arXiv subjects

T. M. Davis

Publications and source records attributed to T. M. Davis.

At least 73 records · Page 4Linked to original sources

arXiv2024

DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations

We present cosmological results from the measurement of baryon acoustic oscillations (BAO) in galaxy, quasar and Lyman-$α$ forest tracers from the first year of observations from the Dark Energy Spectroscopic Instrument (DESI), to be released in the DESI Data Release 1. DESI BAO provide robust measurements of the transverse comoving distance and Hubble rate, or their combination, relative to the sound horizon, in seven redshift bins from over 6 million extragalactic objects in the redshift range $0.1 -1$ and $w_a<0$. This preference is 2.6$σ$ for the DESI+CMB combination, and persists or grows when SN~Ia are added in, giving results discrepant with the $Λ$CDM model at the $2.5σ$, $3.5σ$ or $3.9σ$ levels for the addition of Pantheon+, Union3, or DES-SN5YR datasets respectively. For the flat $Λ$CDM model with the sum of neutrino mass $\sum m_ν$ free, combining the DESI and CMB data yields an upper limit $\sum m_ν< 0.072$ $(0.113)$ eV at 95% confidence for a $\sum m_ν>0$ $(\sum m_ν>0.059)$ eV prior. These neutrino-mass constraints are substantially relaxed in models beyond $Λ$CDM. [Abridged.]

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arXiv2024

DESI 2024: Reconstructing Dark Energy using Crossing Statistics with DESI DR1 BAO data

We implement Crossing Statistics to reconstruct in a model-agnostic manner the expansion history of the universe and properties of dark energy, using DESI Data Release 1 (DR1) BAO data in combination with one of three different supernova compilations (PantheonPlus, Union3, and DES-SN5YR) and Planck CMB observations. Our results hint towards an evolving and emergent dark energy behaviour, with negligible presence of dark energy at $z\gtrsim 1$, at varying significance depending on the data sets combined. In all these reconstructions, the cosmological constant lies outside the $95\%$ confidence intervals for some redshift ranges. This dark energy behaviour, reconstructed using Crossing Statistics, is in agreement with results from the conventional $w_0$--$w_a$ dark energy equation of state parametrization reported in the DESI Key cosmology paper. Our results add an extensive class of model-agnostic reconstructions with acceptable fits to the data, including models where cosmic acceleration slows down at low redshifts. We also report constraints on $H_0r_d$ from our model-agnostic analysis, independent of the pre-recombination physics.

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arXiv2024

The Early Data Release of the Dark Energy Spectroscopic Instrument

The Dark Energy Spectroscopic Instrument (DESI) completed its five-month Survey Validation in May 2021. Spectra of stellar and extragalactic targets from Survey Validation constitute the first major data sample from the DESI survey. This paper describes the public release of those spectra, the catalogs of derived properties, and the intermediate data products. In total, the public release includes good-quality spectral information from 466,447 objects targeted as part of the Milky Way Survey, 428,758 as part of the Bright Galaxy Survey, 227,318 as part of the Luminous Red Galaxy sample, 437,664 as part of the Emission Line Galaxy sample, and 76,079 as part of the Quasar sample. In addition, the release includes spectral information from 137,148 objects that expand the scope beyond the primary samples as part of a series of secondary programs. Here, we describe the spectral data, data quality, data products, Large-Scale Structure science catalogs, access to the data, and references that provide relevant background to using these spectra.

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arXiv2024

DESI 2024 IV: Baryon Acoustic Oscillations from the Lyman Alpha Forest

We present the measurement of Baryon Acoustic Oscillations (BAO) from the Lyman-$α$ (Ly$α$) forest of high-redshift quasars with the first-year dataset of the Dark Energy Spectroscopic Instrument (DESI). Our analysis uses over $420\,000$ Ly$α$ forest spectra and their correlation with the spatial distribution of more than $700\,000$ quasars. An essential facet of this work is the development of a new analysis methodology on a blinded dataset. We conducted rigorous tests using synthetic data to ensure the reliability of our methodology and findings before unblinding. Additionally, we conducted multiple data splits to assess the consistency of the results and scrutinized various analysis approaches to confirm their robustness. For a given value of the sound horizon ($r_d$), we measure the expansion at $z_{\rm eff}=2.33$ with 2\% precision, $H(z_{\rm eff}) = (239.2 \pm 4.8) (147.09~{\rm Mpc} /r_d)$ km/s/Mpc. Similarly, we present a 2.4\% measurement of the transverse comoving distance to the same redshift, $D_M(z_{\rm eff}) = (5.84 \pm 0.14) (r_d/147.09~{\rm Mpc})$ Gpc. Together with other DESI BAO measurements at lower redshifts, these results are used in a companion paper to constrain cosmological parameters.

