaxy shear-CMB lensing correlations will on their own provide a constraint on S 8 =σ 8 $\sqrt{Ωm/0.3}$ at the few percent level, providing a powerful consistency check for the DES-only constraints. Finally, we explore scenarios where external priors on shear calibration are removed, finding that the joint analysis of CMB lensing cross-correlations can provide constraints on the shear calibration amplitude at the 5% to 10% level.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Joint analysis of Dark Energy Survey Year 3 data and CMB lensing from SPT and P l a n c k . II. Cross-correlation measurements and cosmological constraints

Cross-correlations of galaxy positions and galaxy shears with maps of gravitational lensing of the cosmic microwave background (CMB) are sensitive to the distribution of large-scale structure in the Universe. Such cross-correlations are also expected to be immune to some of the systematic effects that complicate correlation measurements internal to galaxy surveys. We present measurements and modeling of the cross-correlations between galaxy positions and galaxy lensing measured in the first three years of data from the Dark Energy Survey with CMB lensing maps derived from a combination of data from the 2500 deg 2 SPT-SZ survey conducted with the South Pole Telescope and full-sky data from the Planck satellite. The CMB lensing maps used in this analysis have been constructed in a way that minimizes biases from the thermal Sunyaev Zel’dovich effect, making them well suited for cross-correlation studies. The total signal-to-noise of the cross-correlation measurements is 23.9 (25.7) when using a choice of angular scales optimized for a linear (nonlinear) galaxy bias model. Here we use the cross-correlation measurements to obtain constraints on cosmological parameters. For our fiducial galaxy sample, which consist of four bins of magnitude-selected galaxies, we find constraints of Ω m =0.272$^{+0.032}_{-0.052}$ and S 8 ≡σ8$\sqrt{Ω_m/0.3}$=0.736$^{+0.032}_{-0.028}$ (Ω m =0.245$^{+0.026}_{-0.044}$ and S 8 =0.734$^{+0.035}_{-0.028}$) when assuming linear (nonlinear) galaxy bias in our modeling. Considering only the cross-correlation of galaxy shear with CMB lensing, we find Ω m =0.270$^{+0.043}_{-0.061}$ and S 8 =0.740$^{+0.034}_{-0.029}$. Our constraints on S8 are consistent with recent cosmic shear measurements, but lower than the values preferred by primary CMB measurements from Planck.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Cross-correlation of Dark Energy Survey Year 3 lensing data with ACT and P l a n c k thermal Sunyaev-Zel’dovich effect observations. 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. Phys. Rev. D 105, 123525 (2022)), 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 (B ≡ M 500c /M SZ 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.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Optimal parameterizations for observational constraints on thawing dark energy

Time-varying dark energy is often modeled in observational analyses through generic parameterizations of its equation of state w(z), which typically use two free parameters {w 0 , w a } to span a broad range of behaviors as a function of redshift. However, this broad range of behaviors can only approximately capture the dynamics of any given microphysical theory of dark energy. A complementary approach is to use targeted parameterizations designed to model specific classes of dynamical dark energy with greater precision. Focusing on the class of thawing dark energy, we quantify and compare the precision with which nineteen generic and targeted parameterizations can capture the dynamics of physically motivated thawing quintessence theories. We find that a targeted parameterization derived from a Padé expansion of w is the most reliable of these, producing accurate reconstructions of w(z), the expansion history H(z), and cosmological parameters such as H 0 and Ω m for a broad range of microphysical theories.

dark energy experiments↗
DOE OSTI2022

Atacama Cosmology Telescope: Constraints on prerecombination early dark energy

The early dark energy (EDE) scenario aims to increase the value of the Hubble constant (H0) inferred from cosmic microwave background (CMB) data over that found in the standard cosmological model (Λ CDM ), via the introduction of a new form of energy density in the early Universe. The EDE component briefly accelerates cosmic expansion just prior to recombination, which reduces the physical size of the sound horizon imprinted in the CMB. Previous work has found that nonzero EDE is not preferred by Planck CMB power spectrum data alone, which yield a 95% confidence level (C.L.) upper limit f EDE < 0.087 on the maximal fractional contribution of the EDE field to the cosmic energy budget. In this paper, we fit the EDE model to CMB data from the Atacama Cosmology Telescope (ACT) data release 4. We find that a combination of ACT, large-scale Planck TT (similar to WMAP), Planck CMB lensing, and BAO data prefers the existence of EDE at >99.7 % C .L . : f EDE = 0.091$^{+0.020}_{-0.036}$, with H 0 = 70.9$^{+1.0}_{-2.0}$ km/s/Mpc (both 68% C.L.). From a model-selection standpoint, we find that EDE is favored over Λ CDM by these data at roughly 3 σ significance. In contrast, a joint analysis of the full Planck and ACT data yields no evidence for EDE, as previously found for Planck alone. We show that the preference for EDE in ACT alone is driven by its TE and EE power spectrum data. The tight constraint on EDE from Planck alone is driven by its high-ℓ TT power spectrum data. Understanding whether these differing constraints are physical in nature, due to systematics, or simply a rare statistical fluctuation is of high priority. Here, the best-fit EDE models to ACT and Planck exhibit coherent differences across a wide range of multipoles in TE and EE, indicating that a powerful test of this scenario is anticipated with near-future data from ACT and other ground-based experiments.

