Application of Bayesian statistics in Supernovae Ia cosmology

Abstract

The purpose of this thesis is to apply Bayesian analysis to supernovae type Ia (SNIa) cosmology to derive more accurate parameter estimation including cosmological parameters. Additionally, it aims to improve the standard SALT2 light-curve fitting procedure by providing empirical and physically motivated correction to the linear Tripp formalism. \n BAHAMAS \n We develop BAyesian HierArchical Modelling for the Analysis of Supernova cosmology (BAHAMAS) software package for the analysis of SNIa cosmology in a statistically consistent manner. We apply our algorithm to a sample of 740 spectroscopically confirmed SNIa from the Joint Light-curve Analysis (JLA) dataset and simultaneously determine cosmological parameters and population level parameters, including residual scatter. Combining JLA and Planck Cosmic Microwave Background data, we find significant discrepancies in cosmological parameter constraints with respect to the standard analysis: we find omega_m = 0.399 \pm 0.027, 2.8 \sigma higher than previously reported and w = -0.910 \pm 0.045, 1.6 \sigma higher than the standard analysis. \n Extensions to SALT2 \n BAHAMAS provides a framework for analysing to extensions the classical SALT2 light-curve fitting procedure including empirical corrections to the standard Phillips relationship. We analyse four extensions in this thesis. We use the host galaxy mass as an additional covariate in the linear regression and allow for a redshift dependence for the colour-magnitude slope, \beta(z). We use the time of the second peak in the NIR band due to re-brightening, t_2, as an alternative standardization parameter of SNIa peak brightness. Finally we split the SNIa into two groups based on the distance to their host galaxy and investigate if SNIa further from the host galaxy are better standard candles. \n Simple-BayeSN \n Conventional SNIa cosmology analyses currently use a simplistic linear regression of magnitude versus colour and light curve shape. We construct a probabilistic generative model for the dusty distribution of extinguished absolute magnitudes and apparent colours as the convolution of an intrinsic SNIa colour-magnitude distribution and a host galaxy dust reddening-extinction distribution. Additionally, we combine Simple-BayeSN and BAHAMAS to allow for cosmological parameter estimation of "dusty" SNIa light curves. \n Selection Effects \n Most modern SNIa cosmological analyses account for selection effects by a bias correction to the apparent magnitude (or distance modulus). However, within a Bayesian framework, it is possible to consistently account for selection effects by associating a selection probability to each observation. We use SNANA simulations and supervised classifiers to predict the selection probability conditional on the latent variables. Additionally, we use Monte Carlo simulations to integrate the latent variables and derive the selection probability conditional on the hyper-parameters (and redshift).