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arXiv2024

The Dark Energy Survey Supernova Program: Investigating Beyond-$Λ$CDM

We report constraints on a variety of non-standard cosmological models using the full 5-year photometrically-classified type Ia supernova sample from the Dark Energy Survey (DES-SN5YR). Both Akaike Information Criterion (AIC) and Suspiciousness calculations find no strong evidence for or against any of the non-standard models we explore. When combined with external probes, the AIC and Suspiciousness agree that 11 of the 15 models are moderately preferred over Flat-$Λ$CDM suggesting additional flexibility in our cosmological models may be required beyond the cosmological constant. We also provide a detailed discussion of all cosmological assumptions that appear in the DES supernova cosmology analyses, evaluate their impact, and provide guidance on using the DES Hubble diagram to test non-standard models. An approximate cosmological model, used to perform bias corrections to the data holds the biggest potential for harbouring cosmological assumptions. We show that even if the approximate cosmological model is constructed with a matter density shifted by $ΔΩ_m\sim0.2$ from the true matter density of a simulated data set the bias that arises is sub-dominant to statistical uncertainties. Nevertheless, we present and validate a methodology to reduce this bias.

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arXiv2024

Baryon Acoustic Oscillation Theory and Modelling Systematics for the DESI 2024 results

This paper provides a comprehensive overview of how fitting of Baryon Acoustic Oscillations (BAO) is carried out within the upcoming Dark Energy Spectroscopic Instrument's (DESI) 2024 results using its DR1 dataset, and the associated systematic error budget from theory and modelling of the BAO. We derive new results showing how non-linearities in the clustering of galaxies can cause potential biases in measurements of the isotropic ($α_{\mathrm{iso}}$) and anisotropic ($α_{\mathrm{ap}}$) BAO distance scales, and how these can be effectively removed with an appropriate choice of reconstruction algorithm. We then demonstrate how theory leads to a clear choice for how to model the BAO and develop, implement and validate a new model for the remaining smooth-broadband (i.e., without BAO) component of the galaxy clustering. Finally, we explore the impact of all remaining modelling choices on the BAO constraints from DESI using a suite of high-precision simulations, arriving at a set of best-practices for DESI BAO fits, and an associated theory and modelling systematic error. Overall, our results demonstrate the remarkable robustness of the BAO to all our modelling choices and motivate a combined theory and modelling systematic error contribution to the post-reconstruction DESI BAO measurements of no more than $0.1\%$ ($0.2\%$) for its isotropic (anisotropic) distance measurements. We expect the theory and best-practices laid out to here to be applicable to other BAO experiments in the era of DESI and beyond.

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arXiv2024

The Dark Energy Survey Supernova Program: Slow supernovae show cosmological time dilation out to $z \sim 1$

We present a precise measurement of cosmological time dilation using the light curves of 1504 type Ia supernovae from the Dark Energy Survey spanning a redshift range $0.1\lesssim z\lesssim 1.2$. We find that the width of supernova light curves is proportional to $(1+z)$, as expected for time dilation due to the expansion of the Universe. Assuming type Ia supernovae light curves are emitted with a consistent duration $Δt_{\rm em}$, and parameterising the observed duration as $Δt_{\rm obs}=Δt_{\rm em}(1+z)^b$, we fit for the form of time dilation using two methods. Firstly, we find that a power of $b \approx 1$ minimises the flux scatter in stacked subsamples of light curves across different redshifts. Secondly, we fit each target supernova to a stacked light curve (stacking all supernovae with observed bandpasses matching that of the target light curve) and find $b=1.003\pm0.005$ (stat) $\pm\,0.010$ (sys). Thanks to the large number of supernovae and large redshift-range of the sample, this analysis gives the most precise measurement of cosmological time dilation to date, ruling out any non-time-dilating cosmological models at very high significance.

