In the past five years, the discrepancies between local and early value of H0 have attracted much interest and attention since the Planck 2013 (Planck Collaboration et al., 2014) data release revealed a substantially lower value than SH0ES (R11). Since then, the SH0ES data set has grown substan- tially, and numerous reanalyses of both measurements (Section 5.2.2) have taken place. While small oscillations have occurred at both ends, these subsequent works have for the most part reinforced the two clusters of values: the local distance ladder based measurements at ∼73 km s−1Mpc−1, and the CMB measurements at ∼68 km s−1Mpc−1. Of particular interest are the measurements from modes other than SNe or the CMB. The strong lensing measurement from H0LiCOW, like SNe Ia on a distance ladder, is based on distance measurements in the local Universe and is in good agreement with supernovae atH0 = 71.9−+23..40 km s−1Mpc−1 (Bonvin et al., 2017). The inverse distance ladder method in Aubourg et al. (2015), calibrated on the absolute distance scale in the early Universe (via rs, the
sound horizon at radiation drag) agrees with measurements from the CMB. These probes have played a
8This is possible as the combination of SNe Ia and BAO as probes constrains the productr
SH0in a model-independent way.
§5.3 Future directions 99
signifcant role in corroborating measurements at late and early times.
As we have seen in Section 5.2.2, the numerous reanalyses of the distance ladder Hubble con- stant measurements in R11 and R16, including ours in Z17, have steadfastly supported their central numerical results. Moreover, other than numerical agreement, the analyses all show reasonable robustness to choices in the analysis. These results, as well as the new geometric distances to Galactic Cepheids, suggest that a systematic uncertainty in some step of the distance ladder is unlikely. The tension in the numerical value of H0 has persisted over five years. The agreement from external probes and consistencies in reanalyses have lent support to a real physical or cosmological origin of the tension inH0. Whichever of these scenarios we are inclined to believe is true, whether there is something odd in cosmology, whether there is some undetected systematic in one of the measurements, or the two measurements are both in some ways consistent with ΛCDM, or something in between, it is (at least) as clear now as it had been in the past several years that it is crucial that our unconscious biases, or other human factors, do not impact our numerical results, which continue to have profound consequences. The growing trend of blinding cosmological analyses in recent years (Section 1.5) remains as important now as ever before.
Chapter 6
Dark Energy Survey
This chapter concerns the supernova cosmology analysis with the Dark Energy Survey 3-year Spectro- scopic Supernova (DES3YS) sample, focusing on the established maximal likelihood ‘JLA-like’ approach as part of the Dark Energy Survey Supernova working group (DES SNWG). For an overview of DES, see Section 6.1. Following an introduction to context for the analysis in Section 6.1, I describe the JLA-like analysis in Section 6.1.2 and present the equations for the physical Universe’s expansion in Section 6.2. Then I present an overview of the data (Section 6.3), followed by equations and methods for prepar- ing the data and cosmology fitting in Sections 6.4 and 6.5, respectively. My main contributions to the DES SNWG-wide analysis have been developing the computation of systematics (Section 6.5.2) and the cosmology fitting code (Section 6.5.1) for the JLA-like approach. The work described in this section encompasses contributions from several members of the DES SNWG. In particular, I have developed the code for this analysis in collaboration with Chris Lidman; Tamara Davis will continue to run this analysis on updated DES3YS data. I reference papers in preparation for parts of the project where relevant, and otherwise identify the DES SNWG member who was responsible for doing the work for a specific part of the analysis. Section 6.6 contains results, including comparisons of results to other analysis methods on the same data and a breakdown of sources of errors, and discussions. The work in this chapter forms portions of the wider alphabetically-authored DES3YS cosmological results paper Dark Energy Survey Collaboration, in prep..
6.1
Introduction
Type Ia supernovae were pivotal in discovering cosmic acceleration, and remain a leading method in the Dark Energy Survey. Earlier, Section 1.2.1 detailed their significance in modern cosmology, while Section 2.4.5 pinpointed the significance of DES SNe in the context of wider supernova surveys. We refer the reader to the above sections for introductions to those areas. In this section, we will examine DES supernovae in more detail and motivate the JLA-like analysis.
