arXiv subjects

M. Lima

Publications and source records attributed to M. Lima.

At least 73 records · Page 4Linked to original sources

arXiv2021

Probing gravity with the DES-CMASS sample and BOSS spectroscopy

The DES-CMASS sample (DMASS) is designed to optimally combine the weak lensing measurements from the Dark Energy Survey (DES) and redshift-space distortions (RSD) probed by the CMASS galaxy sample from the Baryonic Oscillation Spectroscopic Survey (BOSS). In this paper, we demonstrate the feasibility of adopting DMASS as the equivalent of BOSS CMASS for a joint analysis of DES and BOSS in the framework of modified gravity. We utilize the angular clustering of the DMASS galaxies, cosmic shear of the DES METACALIBRATION sources, and cross-correlation of the two as data vectors. By jointly fitting the combination of the data with the RSD measurements from the BOSS CMASS sample and Planck data, we obtain the constraints on modified gravity parameters $μ_0 = -0.37^{+0.47}_{-0.45}$ and $Σ_0 = 0.078^{+0.078}_{-0.082}$. We do not detect any significant deviation from General Relativity. Our constraints of modified gravity measured with DMASS are tighter than those with the DES Year 1 redMaGiC galaxy sample with the same external data sets by $29\%$ for $μ_0$ and $21\%$ for $Σ_0$, and comparable to the published results of the DES Year 1 modified gravity analysis despite this work using fewer external data sets. This improvement is mainly because the galaxy bias parameter is shared and more tightly constrained by both CMASS and DMASS, effectively breaking the degeneracy between the galaxy bias and other cosmological parameters. Such an approach to optimally combine photometric and spectroscopic surveys using a photometric sample equivalent to a spectroscopic sample can be applied to combining future surveys having a limited overlap such as DESI and LSST.

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arXiv2021

Dark Energy Survey Year 3 Results: Galaxy Sample for BAO Measurement

In this paper we present and validate the galaxy sample used for the analysis of the Baryon Acoustic Oscillation signal (BAO) in the Dark Energy Survey (DES) Y3 data. The definition is based on a colour and redshift-dependent magnitude cut optimized to select galaxies at redshifts higher than 0.5, while ensuring a high quality photometric redshift determination. The sample covers $\approx 4100$ square degrees to a depth of $i = 22.3 \ (AB)$ at $10σ$. It contains 7,031,993 galaxies in the redshift range from $z$= 0.6 to 1.1, with a mean effective redshift of 0.835. Photometric redshifts are estimated with the machine learning algorithm DNF, and are validated using the VIPERS PDR2 sample. We find a mean redshift bias of $z_{\mathrm{bias}} \approx 0.01$ and a mean uncertainty, in units of $1+z$, of $σ_{68} \approx 0.03$. We evaluate the galaxy population of the sample, showing it is mostly built upon Elliptical to Sbc types. Furthermore, we find a low level of stellar contamination of $\lesssim 4\%$. We present the method used to mitigate the effect of spurious clustering coming from observing conditions and other large-scale systematics. We apply it to the DES Y3 BAO sample and calculate sample weights that are used to get a robust estimate of the galaxy clustering signal. This paper is one of a series dedicated to the analysis of the BAO signal in the DES Y3 data. In the companion papers, Ferrero et al. (2021) and DES Collaboration (2021), we present the galaxy mock catalogues used to calibrate the analysis and the angular diameter distance constraints obtained through the fitting to the BAO scale, respectively. The galaxy sample, masks and additional material will be released in the public DES data repository upon acceptance.

