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M. Sako

Publications and source records attributed to M. Sako.

At least 37 records · Page 2Linked to original sources

The Dark Energy Survey Supernova Program: Cosmological Analysis and Systematic Uncertainties

We present the full Hubble diagram of photometrically-classified Type Ia supernovae (SNe Ia) from the Dark Energy Survey supernova program (DES-SN). DES-SN discovered more than 20,000 SN candidates and obtained spectroscopic redshifts of 7,000 host galaxies. Based on the light-curve quality, we select 1635 photometrically-identified SNe Ia with spectroscopic redshift 0.10$< z <$1.13, which is the largest sample of supernovae from any single survey and increases the number of known $z>0.5$ supernovae by a factor of five. In a companion paper, we present cosmological results of the DES-SN sample combined with 194 spectroscopically-classified SNe Ia at low redshift as an anchor for cosmological fits. Here we present extensive modeling of this combined sample and validate the entire analysis pipeline used to derive distances. We show that the statistical and systematic uncertainties on cosmological parameters are $σ_{Ω_M,{\rm stat+sys}}^{Λ{\rm CDM}}=$0.017 in a flat $Λ$CDM model, and $(σ_{Ω_M},σ_w)_{\rm stat+sys}^{w{\rm CDM}}=$(0.082, 0.152) in a flat $w$CDM model. Combining the DES SN data with the highly complementary CMB measurements by Planck Collaboration (2020) reduces uncertainties on cosmological parameters by a factor of 4. In all cases, statistical uncertainties dominate over systematics. We show that uncertainties due to photometric classification make up less than 10% of the total systematic uncertainty budget. This result sets the stage for the next generation of SN cosmology surveys such as the Vera C. Rubin Observatory's Legacy Survey of Space and Time.

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Probing the Consistency of Cosmological Contours for Supernova Cosmology

As the scale of cosmological surveys increases, so does the complexity in the analyses. This complexity can often make it difficult to derive the underlying principles, necessitating statistically rigorous testing to ensure the results of an analysis are consistent and reasonable. This is particularly important in multi-probe cosmological analyses like those used in the Dark Energy Survey and the upcoming Legacy Survey of Space and Time, where accurate uncertainties are vital. In this paper, we present a statistically rigorous method to test the consistency of contours produced in these analyses, and apply this method to the Pippin cosmological pipeline used for Type Ia supernova cosmology with the Dark Energy Survey. We make use of the Neyman construction, a frequentist methodology that leverages extensive simulations to calculate confidence intervals, to perform this consistency check. A true Neyman construction is too computationally expensive for supernova cosmology, so we develop a method for approximating a Neyman construction with far fewer simulations. We find that for a simulated data-set, the 68% contour reported by the Pippin pipeline and the 68% confidence region produced by our approximate Neyman construction differ by less than a percent near the input cosmology, however show more significant differences far from the input cosmology, with a maximal difference of 0.05 in $Ω_{M}$, and 0.07 in $w$. This divergence is most impactful for analyses of cosmological tensions, but its impact is mitigated when combining supernovae with other cross-cutting cosmological probes, such as the Cosmic Microwave Background.

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Searching for universality of dineutron correlation at the surface of Borromean nuclei

The dineutron correlation is systematically studied in three different Borromean nuclei near the neutron dripline, 11Li, 14Be and 17B, via the (p, pn) knockout reaction measured at the RIBF facility in RIKEN. For the three nuclei, the correlation angle between the valence neutrons is found to be largest in the same range of intrinsic momenta, which can be associated to the nuclear surface. This result reinforces the prediction that the formation of the dineutron is universal in environments with low neutron density, such as the surface of neutron-rich Borromean nuclei.

