La Pasión de los Mediocres

The process of going from SN Ia lightcurves to distance moduli using the SALT2 lightcurve fitter involves a number of assumptions, in particular about the parent population distributions and intrinsic scatter of SNe Ia. In JLA, these are taken into account by the work in Mosher et al. (2014) to perform numerous realisations of end-to-end simulations of SALT2 training and fitting, applied to realistic SNLS-like surveys. In particular, they investigate the difference or bias in µ when comparing different colour-dependent scatter models (e.g. G10, C11 for those in Guy et al. (2010) and Chotard et al. (2011) respectively, or COHfor coherent, with no colour-dependence), input models (G10for SALT2 surfaces in Guy et al. (2010), G10’– a second model trained using G10 as a starting point, described in Mosher et al. (2014), orH for Hsiao et al. (2007) templates), and real versus ideal characteristics of the test and training sets.

As in JLA, we assume coherent intrinsic scatter, roughly binned by redshift for each survey, with

σint,SNvalues determined in JLA (fit using the restricted likelihood method in Betoule et al. (section 5.5, 2014)) of 0.08 for DES (similar to SNLS in redshift range) and 0.134 for nearby supernovae. We follow JLA in conservatively using the largest bias in distance modulus from Mosher et al. (2014) (from the G10’–C11–REAL–REAL model in figure 16 therein) to account for the systematic error from the SALT2 lightcurve fitter and model, and assuming a coherent intrinsic scatter. As in computing Cbias and CnonIa, the error vector Emodel is computed for supernova magnitudes using only redshifts, and multiplied by its own transpose (as a matrix product, as in Equation 3.18) to find Cmodel.

Non-Ia contamination

Despite each supernova in our sample having been classified a SN Ia from its spectrum, there is still potential for contamination from primarily SNe Ib/c, which have spectra that at certain epochs and wavelength ranges or redshifts can resemble SN Ia spectra, particularly when signal-to-noise is poor. Our estimation of the systematic error due to potential contamination from misclassified supernovae follows methods in SNLS and JLA, which are described in Conley et al. (2011).

Individual supernovae in the DES3YS sample are spectroscopically classified with two degrees of certainty: as ‘Ia’ or ‘Ia*’, for certain and highly probable SNe Ia, respectively. For calculating CnonIa, the effective bias from potential misclassification is computed as a function of binned redshift. This effective bias is the product of the SN Ia* fraction and the ‘raw’ bias, or expected magnitude bias from a single misclassified supernova. The latter, shown in the second column of Table 3.1, is taken directly from estimates in Conley et al. (section 5.5, 2011) derived from simulations which assumes that contaminants are SNe Ib/c, and using rates and luminosity distributions in Li et al. (2011a), also based on Richardson et al. (2002); Bazin et al. (2009). The third column of Table 3.1 shows the SN Ia* fraction for the DES3YS sample in that bin, taken to represent the probability of misclassification. The product of both is the effective bias, given in millimags in the fourth column.

Table 3.1 .

Redshifta _{Raw bias}b _{SN Ia* Effective}

(mag) fraction bias (mmag)

0.10 0.015 0.0294 0.44

0.26 0.024 0.173 4.2

0.41 0.024 0.102 2.4

0.57 0.024 0.120 2.9

0.72 0.023 0 0

a _{Lower boundary of redshift bin}

b _{Taken directly from Conley et al. (table 14, 2011)}

and the SN Ia* fraction; this is applied to all supernovae in the redshift bin. Then,

CnonIa=EnonIa×ETnonIa. (3.22)

For future DES supernova analyses where the sample consists of photometrically classified supernovae, the above method will need to be revised with more simulations involving intricacies of photometric classification, as well as possibly newer estimates of the raw magnitude bias due to SN Ib/c contamination.