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arXiv2021

Dark Energy Survey Year 3 results: Cosmology with peaks using an emulator approach

We constrain the matter density $Ω_{\mathrm{m}}$ and the amplitude of density fluctuations $σ_8$ within the $Λ$CDM cosmological model with shear peak statistics and angular convergence power spectra using mass maps constructed from the first three years of data of the Dark Energy Survey (DES Y3). We use tomographic shear peak statistics, including cross-peaks: peak counts calculated on maps created by taking a harmonic space product of the convergence of two tomographic redshift bins. Our analysis follows a forward-modelling scheme to create a likelihood of these statistics using N-body simulations, using a Gaussian process emulator. We include the following lensing systematics: multiplicative shear bias, photometric redshift uncertainty, and galaxy intrinsic alignment. Stringent scale cuts are applied to avoid biases from unmodelled baryonic physics. We find that the additional non-Gaussian information leads to a tightening of the constraints on the structure growth parameter yielding $S_8~\equiv~σ_8\sqrt{Ω_{\mathrm{m}}/0.3}~=~0.797_{-0.013}^{+0.015}$ (68% confidence limits), with a precision of 1.8%, an improvement of ~38% compared to the angular power spectra only case. The results obtained with the angular power spectra and peak counts are found to be in agreement with each other and no significant difference in $S_8$ is recorded. We find a mild tension of $1.5 \thinspace σ$ between our study and the results from Planck 2018, with our analysis yielding a lower $S_8$. Furthermore, we observe that the combination of angular power spectra and tomographic peak counts breaks the degeneracy between galaxy intrinsic alignment $A_{\mathrm{IA}}$ and $S_8$, improving cosmological constraints. We run a suite of tests concluding that our results are robust and consistent with the results from other studies using DES Y3 data.

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arXiv2021

Galaxy-galaxy lensing with the DES-CMASS catalogue: measurement and constraints on the galaxy-matter cross-correlation

The DMASS sample is a photometric sample from the DES Year 1 data set designed to replicate the properties of the CMASS sample from BOSS, in support of a joint analysis of DES and BOSS beyond the small overlapping area. In this paper, we present the measurement of galaxy-galaxy lensing using the DMASS sample as gravitational lenses in the DES Y1 imaging data. We test a number of potential systematics that can bias the galaxy-galaxy lensing signal, including those from shear estimation, photometric redshifts, and observing conditions. After careful systematic tests, we obtain a highly significant detection of the galaxy-galaxy lensing signal, with total $S/N=25.7$. With the measured signal, we assess the feasibility of using DMASS as gravitational lenses equivalent to CMASS, by estimating the galaxy-matter cross-correlation coefficient $r_{\rm cc}$. By jointly fitting the galaxy-galaxy lensing measurement with the galaxy clustering measurement from CMASS, we obtain $r_{\rm cc}=1.09^{+0.12}_{-0.11}$ for the scale cut of $4~h^{-1}{\rm Mpc}$ and $r_{\rm cc}=1.06^{+0.13}_{-0.12}$ for $12~h^{-1}{\rm Mpc}$ in fixed cosmology. By adding the angular galaxy clustering of DMASS, we obtain $r_{\rm cc}=1.06\pm 0.10$ for the scale cut of $4~h^{-1}{\rm Mpc}$ and $r_{\rm cc}=1.03\pm 0.11$ for $12~h^{-1}{\rm Mpc}$. The resulting values of $r_{\rm cc}$ indicate that the lensing signal of DMASS is statistically consistent with the one that would have been measured if CMASS had populated the DES region within the given statistical uncertainty. The measurement of galaxy-galaxy lensing presented in this paper will serve as part of the data vector for the forthcoming cosmology analysis in preparation.

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arXiv2021

Finding quadruply imaged quasars with machine learning. I. Methods

Strongly lensed quadruply imaged quasars (quads) are extraordinary objects. They are very rare in the sky -- only a few tens are known to date -- and yet they provide unique information about a wide range of topics, including the expansion history and the composition of the Universe, the distribution of stars and dark matter in galaxies, the host galaxies of quasars, and the stellar initial mass function. Finding them in astronomical images is a classic "needle in a haystack" problem, as they are outnumbered by other (contaminant) sources by many orders of magnitude. To solve this problem, we develop state-of-the-art deep learning methods and train them on realistic simulated quads based on real images of galaxies taken from the Dark Energy Survey, with realistic source and deflector models, including the chromatic effects of microlensing. The performance of the best methods on a mixture of simulated and real objects is excellent, yielding area under the receiver operating curve in the range 0.86 to 0.89. Recall is close to 100% down to total magnitude i~21 indicating high completeness, while precision declines from 85% to 70% in the range i~17-21. The methods are extremely fast: training on 2 million samples takes 20 hours on a GPU machine, and 10^8 multi-band cutouts can be evaluated per GPU-hour. The speed and performance of the method pave the way to apply it to large samples of astronomical sources, bypassing the need for photometric pre-selection that is likely to be a major cause of incompleteness in current samples of known quads.