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arXiv2024

The Dark Energy Survey 5-year photometrically classified type Ia supernovae without host-galaxy redshifts

Current and future Type Ia Supernova (SN Ia) surveys will need to adopt new approaches to classifying SNe and obtaining their redshifts without spectra if they wish to reach their full potential. We present here a novel approach that uses only photometry to identify SNe Ia in the 5-year Dark Energy Survey (DES) dataset using the SuperNNova classifier. Our approach, which does not rely on any information from the SN host-galaxy, recovers SNe Ia that might otherwise be lost due to a lack of an identifiable host. We select 2,298 high-quality SNe Ia from the DES 5-year dataset an almost complete sample of detected SNe Ia. More than 700 of these have no spectroscopic host redshift and are potentially new SNIa compared to the DES-SN5YR cosmology analysis. To analyse these SNe Ia, we derive their redshifts and properties using only their light-curves with a modified version of the SALT2 light-curve fitter. Compared to other DES SN Ia samples with spectroscopic redshifts, our new sample has in average higher redshift, bluer and broader light-curves, and fainter host-galaxies. Future surveys such as LSST will also face an additional challenge, the scarcity of spectroscopic resources for follow-up. When applying our novel method to DES data, we reduce the need for follow-up by a factor of four and three for host-galaxy and live SN respectively compared to earlier approaches. Our novel method thus leads to better optimisation of spectroscopic resources for follow-up.

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arXiv2024

Evaluating Cosmological Biases using Photometric Redshifts for Type Ia Supernova Cosmology with the Dark Energy Survey Supernova Program

Cosmological analyses with Type Ia Supernovae (SNe Ia) have traditionally been reliant on spectroscopy for both classifying the type of supernova and obtaining reliable redshifts to measure the distance-redshift relation. While obtaining a host-galaxy spectroscopic redshift for most SNe is feasible for small-area transient surveys, it will be too resource intensive for upcoming large-area surveys such as the Vera Rubin Observatory Legacy Survey of Space and Time, which will observe on the order of millions of SNe. Here we use data from the Dark Energy Survey (DES) to address this problem with photometric redshifts (photo-z) inferred directly from the SN light-curve in combination with Gaussian and full p(z) priors from host-galaxy photo-z estimates. Using the DES 5-year photometrically-classified SN sample, we consider several photo-z algorithms as host-galaxy photo-z priors, including the Self-Organizing Map redshifts (SOMPZ), Bayesian Photometric Redshifts (BPZ), and Directional-Neighbourhood Fitting (DNF) redshift estimates employed in the DES 3x2 point analyses. With detailed catalog-level simulations of the DES 5-year sample, we find that the simulated w can be recovered within $\pm$0.02 when using SN+SOMPZ or DNF prior photo-z, smaller than the average statistical uncertainty for these samples of 0.03. With data, we obtain biases in w consistent with simulations within ~1$σ$ for three of the five photo-z variants. We further evaluate how photo-z systematics interplay with photometric classification and find classification introduces a subdominant systematic component. This work lays the foundation for next-generation fully photometric SNe Ia cosmological analyses.

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arXiv2024

SPT Clusters with DES and HST Weak Lensing. II. Cosmological Constraints from the Abundance of Massive Halos

We present cosmological constraints from the abundance of galaxy clusters selected via the thermal Sunyaev-Zel'dovich (SZ) effect in South Pole Telescope (SPT) data with a simultaneous mass calibration using weak gravitational lensing data from the Dark Energy Survey (DES) and the Hubble Space Telescope (HST). The cluster sample is constructed from the combined SPT-SZ, SPTpol ECS, and SPTpol 500d surveys, and comprises 1,005 confirmed clusters in the redshift range $0.25-1.78$ over a total sky area of 5,200 deg$^2$. We use DES Year 3 weak-lensing data for 688 clusters with redshifts $z<0.95$ and HST weak-lensing data for 39 clusters with $0.6<z<1.7$. The weak-lensing measurements enable robust mass measurements of sample clusters and allow us to empirically constrain the SZ observable--mass relation. For a flat $Λ$CDM cosmology, and marginalizing over the sum of massive neutrinos, we measure $Ω_\mathrm{m}=0.286\pm0.032$, $σ_8=0.817\pm0.026$, and the parameter combination $σ_8\,(Ω_\mathrm{m}/0.3)^{0.25}=0.805\pm0.016$. Our measurement of $S_8\equivσ_8\,\sqrt{Ω_\mathrm{m}/0.3}=0.795\pm0.029$ and the constraint from Planck CMB anisotropies (2018 TT,TE,EE+lowE) differ by $1.1σ$. In combination with that Planck dataset, we place a 95% upper limit on the sum of neutrino masses $\sum m_ν<0.18$ eV. When additionally allowing the dark energy equation of state parameter $w$ to vary, we obtain $w=-1.45\pm0.31$ from our cluster-based analysis. In combination with Planck data, we measure $w=-1.34^{+0.22}_{-0.15}$, or a $2.2σ$ difference with a cosmological constant. We use the cluster abundance to measure $σ_8$ in five redshift bins between 0.25 and 1.8, and we find the results to be consistent with structure growth as predicted by the $Λ$CDM model fit to Planck primary CMB data.