Chapter 4

A blinded redetermination of the

Hubble constant

The following two chapters address the issue of the current tension in the Hubble constant (Sec- tion 1.2.2) using methods in Chapter 3. My work here has focused on determining the Hubble constant, using data in recent SN Ia based calculations in Riess et al. (2011) (hereafter R11). We approach these data sets using a renewed approach in modern SN Ia cosmology studies (Conley et al., 2011; Betoule et al., 2014), notably including using full covariance matrices to capture correlated supernova systematics, and a simultaneous fit of all data to a set of equations. This chapter is based around (and makes use of portions of text from) the refereed paper Zhang et al. (2017) (hereafter Z17) which sets up the analysis framework using the established R11 data, while Chapter 5 discusses the conclusions of this chapter, particularly the increased error, in the context of the unresolved tension inH0. The structure of this chapter of is similar to Z17: we start in Section 4.1 by motivating the work presented therein, and framing its place within the literature. This is followed by an outline of the data in Section 4.2 and establishing the equations for measuringH0 in Section 4.3. In Section 4.4 we discuss the fitting the sample of Cepheid variables used for calibrating the supernova distance measurements and the systematics which affect them. Sections 4.5.4 presents preliminary SN Ia-only fits while Section 4.6 contains results from the combined simultaneous fits.

4.1

Introduction

In Section 1.2 we introduced the current discrepancy between values of the Hubble constant derived from local distance measurements, and from observations of the CMB in the early Universe extrapolated to the present time assuming ΛCDM. The effort to measure H0 from a distance ladder have been led by SH0ES (Riess et al., 2009b, 2011, 2016). Numerous reanalyses of the SN Ia-based measurement have followed, many of which have focussed on the methods for the rejection of Cepheid outliers. Efstathiou (2014, hereafter E14) questions and revises the outlier rejection algorithm in R11, concluding

H0 = 72.5±2.5 km s−1Mpc−1 assuming a null metallicity dependence of the Leavitt law. Recently, Cardona et al. (2017) uses Bayesian hyper-parameters to down-weight portions of the Cepheid data for both R11 and R16 data sets, finding H0= 73.75±2.11 km s−1Mpc−1 for the R16 data. Moreover, the dependence of the intrinsic magnitude of SNe Ia on host galaxy properties has been explored in recent years (e.g. Sullivan et al., 2010). Rigault et al. (2013, 2015) find a relationship between peak brightness and star formation rate, and infer an overestimate of ∼3 km s−1_Mpc−1 _{in the R11 value of H}

0 arising from the fact that the calibration set of SNe Ia exist in galaxies which necessarily contain Cepheids, hence are likely to be late-type galaxies. However, Jones et al. (2015) repeat the same analysis, with an increased sample size and the R11 selection criteria applied, and find no significant difference in the brightness of SNe Ia in star-forming and passive environments.

The CMB data in Planck has been reanalysed in Spergel et al. (2015), who find a similar value to Planck Collaboration et al. (2014), ofH0= 68.0±1.1 km s−1Mpc−1. Bennett et al. (2014) provides a CMB-based measurement which is independent of Planck, by combining data from WMAP9, the South

Pole Telescope (SPT) and Atacama Cosmology Telescope (ACT), and baryon acoustic oscillation (BAO) measurements from BOSS, finding a value ofH0 = 69.3±0.7 km s−1Mpc−1 (with a slight increase to

H0= 69.7±0.7 km s−1Mpc−1if SN Ia data from R11 are included), which is slightly less discrepant with SN Ia-based values. Strong lensing provides an independent but model-dependent local measurement of H0: the Suyu et al. (2017, (H0LiCOW)) program studies time delays between multiple images of quasars in strong gravitational lens systems, and findH0 = 71.9−+23..40 km s−1Mpc−1in flat ΛCDM. It is noteworthy that the H0LiCOW analysis was performed blind to derived cosmological parameters. One of the greatest open questions in cosmology today is whether the tension in H0 signifies new physics – where inconsistencies between results from supernovae and the CMB arise from the model- dependence of the measurement, and disappear when the correct model is used – or is the result of some systematic error in one or both measurements that has yet to be accounted for.

A genuine inconsistency in the value of the Hubble constant at low and high redshifts would have profound consequences. Therefore it is imperative to fully understand uncertainties in the measured values ofH0, and to preclude possible human biases on the result, as introduced earlier in Section 1.5. The most effective way of achieving the latter is to blind the value ofH0 throughout the analysis, as described in Section 4.3.4.