6.1.1
DES supernovae
The final DES SN Ia sample is expected to number ∼2500, and will consist predominantly of photo- metrically classified supernovae. A smaller proportion of supernovae will be spectroscopically classified. Current analyses within the DES SNWG are focused on the DES 3-year spectroscopic (DES3YS) SN Ia sample. The analyses of this sample, including the JLA-like method presented in this chapter and those in Brout et al., (in prep.) and Hinton et al., (in prep.), are intended as an intermediate stepping stone on the way to the final 5-year photometric sample, allowing the development and verification of techniques that will be used then. Constraints from the DES3YS sample were expected to be comparable with constraints in the Joint Lightcurve Analysis (JLA) of SNLS-SDSS supernovae (Betoule et al., 2014, hereafter B14) and have been largely so (see preliminary results in Sections 6.6 and 6.7). JLA follows a series of developments focusing on improving and enlarging collections of SNe Ia for cosmological studies, including notably the Supernova Legacy Survey (SNLS) at high redshift, the SDSS supernova survey at intermediate redshifts, and a collection of low-redshift surveys including the Harvard-Smithsonian Center for Astrophysics (CfA) supernova survey, Carnegie Supernova Project (CSP), and Lick Obser-
vatory Supernova Survey (LOSS). A major lesson from Conley et al. (SNLS; 2011); Guy et al. (SNLS; 2010); Sullivan et al. (SNLS; 2011) has been that uncertainties in photometric calibration significantly dominate the systematic error budget. JLA originated as an effort to reduce the impact of calibration (Betoule et al., 2013), while combining the aforementioned notable surveys over different redshift ranges. This chapter focuses on the JLA-like method, based on methods and in particular techniques for quantifying systematic errors developed in SNLS and JLA.
While DECam will obtain photometry for all supernovae to determine distances for the SN Ia Hubble diagram, and photometric redshifts are possible, (e.g. Bolzonella et al., 2000; Salvato et al., 2009; Ben´ıtez, 2000; Laurino et al., 2011) spectroscopic redshifts for DES supernovae and their host galaxies will come from a variety of external spectroscopic facilities, the primary one being the Australian Dark Energy Survey (OzDES; Yuan et al., 2015; Childress et al., 2017). OzDES and the other sources of spectroscopy are described in Sections 2.4.5 and 6.3.2. In the first three years of DES,∼250 SNe Ia were spectroscopically confirmed by OzDES and other sources of spectroscopy D’Andrea et al., (in prep.); around 2500 host galaxy redshifts have been observed by OzDES.
As discussed in Sections 1.2.1 and 2.4.5, DES is necessary for improving the statistical constrain- ing power at high redshift, and will enable measurements of cosmological parameters to a new degree of accuracy. These parameters and SN Ia-specific parameters are presented in Section 6.2, and notably include the densities1 Ω
m,ΩDE of matter (both baryonic and dark) and dark energy,2 the equation-of- state parameterw for dark energy, and H0. The Hubble constant H0 – the focus of Chapters 4 and 5 and discussed in more detail there – represents the Universe’s current expansion rate. This is degenerate with the absolute SN Ia peak magnitude, and is often written as the dimensionless Hubble parameter
h:=H0/100 km s−1Mpc−1.
In particular, DES sets out to affirm or refute, with unprecedented precision, the default scenario where dark energy takes the form of a cosmological constant with equation-of-state parameterw=−1. Finally, DES will pave the way for the next generation of large-scale cosmology experiments starting with the Large Synoptic Survey Telescope (LSST).
6.1.2
JLA-like cosmological analysis
There are three analysis methods within the DES SNWG for performing cosmological analyses of the DES3YS sample: the BEAMS with Bias Corrections Brout et al., (in prep.), the Bayesian Hierarchical Model (BHM) method Hinton et al., (in prep.), and the JLA-like analysis, which we focus on in this chapter.
We present a maximal-likelihood (or χ2-minimising) fit of the DES3YS sample supplemented by a hybrid sample of low-redshift supernovae from CfA3/4 and CSP. We closely follow methods in JLA, which estimate and correct for systematics, namely Malmquist bias, host galaxy mass dependence, and peculiar velocities (discussed in Section 6.4.3), and use covariance matrices to account for correlated uncertainties: in these corrections, in statistical uncertainties, and in other systematics (specifically photometric calibration, scatter model dependence, non-Ia contamination, Milky Way extinctions; see Section 6.5.2). The corrected SN Ia distance moduli and redshifts are fitted for parameters of thewCDM or ΛCDM cosmological models according to equations in Section 6.2, using standard Markov Chain Monte Carlo methods for parameter estimation, described in Section 6.5.1.
In short, the analysis of the DES3YS data set using the JLA-like method is a proof of concept, which demonstrates what is possible using currently available DES data and existing techniques. It allows comparisons (i) between established JLA-like techniques and the newer methods of BHM and BBC, and (ii) between the present DES sample and the existing JLA data set. SNLS, and by extension JLA and subsequently Pantheon, remains the benchmark for high-redshift SN Ia surveys until DES is
1Written as fractions of the Universe’s critical density (Equation 6.5). 2The latter is often written Ω
Λfor a cosmological constant, but in a generalised situation where we do not assume that dark energy takes this form, we write it as a more general ΩDE.