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arXiv2024

Mass calibration of DES Year-3 clusters via SPT-3G CMB cluster lensing

We measure the stacked lensing signal in the direction of galaxy clusters in the Dark Energy Survey Year 3 (DES Y3) redMaPPer sample, using cosmic microwave background (CMB) temperature data from SPT-3G, the third-generation CMB camera on the South Pole Telescope (SPT). We estimate the lensing signal using temperature maps constructed from the initial 2 years of data from the SPT-3G 'Main' survey, covering 1500 deg$^2$ of the Southern sky. We then use this signal as a proxy for the mean cluster mass of the DES sample. In this work, we employ three versions of the redMaPPer catalogue: a Flux-Limited sample containing 8865 clusters, a Volume-Limited sample with 5391 clusters, and a Volume&Redshift-Limited sample with 4450 clusters. For the three samples, we find the mean cluster masses to be ${M}_{200{\rm{m}}}=1.66\pm0.13$ [stat.]$\pm0.03$ [sys.], $1.97\pm0.18$ [stat.]$\pm0.05$ [sys.], and $2.11\pm0.20$ [stat.]$\pm0.05$ [sys.]$\times{10}^{14}\ {\rm{M}}_{\odot }$, respectively. This is a factor of $\sim2$ improvement relative to the precision of measurements with previous generations of SPT surveys and the most constraining cluster mass measurements using CMB cluster lensing to date. Overall, we find no significant tensions between our results and masses given by redMaPPer mass-richness scaling relations of previous works, which were calibrated using CMB cluster lensing, optical weak lensing, and velocity dispersion measurements from various combinations of DES, SDSS and Planck data. We then divide our sample into 3 redshift and 3 richness bins, finding no significant tensions with optical weak-lensing calibrated masses in these bins. We forecast a $5.7\%$ constraint on the mean cluster mass of the DES Y3 sample with the complete SPT-3G surveys when using both temperature and polarization data and including an additional $\sim1400$ deg$^2$ of observations from the 'Extended' SPT-3G survey.

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arXiv2024

The Dark Energy Survey Supernova Program: Light curves and 5-Year data release

We present $griz$ photometric light curves for the full 5 years of the Dark Energy Survey Supernova program (DES-SN), obtained with both forced Point Spread Function (PSF) photometry on Difference Images (DIFFIMG) performed during survey operations, and Scene Modelling Photometry (SMP) on search images processed after the survey. This release contains $31,636$ DIFFIMG and $19,706$ high-quality SMP light curves, the latter of which contains $1635$ photometrically-classified supernovae that pass cosmology quality cuts. This sample spans the largest redshift ($z$) range ever covered by a single SN survey ($0.1<z<1.13$) and is the largest single sample from a single instrument of SNe ever used for cosmological constraints. We describe in detail the improvements made to obtain the final DES-SN photometry and provide a comparison to what was used in the DES-SN3YR spectroscopically-confirmed SN Ia sample. We also include a comparative analysis of the performance of the SMP photometry with respect to the real-time DIFFIMG forced photometry and find that SMP photometry is more precise, more accurate, and less sensitive to the host-galaxy surface brightness anomaly. The public release of the light curves and ancillary data can be found at https://github.com/des-science/DES-SN5YR. Finally, we discuss implications for future transient surveys, such as the forthcoming Vera Rubin Observatory Legacy Survey of Space and Time (LSST).