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The Dark Energy Survey Supernova Program: Corrections on photometry due to wavelength-dependent atmospheric effects

Wavelength-dependent atmospheric effects impact photometric supernova flux measurements for ground-based observations. We present corrections on supernova flux measurements from the Dark Energy Survey Supernova Program's 5YR sample (DES-SN5YR) for differential chromatic refraction (DCR) and wavelength-dependent seeing, and we show their impact on the cosmological parameters $w$ and $Ω_m$. We use $g-i$ colors of Type Ia supernovae (SNe Ia) to quantify astrometric offsets caused by DCR and simulate point spread functions (PSFs) using the GalSIM package to predict the shapes of the PSFs with DCR and wavelength-dependent seeing. We calculate the magnitude corrections and apply them to the magnitudes computed by the DES-SN5YR photometric pipeline. We find that for the DES-SN5YR analysis, not accounting for the astrometric offsets and changes in the PSF shape cause an average bias of $+0.2$ mmag and $-0.3$ mmag respectively, with standard deviations of $0.7$ mmag and $2.7$ mmag across all DES observing bands (\textit{griz}) throughout all redshifts. When the DCR and seeing effects are not accounted for, we find that $w$ and $Ω_m$ are lower by less than $0.004\pm0.02$ and $0.001\pm0.01$ respectively, with $0.02$ and $0.01$ being the $1σ$ statistical uncertainties. Although we find that these biases do not limit the constraints of the DES-SN5YR sample, future surveys with much higher statistics, lower systematics, and especially those that observe in the $u$ band will require these corrections as wavelength-dependent atmospheric effects are larger at shorter wavelengths. We also discuss limitations of our method and how they can be better accounted for in future surveys.

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Cosmological Results from the RAISIN Survey: Using Type Ia Supernovae in the Near Infrared as a Novel Path to Measure the Dark Energy Equation of State

Type Ia supernovae (SNe Ia) are more precise standardizable candles when measured in the near-infrared (NIR) than in the optical. With this motivation, from 2012-2017 we embarked on the RAISIN program with the Hubble Space Telescope (HST) to obtain rest-frame NIR light curves for a cosmologically distant sample of 37 SN Ia ($0.2 \lesssim z \lesssim 0.6$) discovered by Pan-STARRS and the Dark Energy Survey. By comparing higher-$z$ HST data with 42 SN Ia at $z<0.1$ observed in the NIR by the Carnegie Supernova Project, we construct a Hubble diagram from NIR observations (with only time of maximum light and some selection cuts from optical data) to pursue a unique avenue to constrain the dark energy equation of state parameter, $w$. We analyze the dependence of the full set of Hubble residuals on the SN Ia host galaxy mass and find Hubble residual steps of size $\sim$0.06-0.1~mag with 1.5- to 2.5-$σ$ significance depending on the method and step location. Combining our NIR sample with CMB constraints, we find $1+w=-0.17\pm0.12$ (stat$+$syst). The largest systematic errors are the redshift-dependent SN selection biases and the properties of the NIR mass step. We also use these data to measure $H_0=75.9\pm 2.2$ km s$^{-1}$ Mpc$^{-1}$ from stars with geometric distance calibration in the hosts of 8 SNe Ia observed in the NIR versus $H_0=71.2\pm3.8$ km s$^{-1}$ Mpc$^{-1}$ using an inverse distance ladder approach tied to Planck. Using optical data we find $1+w=-0.10\pm0.09$ and with optical and NIR data combined, we find $1+w=-0.06\pm0.07$; these shifts of up to 0.11 in $w$ could point to inconsistency in optical versus NIR SN models. There will be many opportunities to improve this NIR measurement and better understand systematic uncertainties through larger low-$z$ samples, new light-curve models, calibration improvements, and by building high-$z$ samples from the Roman Space Telescope.

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The Dark Energy Survey 5-year photometrically identified Type Ia Supernovae

As part of the cosmology analysis using Type Ia Supernovae (SN Ia) in the Dark Energy Survey (DES), we present photometrically identified SN Ia samples using multi-band light-curves and host galaxy redshifts. For this analysis, we use the photometric classification framework SuperNNova (SNN; Möller et al. 2019) trained on realistic DES-like simulations. For reliable classification, we process the DES SN programme (DES-SN) data and introduce improvements to the classifier architecture, obtaining classification accuracies of more than 98 per cent on simulations. This is the first SN classification to make use of ensemble methods, resulting in more robust samples. Using photometry, host galaxy redshifts, and a classification probability requirement, we identify 1,863 SNe Ia from which we select 1,484 cosmology-grade SNe Ia spanning the redshift range of 0.07 < z < 1.14. We find good agreement between the light-curve properties of the photometrically-selected sample and simulations. Additionally, we create similar SN Ia samples using two types of Bayesian Neural Network classifiers that provide uncertainties on the classification probabilities. We test the feasibility of using these uncertainties as indicators for out-of-distribution candidates and model confidence. Finally, we discuss the implications of photometric samples and classification methods for future surveys such as Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST).