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arXiv2021

Cross-correlation of DES Y3 lensing and ACT/${\it Planck}$ thermal Sunyaev Zel'dovich Effect I: Measurements, systematics tests, and feedback model constraints

We present a tomographic measurement of the cross-correlation between thermal Sunyaev-Zeldovich (tSZ) maps from ${\it Planck}$ and the Atacama Cosmology Telescope (ACT) and weak galaxy lensing shears measured during the first three years of observations of the Dark Energy Survey (DES Y3). 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 (CIB) and radio sources, finding that CIB 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 marginalises over redshift uncertainties, shear calibration biases, and intrinsic alignment effects. We also marginalise over $Ω_{\rm m}$ and $σ_8$ using ${\it Planck}$ or DES priors. We find that the data prefers the model with a low amplitude of the pressure profile at small scales, compatible with a scenario with strong AGN 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.

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arXiv2021

Dark Energy Survey Year 3 Results: Covariance Modelling and its Impact on Parameter Estimation and Quality of Fit

We describe and test the fiducial covariance matrix model for the combined 2-point function analysis of the Dark Energy Survey Year 3 (DES-Y3) dataset. Using a variety of new ansatzes for covariance modelling and testing we validate the assumptions and approximations of this model. These include the assumption of a Gaussian likelihood, the trispectrum contribution to the covariance, the impact of evaluating the model at a wrong set of parameters, the impact of masking and survey geometry, deviations from Poissonian shot-noise, galaxy weighting schemes and other, sub-dominant effects. We find that our covariance model is robust and that its approximations have little impact on goodness-of-fit and parameter estimation. The largest impact on best-fit figure-of-merit arises from the so-called $f_{\mathrm{sky}}$ approximation for dealing with finite survey area, which on average increases the $χ^2$ between maximum posterior model and measurement by $3.7\%$ ($Δχ^2 \approx 18.9$). Standard methods to go beyond this approximation fail for DES-Y3, but we derive an approximate scheme to deal with these features. For parameter estimation, our ignorance of the exact parameters at which to evaluate our covariance model causes the dominant effect. We find that it increases the scatter of maximum posterior values for $Ω_m$ and $σ_8$ by about $3\%$ and for the dark energy equation of state parameter by about $5\%$.

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arXiv2021

Density split statistics: joint model of counts and lensing in cells

We present density split statistics, a framework that studies lensing and counts-in-cells as a function of foreground galaxy density, thereby providing a large-scale measurement of both 2-point and 3-point statistics. Our method extends our earlier work on trough lensing and is summarized as follows: given a foreground (low redshift) population of galaxies, we divide the sky into subareas of equal size but distinct galaxy density. We then measure lensing around uniformly spaced points separately in each of these subareas, as well as counts-in-cells statistics (CiC). The lensing signals trace the matter density contrast around regions of fixed galaxy density. Through the CiC measurements this can be related to the density profile around regions of fixed matter density. Together, these measurements constitute a powerful probe of cosmology, the skewness of the density field and the connection of galaxies and matter. In this paper we show how to model both the density split lensing signal and CiC from basic ingredients: a non-linear power spectrum, clustering hierarchy coefficients from perturbation theory and a parametric model for galaxy bias and shot-noise. Using N-body simulations, we demonstrate that this model is sufficiently accurate for a cosmological analysis on year 1 data from the Dark Energy Survey.