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arXiv2024

The Dark Energy Survey : Detection of weak lensing magnification of supernovae and constraints on dark matter haloes

The residuals of the distance moduli of Type Ia supernovae (SN Ia) relative to a Hubble diagram fit contain information about the inhomogeneity of the universe, due to weak lensing magnification by foreground matter. By correlating the residuals of the Dark Energy Survey Year 5 SN Ia sample (DES-SN5YR) with extra-galactic foregrounds from the DES Y3 Gold catalog, we detect the presence of lensing at $6.0 σ$ significance. This is the first detection with a significance level above $5σ$. Constraints on the effective mass-to-light ratios and radial profiles of dark-matter haloes surrounding individual galaxies are also obtained. We show that the scatter of SNe Ia around the Hubble diagram is reduced by modifying the standardisation of the distance moduli to include an easily calculable de-lensing (i.e., environmental) term. We use the de-lensed distance moduli to recompute cosmological parameters derived from SN Ia, finding in Flat $w$CDM a difference of $ΔΩ_{\rm M} = +0.036$ and $Δw = -0.056$ compared to the unmodified distance moduli, a change of $\sim 0.3σ$. We argue that our modelling of SN Ia lensing will lower systematics on future surveys with higher statistical power. We use the observed dispersion of lensing in DES-SN5YR to constrain $σ_8$, but caution that the fit is sensitive to uncertainties at small scales. Nevertheless, our detection of SN Ia lensing opens a new pathway to study matter inhomogeneity that complements galaxy-galaxy lensing surveys and has unrelated systematics.

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arXiv2024

The Dark Energy Survey Supernova Program: An updated measurement of the Hubble constant using the Inverse Distance Ladder

We measure the current expansion rate of the Universe, Hubble's constant $H_0$, by calibrating the absolute magnitudes of supernovae to distances measured by Baryon Acoustic Oscillations. This `inverse distance ladder' technique provides an alternative to calibrating supernovae using nearby absolute distance measurements, replacing the calibration with a high-redshift anchor. We use the recent release of 1829 supernovae from the Dark Energy Survey spanning $0.01\lt z \lt1.13$ anchored to the recent Baryon Acoustic Oscillation measurements from DESI spanning $0.30 \lt z_{\mathrm{eff}} \lt 2.33$. To trace cosmology to $z=0$, we use the third-, fourth- and fifth-order cosmographic models, which, by design, are agnostic about the energy content and expansion history of the universe. With the inclusion of the higher-redshift DESI-BAO data, the third-order model is a poor fit to both data sets, with the fourth-order model being preferred by the Akaike Information Criterion. Using the fourth-order cosmographic model, we find $H_0=67.19^{+0.66}_{-0.64}\mathrm{~km} \mathrm{~s}^{-1} \mathrm{~Mpc}^{-1}$, in agreement with the value found by Planck without the need to assume Flat-$Λ$CDM. However the best-fitting expansion history differs from that of Planck, providing continued motivation to investigate these tensions.

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arXiv2024

Modelling the impact of host galaxy dust on type Ia supernova distance measurements

Type Ia Supernovae (SNe Ia) are a critical tool in measuring the accelerating expansion of the universe. Recent efforts to improve these standard candles have focused on incorporating the effects of dust on distance measurements with SNe Ia. In this paper, we use the state-of-the-art Dark Energy Survey 5 year sample to evaluate two different families of dust models: empirical extinction models derived from SNe Ia data, and physical attenuation models from the spectra of galaxies. Among the SNe Ia-derived models, we find that a logistic function of the total-to-selective extinction RV best recreates the correlations between supernova distance measurements and host galaxy properties, though an additional 0.02 magnitudes of grey scatter are needed to fully explain the scatter in SNIa brightness in all cases. These empirically-derived extinction distributions are highly incompatible with the physical attenuation models from galactic spectral measurements. From these results, we conclude that SNe Ia must either preferentially select extreme ends of galactic dust distributions, or that the characterisation of dust along the SNe Ia line-of-sight is incompatible with that of galactic dust distributions.