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A DECam Search for Explosive Optical Transients Associated with IceCube Neutrinos

In this work, we investigate the likelihood of association between realtime, TeV-PeV energy neutrino alerts from IceCube and optical counterparts in the form of core-collapse supernovae (CC SNe). The optical follow-up of IceCube alerts requires two main instrumental capabilities: (1) deep imaging, since 73\% of neutrinos would come from CC SNe at redshifts $z > 0.3$, and (2) a large field of view (FoV), since typical IceCube muon neutrino pointing accuracy is on the order of $\sim1$~deg. With Blanco/DECam ($gri$ to 24th magnitude and $2.2$~deg diameter FoV), we performed a triggered optical follow-up observation of two IceCube alerts, IC170922A and IC171106A on $\sim6$~nights during the $\sim3$~weeks following each alert. For the IC170922A (IC171106A) follow-up observations, we expect that 12.1\% (9.5\%) of coincident CC SNe at $z \lesssim 0.3$ are detectable, and that on average, 0.23 (0.07) unassociated SNe in the neutrino 90\% containment regions also pass our selection criteria. We find two candidate CC SNe that are temporally coincident with the neutrino alerts in the FoV, but none in the 90\% containment regions, which is statistically consistent with expected rates of background CC SNe for these observations. If CC SNe are the dominant source of TeV-PeV neutrinos, we would expect an excess of coincident CC SNe to be detectable at the $3σ$ confidence level using DECam observations similar to those of this work for $\sim60$ ($\sim200$) neutrino alerts with (without) redshift information for all candidates.

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Constraints on the Physical Properties of GW190814 through Simulations based on DECam Follow-up Observations by the Dark Energy Survey

On 14 August 2019, the LIGO and Virgo Collaborations detected gravitational waves from a black hole and a 2.6 solar mass compact object, possibly the first neutron star -- black hole (NSBH) merger. In search of an optical counterpart, the Dark Energy Survey (DES) obtained deep imaging of the entire 90 percent confidence level localization area with Blanco/DECam 0, 1, 2, 3, 6, and 16 nights after the merger. Objects with varying brightness were detected by the DES Pipeline and we systematically reduced the candidate counterparts through catalog matching, light curve properties, host-galaxy photometric redshifts, SOAR spectroscopic follow-up observations, and machine-learning-based photometric classification. All candidates were rejected as counterparts to the merger. To quantify the sensitivity of our search, we applied our selection criteria to full light curve simulations of supernovae and kilonovae as they would appear in the DECam observations. Since the source class of the merger was uncertain, we utilized an agnostic, three-component kilonova model based on tidally-disrupted NS ejecta properties to quantify our detection efficiency of a counterpart if the merger included a NS. We find that if a kilonova occurred during this merger, configurations where the ejected matter is greater than 0.07 solar masses, has lanthanide abundance less than $10^{-8.56}$, and has a velocity between $0.18c$ and $0.21c$ are disfavored at the $2σ$ level. Furthermore, we estimate that our background reduction methods are capable of associating gravitational wave signals with a detected electromagnetic counterpart at the $4σ$ level in $95\%$ of future follow-up observations.

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The DECam Local Volume Exploration Survey Data Release 2

We present the second public data release (DR2) from the DECam Local Volume Exploration survey (DELVE). DELVE DR2 combines new DECam observations with archival DECam data from the Dark Energy Survey, the DECam Legacy Survey, and other DECam community programs. DELVE DR2 consists of ~160,000 exposures that cover >21,000 deg^2 of the high Galactic latitude (|b| > 10 deg) sky in four broadband optical/near-infrared filters (g, r, i, z). DELVE DR2 provides point-source and automatic aperture photometry for ~2.5 billion astronomical sources with a median 5σ point-source depth of g=24.3, r=23.9, i=23.5, and z=22.8 mag. A region of ~17,000 deg^2 has been imaged in all four filters, providing four-band photometric measurements for ~618 million astronomical sources. DELVE DR2 covers more than four times the area of the previous DELVE data release and contains roughly five times as many astronomical objects. DELVE DR2 is publicly available via the NOIRLab Astro Data Lab science platform.