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arXiv2021

The Observed Evolution of the Stellar Mass - Halo Mass Relation for Brightest Central Galaxies

We quantify evolution in the cluster scale stellar mass - halo mass (SMHM) relation's parameters using 2323 clusters and brightest central galaxies (BCGs) over the redshift range $0.03 \le z \le 0.60$. The precision on inferred SMHM parameters is improved by including the magnitude gap ($\rm m_{gap}$) between the BCG and fourth brightest cluster member (M14) as a third parameter in the SMHM relation. At fixed halo mass, accounting for $\rm m_{gap}$, through a stretch parameter, reduces the SMHM relation's intrinsic scatter. To explore this redshift range, we use clusters, BCGs, and cluster members identified using the Sloan Digital Sky Survey C4 and redMaPPer cluster catalogs and the Dark Energy Survey redMaPPer catalog. Through this joint analysis, we detect no systematic differences in BCG stellar mass, $\rm m_{gap}$, and cluster mass (inferred from richness) between the datsets. We utilize the Pareto function to quantify each parameter's evolution. We confirm prior findings of negative evolution in the SMHM relation's slope (3.5$σ$) and detect negative evolution in the stretch parameter (4.0$σ$) and positive evolution in the offset parameter (5.8$σ$). This observed evolution, combined with the absence of BCG growth, when stellar mass is measured within 50kpc, suggests that this evolution results from changes in the cluster's $\rm m_{gap}$. For this to occur, late-term growth must be in the intra-cluster light surrounding the BCG. We also compare the observed results to Illustris TNG 300-1 cosmological hydrodynamic simulations and find modest qualitative agreement. However, the simulations lack the evolutionary features detected in the real data.

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arXiv2021

Dark Energy Survey Year 3 Results: Redshift Calibration of the Weak Lensing Source Galaxies

Determining the distribution of redshifts of galaxies observed by wide-field photometric experiments like the Dark Energy Survey is an essential component to mapping the matter density field with gravitational lensing. In this work we describe the methods used to assign individual weak lensing source galaxies from the Dark Energy Survey Year 3 Weak Lensing Source Catalogue to four tomographic bins and to estimate the redshift distributions in these bins. As the first application of these methods to data, we validate that the assumptions made apply to the DES Y3 weak lensing source galaxies and develop a full treatment of systematic uncertainties. Our method consists of combining information from three independent likelihood functions: Self-Organizing Map $p(z)$ (SOMPZ), a method for constraining redshifts from galaxy photometry; clustering redshifts (WZ), constraints on redshifts from cross-correlations of galaxy density functions; and shear ratios (SR), which provide constraints on redshifts from the ratios of the galaxy-shear correlation functions at small scales. Finally, we describe how these independent probes are combined to yield an ensemble of redshift distributions encapsulating our full uncertainty. We calibrate redshifts with combined effective uncertainties of $σ_{\langle z \rangle}\sim 0.01$ on the mean redshift in each tomographic bin.

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arXiv2021

Assessing tension metrics with Dark Energy Survey and Planck data

Quantifying tensions -- inconsistencies amongst measurements of cosmological parameters by different experiments -- has emerged as a crucial part of modern cosmological data analysis. Statistically-significant tensions between two experiments or cosmological probes may indicate new physics extending beyond the standard cosmological model and need to be promptly identified. We apply several tension estimators proposed in the literature to the Dark Energy Survey (DES) large-scale structure measurement and Planck cosmic microwave background data. We first evaluate the responsiveness of these metrics to an input tension artificially introduced between the two, using synthetic DES data. We then apply the metrics to the comparison of Planck and actual DES Year 1 data. We find that the parameter differences, Eigentension, and Suspiciousness metrics all yield similar results on both simulated and real data, while the Bayes ratio is inconsistent with the rest due to its dependence on the prior volume. Using these metrics, we calculate the tension between DES Year 1 $3\times 2$pt and Planck, finding the surveys to be in $\sim 2.3σ$ tension under the $Λ$CDM paradigm. This suite of metrics provides a toolset for robustly testing tensions in the DES Year 3 data and beyond.