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 OSTI2024

Cosmology of dark energy radiation

In this work, we quantify the cosmological signatures of dark energy radiation—a novel description of dark energy, which proposes that the dynamical component of dark energy is comprised of a thermal bath of relativistic particles sourced by thermal friction from a slowly rolling scalar field. For a minimal model with particle production emerging from first principles, we find that the abundance of radiation sourced by dark energy can be as large as Ω DER = 0.03, exceeding the bounds on relic dark radiation by three orders of magnitude. Although the background and perturbative evolution of dark energy radiation are distinct from Quintessence, we find that current and near-future cosmic microwave background and supernova data will not distinguish these models of dark energy. We also find that our constraints on all models are dominated by their impact on the expansion rate of the Universe. Considering extensions that allow the dark radiation to populate neutrinos, axions, and dark photons, we evaluate the direct detection prospects of a thermal background comprised of these candidates consistent with cosmological constraints on dark energy radiation. Our study indicates that a resolution of ~6 meV is required to achieve sensitivity to relativistic neutrinos compatible with dark energy radiation in a neutrino capture experiment on tritium. We also find that dark matter axion experiments lack sensitivity to a relativistic thermal axion background, even if enhanced by dark energy radiation, and dedicated search strategies are required to probe new parameter space. We derive constraints arising from a dark photon background from oscillations into visible photons, and find that viable parameter space can be explored with the late dark energy radiation experiment.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Overview of the Fiber System for the Dark Energy Spectroscopic Instrument

The Dark Energy Spectroscopic Instrument (DESI) is a revolutionary instrument designed for precise measurements of cosmic distances and the investigation of dark energy. DESI utilizes 5000 optical fibers to simultaneously measure the spectra of distant objects and aims to measure 40 million galaxies and quasars in a 5 yr survey. One of the critical challenges to DESI's success was ensuring that the fiber system was not only highly efficient but also delivered a highly stable beam enabling more reliable sky subtraction for measurements of faint objects. We achieved this stability by minimizing the stress on the fiber system during the manufacture and operation of the telescope and fiber positioning robots. We installed the DESI fiber system on the 4 m Mayall telescope with ≥99% of fibers intact, and the instrument has delivered superb optical performance throughout the initial years of the DESI survey, including ≥90% average throughput when injected with a focal ratio of ~f/3.9 as delivered by the primary focus corrector, excluding fiber absorption losses. The design of DESI required multiple innovations to achieve these requirements, such as cleaved fibers bonded with a UV-curing epoxy to glass ferrules in the focal plane and fusion splicing instead of physical connectors. In this paper, we describe the development, delivery, and installation of the fiber system, the innovations that made the state-of-the-art performance possible, and the key lessons learned that could benefit future projects.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Chameleon early dark energy and the Hubble tension

Early dark energy (EDE) offers a particularly interesting theoretical approach to the Hubble tension, albeit one that introduces its own set of challenges, including a new “why then” problem related to the EDE injection time at matter-radiation equality, and a mild worsening of the large-scale structure (LSS) tension. Both these challenges center on the properties of dark matter, which becomes the dominant component of the Universe at EDE injection and is also responsible for seeding LSS. Driven by this, we present the potential of couplings between EDE and dark matter to address these challenges, focusing on a mechanism similar to chameleon dark energy theories, deeming this chameleon early dark energy (CEDE). We present relevant background and perturbation equations and study the dynamics of the case of a quartic scalar potential and an exponential coupling.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2010

James Webb Space Telescope Studies of Dark Energy

The Hubble Space Telescope (HST) has contributed significantly to studies of dark energy. It was used to find the first evidence of deceleration at z=1.8 (Riess et al. 2001) through the serendipitous discovery of a type 1a supernova (SN1a) in the Hubble Deep Field. The discovery of deceleration at z greater than 1 was confirmation that the apparent acceleration at low redshift (Riess et al. 1998; Perlmutter et al. 1999) was due to dark energy rather than observational or astrophysical effects such as systematic errors, evolution in the SN1a population or intergalactic dust. The GOODS project and associated follow-up discovered 21 SN1a, expanding on this result (Riess et al. 2007). HST has also been used to constrain cosmological parameters and dark energy through weak lensing measurements in the COSMOS survey (Massey et al 2007; Schrabback et al 2009) and strong gravitational lensing with measured time delays (Suyu et al 2010). Constraints on dark energy are often parameterized as the equation of state, w = P/p. For the cosmological constant model, w = -1 at all times; other models predict a change with time, sometimes parameterized generally as w(a) or approximated as w(sub 0)+(1-a)w(sub a), where a = (1+z)(sup -1) is the scale factor of the universe relative to its current scale. Dark energy can be constrained through several measurements. Standard candles, such as SN1a, provide a direct measurement of the luminosity distance as a function of redshift, which can be converted to H(z), the change in the Hubble constant with redshift. An analysis of weak lensing in a galaxy field can be used to derive the angular-diameter distance from the weak-lensing equation and to measure the power spectrum of dark-matter halos, which constrains the growth of structure in the Universe. Baryonic acoustic oscillations (BAO), imprinted on the distribution of matter at recombination, provide a standard rod for measuring the cosmological geometry. Strong gravitational lensing of a time-variable source gives the angular diameter distance through measured time delays of multiple images. Finally, the growth of structure can also be constrained by measuring the mass of the largest galaxy clusters over cosmic time. HST has contributed to the study of dark energy through SN1a and gravitational lensing, as discussed above. HST has also helped to characterize galaxy clusters and the HST-measured constraints on the current Hubble constant H(sub 0) are relevant to the interpretation of dark energy measurements (Riess et al 2009a). HST has not been used to constrain BAO as the large number of galaxy redshifts required, of order 100 million, is poorly matched to HST's capabilities. As the successor to HST, the James Webb Space Telescope (JWST; Gardner et al 2006) will continue and extend HST's dark energy work in several ways.

Gardner, Jonathan P.↗