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Measuring Cosmological Parameters with Type Ia Supernovae in redMaGiC galaxies

Current and future cosmological analyses with Type Ia Supernovae (SNe Ia) face three critical challenges: i) measuring redshifts from the supernova or its host galaxy; ii) classifying SNe without spectra; and iii) accounting for correlations between the properties of SNe Ia and their host galaxies. We present here a novel approach that addresses each challenge. In the context of the Dark Energy Survey (DES), we analyze a SNIa sample with host galaxies in the redMaGiC galaxy catalog, a selection of Luminous Red Galaxies. Photo-$z$ estimates for these galaxies are expected to be accurate to $σ_{Δz/(1+z)}\sim0.02$. The DES-5YR photometrically classified SNIa sample contains approximately 1600 SNe and 125 of these SNe are in redMaGiC galaxies. We demonstrate that redMaGiC galaxies almost exclusively host SNe Ia, reducing concerns with classification uncertainties. With this subsample, we find similar Hubble scatter (to within $\sim0.01$ mag) using photometric redshifts in place of spectroscopic redshifts. With detailed simulations, we show the bias due to using photo-$z$s from redMaGiC host galaxies on the measurement of the dark energy equation-of-state $w$ is up to $Δw \sim 0.01-0.02$. With real data, we measure a difference in $w$ when using redMaGiC photometric redshifts versus spectroscopic redshifts of $Δw = 0.005$. Finally, we discuss how SNe in redMaGiC galaxies appear to be a more standardizable population due to a weaker relation between color and luminosity ($β$) compared to the DES-3YR population by $\sim5σ$; this finding is consistent with predictions that redMaGiC galaxies exhibit lower reddening ratios ($\textrm{R}_\textrm{V}$) than the general population of SN host galaxies. These results establish the feasibility of performing redMaGiC SN cosmology with photometric survey data in the absence of spectroscopic data.

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The Dark Energy Survey Supernova Program: Cosmological biases from supernova photometric classification

Cosmological analyses of samples of photometrically-identified Type Ia supernovae (SNe Ia) depend on understanding the effects of 'contamination' from core-collapse and peculiar SN Ia events. We employ a rigorous analysis on state-of-the-art simulations of photometrically identified SN Ia samples and determine cosmological biases due to such 'non-Ia' contamination in the Dark Energy Survey (DES) 5-year SN sample. As part of the analysis, we test on our DES simulations the performance of SuperNNova, a photometric SN classifier based on recurrent neural networks. Depending on the choice of non-Ia SN models in both the simulated data sample and training sample, contamination ranges from 0.8-3.5 %, with the efficiency of the classification from 97.7-99.5 %. Using the Bayesian Estimation Applied to Multiple Species (BEAMS) framework and its extension 'BEAMS with Bias Correction' (BBC), we produce a redshift-binned Hubble diagram marginalised over contamination and corrected for selection effects and we use it to constrain the dark energy equation-of-state, $w$. Assuming a flat universe with Gaussian $Ω_M$ prior of $0.311\pm0.010$, we show that biases on $w$ are $<0.008$ when using SuperNNova and accounting for a wide range of non-Ia SN models in the simulations. Systematic uncertainties associated with contamination are estimated to be at most $σ_{w, \mathrm{syst}}=0.004$. This compares to an expected statistical uncertainty of $σ_{w,\mathrm{stat}}=0.039$ for the DES-SN sample, thus showing that contamination is not a limiting uncertainty in our analysis. We also measure biases due to contamination on $w_0$ and $w_a$ (assuming a flat universe), and find these to be $<$0.009 in $w_0$ and $<$0.108 in $w_a$, hence 5 to 10 times smaller than the statistical uncertainties expected from the DES-SN sample.