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arXiv2021

Dark Energy Survey Year 3 Results: Multi-Probe Modeling Strategy and Validation

This paper details the modeling pipeline and validates the baseline analysis choices of the DES Year 3 joint analysis of galaxy clustering and weak lensing (a so-called "3$\times$2pt" analysis). These analysis choices include the specific combination of cosmological probes, priors on cosmological and systematics parameters, model parameterizations for systematic effects and related approximations, and angular scales where the model assumptions are validated. We run a large number of simulated likelihood analyses using synthetic data vectors to test the robustness of our baseline analysis. We demonstrate that the DES Year 3 modeling pipeline, including the calibrated scale cuts, is sufficiently accurate relative to the constraining power of the DES Year 3 analyses. Our systematics mitigation strategy accounts for astrophysical systematics, such as galaxy bias, intrinsic alignments, source and lens magnification, baryonic effects, and source clustering, as well as for uncertainties in modeling the matter power spectrum, reduced shear, and estimator effects. We further demonstrate excellent agreement between two independently-developed modeling pipelines, and thus rule out any residual uncertainties due to the numerical implementation.

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arXiv2021

Dark Energy Survey Year 3 Results: Galaxy clustering and systematics treatment for lens galaxy samples

In this work we present the galaxy clustering measurements of the two DES lens galaxy samples: a magnitude-limited sample optimized for the measurement of cosmological parameters, MagLim, and a sample of luminous red galaxies selected with the redMaGiC algorithm. MagLim / redMaGiC sample contains over 10 million / 2.5 million galaxies and is divided into six / five photometric redshift bins spanning the range $z\in[0.20,1.05]$ / $z\in[0.15,0.90]$. Both samples cover 4143 deg$^2$ over which we perform our analysis blind, measuring the angular correlation function with a S/N $\sim 63$ for both samples. In a companion paper (DES Collaboration et al. 2021)), these measurements of galaxy clustering are combined with the correlation functions of cosmic shear and galaxy-galaxy lensing of each sample to place cosmological constraints with a 3$\times$2pt analysis. We conduct a thorough study of the mitigation of systematic effects caused by the spatially varying survey properties and we correct the measurements to remove artificial clustering signals. We employ several decontamination methods with different configurations to ensure the robustness of our corrections and to determine the systematic uncertainty that needs to be considered for the final cosmology analyses. We validate our fiducial methodology using log-normal mocks, showing that our decontamination procedure induces biases no greater than $0.5σ$ in the $(Ω_m, b)$ plane, where $b$ is galaxy bias. We demonstrate that failure to remove the artificial clustering would introduce strong biases up to $\sim 7 σ$ in $Ω_m$ and of more than $4 σ$ in galaxy bias.

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arXiv2021

Dark Energy Survey Year 3 results: cosmology from combined galaxy clustering and lensing -- validation on cosmological simulations

We present a validation of the Dark Energy Survey Year 3 (DES Y3) $3\times2$-point analysis choices by testing them on Buzzard v2.0, 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 Buzzard v2.0 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 $3\times2$-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 non-linear matter power spectrum, non-linear 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.

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arXiv2021

Dark Energy Survey Year 3 Results: Photometric Data Set for Cosmology

We describe the Dark Energy Survey (DES) photometric data set assembled from the first three years of science operations to support DES Year 3 cosmology analyses, and provide usage notes aimed at the broad astrophysics community. Y3 Gold improves on previous releases from DES, Y1 Gold and Data Release 1 (DES DR1), presenting an expanded and curated data set that incorporates algorithmic developments in image detrending and processing, photometric calibration, and object classification. Y3 Gold comprises nearly 5000 square degrees of grizY imaging in the south Galactic cap, including nearly 390 million objects, with depth reaching S/N ~ 10 for extended objects up to $i_{AB}\sim 23.0$, and top-of-the-atmosphere photometric uniformity $< 3$ mmag. Compared to DR1, photometric residuals with respect to Gaia are reduced by $50\%$, and per-object chromatic corrections are introduced. Y3 Gold augments DES DR1 with simultaneous fits to multi-epoch photometry for more robust galaxy color measurements and corresponding photometric redshift estimates. Y3 Gold features improved morphological star-galaxy classification with efficiency $>98\%$ and purity $>99\%$ for galaxies with $19 < i_{AB} < 22.5$. Additionally, it includes per-object quality information, and accompanying maps of the footprint coverage, masked regions, imaging depth, survey conditions, and astrophysical foregrounds that are used to select the cosmology analysis samples. This paper will be complemented by online resources.

