Observations of known-brightness objects are used to obtain distance measurements, which in turn allow for constraints on the fundamental cosmological parameters that describe our Universe. As we enter a new era of precision cosmology with the advent of 'Big Data' surveys such as PS1, DES and LSST, robust control of systematic uncertainties is paramount in yielding unbiased distance estimates.

This project will explore the connection between Type 1a Supernovae (SNe 1a) ejecta velocity and the underlying SNe spectral energy distribution (SED), using a state-of-the-art hierarchical Bayesian model BayeSN, so as to control velocity-dependent correlations, and further refine distance measurements for cosmological analysis.

Conditioned on supernova optical-NIR light-curve data, BayeSN marries Bayesian statistics with functional data analysis techniques to infer an intrinsic population flux model on time and wavelength, that is further warped on a supernova-by-supernova basis by functional principal components, dust, and a residual covariance function.

Foremostly, we will continue to examine whether velocity measurements of the Silicon-II line at supernova peak brightness serve to discriminate between sub-populations of SNe. Historically, a 'redder-faster' relation has been reported, whereby observations of redder (B-V) optical colours are typically coupled to higher ejecta velocities (v<-11km/s). However, owing to the confounding of dust and intrinsic colour variation, this correlation may be an artefact. By contrast, BayeSN models the effects of intrinsic colour and dust extinction independently, meaning we are primed to discern whether this correlation is legitimate. Gaussian mixture models may be exploited to efficiently explore and identify correlated features.

Moving forward, velocity measurements at peak will be included in the BayeSN framework, with the expectation that underlying correlations, if any, will be captured, leading to improved distance estimates. In a similar vein, measurements of host-galaxy mass, distance from galaxy-centre, galaxy reddening etc. can also be implemented.

Finally, this work could lead to the implementation of velocity measurements as a function of time, to provide even tighter constraints. Alternatively, BayeSN could be adapted to perform a full cosmological analysis, coupled with measurements from the first rung of the distance ladder, e.g. Cepheid variables, Mira Variables, Tip of the Red Giant Branch stars etc. This work will contribute towards the growing community-wide effort to control systematic uncertainties that may bias cosmological analyses.