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A Reference Survey for Supernova Cosmology with the Nancy Grace Roman Space Telescope

This note presents an initial survey design for the Nancy Grace Roman High-latitude Time Domain Survey. This is not meant to be a final or exhaustive list of all the survey strategy choices, but instead presents a viable path towards achieving the desired precision and accuracy of dark energy measurements using Type Ia supernovae (SNe Ia). We describe a survey strategy that use six filters (RZYJH and F) and the prism on the Roman Wide Field Instrument. This survey has two tiers, one "wide" which targets SNe Ia at redshifts up to 1 and one "deep" targeting redshifts up to 1.7; for each, four filters are used (with Y and J used in both tiers). We propose one field each in the north and south continuous viewing zones, and expect to obtain high-quality distances of $\sim$12,000 SNe Ia with $\sim$5,000 at z > 1. We propose a wide-tier area of $\sim$19 deg$^2$ and a deep tier of $\sim$5 deg$^2$. Exposure times range from 100 s to 900 s for imaging and 900 s to 3600 s for the prism. These exposure times would reach $\sim$25.5 mag and $\sim$26.5 mag for the wide and deep tiers respectively, with deep co-add stacks reaching $\sim$28 mag and $\sim$29 mag. The total survey spans two years, with a total allocation time of six months, and a cadence of $\sim$5 days.

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The Dark Energy Survey Data Release 2

We present the second public data release of the Dark Energy Survey, DES DR2, based on optical/near-infrared imaging by the Dark Energy Camera mounted on the 4-m Blanco telescope at Cerro Tololo Inter-American Observatory in Chile. DES DR2 consists of reduced single-epoch and coadded images, a source catalog derived from coadded images, and associated data products assembled from 6 years of DES science operations. This release includes data from the DES wide-area survey covering ~5000 deg2 of the southern Galactic cap in five broad photometric bands, grizY. DES DR2 has a median delivered point-spread function full-width at half maximum of g= 1.11, r= 0.95, i= 0.88, z= 0.83, and Y= 0.90 arcsec photometric uniformity with a standard deviation of < 3 mmag with respect to Gaia DR2 G-band, a photometric accuracy of ~10 mmag, and a median internal astrometric precision of ~27 mas. The median coadded catalog depth for a 1.95 arcsec diameter aperture at S/N= 10 is g= 24.7, r= 24.4, i= 23.8, z= 23.1 and Y= 21.7 mag. DES DR2 includes ~691 million distinct astronomical objects detected in 10,169 coadded image tiles of size 0.534 deg2 produced from 76,217 single-epoch images. After a basic quality selection, benchmark galaxy and stellar samples contain 543 million and 145 million objects, respectively. These data are accessible through several interfaces, including interactive image visualization tools, web-based query clients, image cutout servers and Jupyter notebooks. DES DR2 constitutes the largest photometric data set to date at the achieved depth and photometric precision.

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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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Synergies between Vera C. Rubin Observatory, Nancy Grace Roman Space Telescope, and Euclid Mission: Constraining Dark Energy with Type Ia Supernovae

We review the needs of the supernova community for improvements in survey coordination and data sharing that would significantly boost the constraints on dark energy using samples of Type Ia supernovae from the Vera C. Rubin Observatories, the \textit{Nancy Grace Roman Space Telescope}, and the \textit{Euclid} Mission. We discuss improvements to both statistical and systematic precision that the combination of observations from these experiments will enable. For example, coordination will result in improved photometric calibration, redshift measurements, as well as supernova distances. We also discuss what teams and plans should be put in place now to start preparing for these combined data sets. Specifically, we request coordinated efforts in field selection and survey operations, photometric calibration, spectroscopic follow-up, pixel-level processing, and computing. These efforts will benefit not only experiments with Type Ia supernovae, but all time-domain studies, and cosmology with multi-messenger astrophysics.