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arXiv2024

OzDES Reverberation Mapping Program: Stacking analysis with H$β$, Mg II and C IV

Reverberation mapping is the leading technique used to measure direct black hole masses outside of the local Universe. Additionally, reverberation measurements calibrate secondary mass-scaling relations used to estimate single-epoch virial black hole masses. The Australian Dark Energy Survey (OzDES) conducted one of the first multi-object reverberation mapping surveys, monitoring 735 AGN up to $z\sim4$, over 6 years. The limited temporal coverage of the OzDES data has hindered recovery of individual measurements for some classes of sources, particularly those with shorter reverberation lags or lags that fall within campaign season gaps. To alleviate this limitation, we perform a stacking analysis of the cross-correlation functions of sources with similar intrinsic properties to recover average composite reverberation lags. This analysis leads to the recovery of average lags in each redshift-luminosity bin across our sample. We present the average lags recovered for the H$β$, Mg II and C IV samples, as well as multi-line measurements for redshift bins where two lines are accessible. The stacking analysis is consistent with the Radius-Luminosity relations for each line. Our results for the H$β$ sample demonstrate that stacking has the potential to improve upon constraints on the $R-L$ relation, which have been derived only from individual source measurements until now.

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arXiv2024

DESI 2024 III: Baryon Acoustic Oscillations from Galaxies and Quasars

We present the DESI 2024 galaxy and quasar baryon acoustic oscillations (BAO) measurements using over 5.7 million unique galaxy and quasar redshifts in the range 0.1<z<2.1. Divided by tracer type, we utilize 300,017 galaxies from the magnitude-limited Bright Galaxy Survey with 0.1<z<0.4, 2,138,600 Luminous Red Galaxies with 0.4<z<1.1, 2,432,022 Emission Line Galaxies with 0.8<z<1.6, and 856,652 quasars with 0.8<z<2.1, over a ~7,500 square degree footprint. The analysis was blinded at the catalog-level to avoid confirmation bias. All fiducial choices of the BAO fitting and reconstruction methodology, as well as the size of the systematic errors, were determined on the basis of the tests with mock catalogs and the blinded data catalogs. We present several improvements to the BAO analysis pipeline, including enhancing the BAO fitting and reconstruction methods in a more physically-motivated direction, and also present results using combinations of tracers. We present a re-analysis of SDSS BOSS and eBOSS results applying the improved DESI methodology and find scatter consistent with the level of the quoted SDSS theoretical systematic uncertainties. With the total effective survey volume of ~ 18 Gpc$^3$, the combined precision of the BAO measurements across the six different redshift bins is ~0.52%, marking a 1.2-fold improvement over the previous state-of-the-art results using only first-year data. We detect the BAO in all of these six redshift bins. The highest significance of BAO detection is $9.1σ$ at the effective redshift of 0.93, with a constraint of 0.86% placed on the BAO scale. We find our measurements are systematically larger than the prediction of Planck-2018 LCDM model at z<0.8. We translate the results into transverse comoving distance and radial Hubble distance measurements, which are used to constrain cosmological models in our companion paper [abridged].

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arXiv2024

Dark Energy Survey Year 3 results: likelihood-free, simulation-based $w$CDM inference with neural compression of weak-lensing map statistics

We present simulation-based cosmological $w$CDM inference using Dark Energy Survey Year 3 weak-lensing maps, via neural data compression of weak-lensing map summary statistics: power spectra, peak counts, and direct map-level compression/inference with convolutional neural networks (CNN). Using simulation-based inference, also known as likelihood-free or implicit inference, we use forward-modelled mock data to estimate posterior probability distributions of unknown parameters. This approach allows all statistical assumptions and uncertainties to be propagated through the forward-modelled mock data; these include sky masks, non-Gaussian shape noise, shape measurement bias, source galaxy clustering, photometric redshift uncertainty, intrinsic galaxy alignments, non-Gaussian density fields, neutrinos, and non-linear summary statistics. We include a series of tests to validate our inference results. This paper also describes the Gower Street simulation suite: 791 full-sky PKDGRAV dark matter simulations, with cosmological model parameters sampled with a mixed active-learning strategy, from which we construct over 3000 mock DES lensing data sets. For $w$CDM inference, for which we allow $-1<w<-\frac{1}{3}$, our most constraining result uses power spectra combined with map-level (CNN) inference. Using gravitational lensing data only, this map-level combination gives $Ω_{\rm m} = 0.283^{+0.020}_{-0.027}$, ${S_8 = 0.804^{+0.025}_{-0.017}}$, and $w < -0.80$ (with a 68 per cent credible interval); compared to the power spectrum inference, this is more than a factor of two improvement in dark energy parameter ($Ω_{\rm DE}, w$) precision.

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