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arXiv2021

The mass and galaxy distribution around SZ-selected clusters

We present measurements of the radial profiles of the mass and galaxy number density around Sunyaev-Zel'dovich-selected clusters using both weak lensing and galaxy counts. The clusters are selected from the Atacama Cosmology Telescope Data Release 5 and the galaxies from the Dark Energy Survey Year 3 dataset. With signal-to-noise of 62 (43) for galaxy (weak lensing) profiles over scales of about $0.2-20h^{-1}$ Mpc, these are the highest precision measurements for SZ-selected clusters to date. Because SZ selection closely approximates mass selection, these measurements enable several tests of theoretical models of the mass and light distribution around clusters. Our main findings are: 1. The splashback feature is detected at a consistent location in both the mass and galaxy profiles and its location is consistent with predictions of cold dark matter N-body simulations. 2. The full mass profile is also consistent with the simulations; hence it can constrain alternative dark matter models that modify the mass distribution of clusters. 3. The shapes of the galaxy and lensing profiles are remarkably similar for our sample over the entire range of scales, from well inside the cluster halo to the quasilinear regime. This can be used to constrain processes such as quenching and tidal disruption that alter the galaxy distribution inside the halo, and scale-dependent features in the transition regime outside the halo. We measure the dependence of the profile shapes on the galaxy sample, redshift and cluster mass. We extend the Diemer \& Kravtsov model for the cluster profiles to the linear regime using perturbation theory and show that it provides a good match to the measured profiles. We also compare the measured profiles to predictions of the standard halo model and simulations that include hydrodynamics. Applications of these results to cluster mass estimation and cosmology are discussed.

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arXiv2021

The first Hubble diagram and cosmological constraints using superluminous supernova

We present the first Hubble diagram of superluminous supernovae (SLSNe) out to a redshift of two, together with constraints on the matter density, $Ω_{\rm M}$, and the dark energy equation-of-state parameter, $w(\equiv p/ρ)$. We build a sample of 20 cosmologically useful SLSNe~I based on light curve and spectroscopy quality cuts. We confirm the robustness of the peak decline SLSN~I standardization relation with a larger dataset and improved fitting techniques than previous works. We then solve the SLSN model based on the above standardisation via minimisation of the $χ^2$ computed from a covariance matrix which includes statistical and systematic uncertainties. For a spatially flat $Λ$CDM cosmological model, we find $Ω_{\rm M}=0.38^{+0.24}_{-0.19}$, with a rms of 0.27 mag for the residuals of the distance moduli. For a $w_0w_a$CDM cosmological model, the addition of SLSNe~I to a `baseline' measurement consisting of Planck temperature together with type Ia supernovae, results in a small improvement in the constraints of $w_0$ and $w_a$ of 4\%. We present simulations of future surveys with 868 and 492 SLSNe I (depending on the configuration used) and show that such a sample can deliver cosmological constraints in a flat $Λ$CDM model with the same precision (considering only statistical uncertainties) as current surveys that use type Ia supernovae, while providing a factor 2-3 improvement in the precision of the constraints on the time variation of dark energy, $w_0$ and $w_a$. This paper represents the proof-of-concept for superluminous supernova cosmology, and demonstrates they can provide an independent test of cosmology in the high-redshift ($z>1$) universe.

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arXiv2021

Galaxy Clustering in Harmonic Space from the Dark Energy Survey Year 1 Data: Compatibility with Real-Space Results

We perform an analysis in harmonic space of the Dark Energy Survey Year 1 Data (DES-Y1) galaxy clustering data using products obtained for the real-space analysis. We test our pipeline with a suite of lognormal simulations, which are used to validate scale cuts in harmonic space as well as to provide a covariance matrix that takes into account the DES-Y1 mask. We then apply this pipeline to DES-Y1 data taking into account survey property maps derived for the real-space analysis. We compare with real-space DES-Y1 results obtained from a similar pipeline. We show that the harmonic space analysis we develop yields results that are compatible with the real-space analysis for the bias parameters. This verification paves the way to performing a harmonic space analysis for the upcoming DES-Y3 data.

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