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Quasi-free Neutron Knockout Reaction Reveals a Small $s$-orbital Component in the Borromean Nucleus $^{17}$B

A kinematically complete quasi-free $(p,pn)$ experiment in inverse kinematics was performed to study the structure of the Borromean nucleus $^{17}$B, which had long been considered to have neutron halo. By analyzing the momentum distributions and exclusive cross sections, we obtained the spectroscopic factors for $1s_{1/2}$ and $0d_{5/2}$ orbitals, and a surprisingly small percentage of 9(2)$\%$ was determined for $1s_{1/2}$. Our finding of such a small $1s_{1/2}$ component and the halo features reported in prior experiments can be explained by the deformed relativistic Hartree-Bogoliubov theory in continuum, revealing a definite but not dominant neutron halo in $^{17}$B. The present work gives the smallest $s$- or $p$-orbital component among known nuclei exhibiting halo features, and implies that the dominant occupation of $s$ or $p$ orbitals is not a prerequisite for the occurrence of neutron halo.

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DES Y1 results: Splitting growth and geometry to test $Λ$CDM

We analyze Dark Energy Survey (DES) data to constrain a cosmological model where a subset of parameters -- focusing on $Ω_m$ -- are split into versions associated with structure growth (e.g. $Ω_m^{\rm grow}$) and expansion history (e.g. $Ω_m^{\rm geo}$). Once the parameters have been specified for the $Λ$CDM cosmological model, which includes general relativity as a theory of gravity, it uniquely predicts the evolution of both geometry (distances) and the growth of structure over cosmic time. Any inconsistency between measurements of geometry and growth could therefore indicate a breakdown of that model. Our growth-geometry split approach therefore serves as both a (largely) model-independent test for beyond-$Λ$CDM physics, and as a means to characterize how DES observables provide cosmological information. We analyze the same multi-probe DES data as arXiv:1811.02375 : DES Year 1 (Y1) galaxy clustering and weak lensing, which are sensitive to both growth and geometry, as well as Y1 BAO and Y3 supernovae, which probe geometry. We additionally include external geometric information from BOSS DR12 BAO and a compressed Planck 2015 likelihood, and external growth information from BOSS DR12 RSD. We find no significant disagreement with $Ω_m^{\rm grow}=Ω_m^{\rm geo}$. When DES and external data are analyzed separately, degeneracies with neutrino mass and intrinsic alignments limit our ability to measure $Ω_m^{\rm grow}$, but combining DES with external data allows us to constrain both growth and geometric quantities. We also consider a parameterization where we split both $Ω_m$ and $w$, but find that even our most constraining data combination is unable to separately constrain $Ω_m^{\rm grow}$ and $w^{\rm grow}$. Relative to $Λ$CDM, splitting growth and geometry weakens bounds on $σ_8$ but does not alter constraints on $h$.

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The Effect of Environment on Type Ia Supernovae in the Dark Energy Survey Three-Year Cosmological Sample

Analyses of type Ia supernovae (SNe Ia) have found puzzling correlations between their standardised luminosities and host galaxy properties: SNe Ia in high-mass, passive hosts appear brighter than those in lower-mass, star-forming hosts. We examine the host galaxies of SNe Ia in the Dark Energy Survey three-year spectroscopically-confirmed cosmological sample, obtaining photometry in a series of "local" apertures centred on the SN, and for the global host galaxy. We study the differences in these host galaxy properties, such as stellar mass and rest-frame $U-R$ colours, and their correlations with SN Ia parameters including Hubble residuals. We find all Hubble residual steps to be $>3σ$ in significance, both for splitting at the traditional environmental property sample median and for the step of maximum significance. For stellar mass, we find a maximal local step of $0.098\pm0.018$ mag; $\sim 0.03$ mag greater than the largest global stellar mass step in our sample ($0.070 \pm 0.017$ mag). When splitting at the sample median, differences between local and global $U-R$ steps are small, both $\sim 0.08$ mag, but are more significant than the global stellar mass step ($0.057\pm0.017$ mag). We split the data into sub-samples based on SN Ia light curve parameters: stretch ($x_1$) and colour ($c$), finding that redder objects ($c > 0$) have larger Hubble residual steps, for both stellar mass and $U-R$, for both local and global measurements, of $\sim0.14$ mag. Additionally, the bluer (star-forming) local environments host a more homogeneous SN Ia sample, with local $U-R$ r.m.s. scatter as low as $0.084 \pm 0.017$ mag for blue ($c < 0$) SNe Ia in locally blue $U-R$ environments.

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