Type Ia supernovae (SNe) have long been the gold standard for precision cosmology and after several decades of intense research the supernova (SN) community was in 2011 honored by giving the Nobel Prize in physics for the discovery of Dark Energy to the leaders of the two big SN collaborations: Saul Perlmutter (Supernova Cosmology Project), Adam Riess, and Brian Schmidt (High-Z team).

After decades of study we still do not know the detailed mechanism that governed SNe explosions, but we are today in the situation where the SN sample size has became large enough for the statistical errors to be smaller then the systematic errors. The down side to this is that we can not improve the SNe further as cosmological probes before we know the source of the systematic dispersions. On the other hand the systematic offsets might actually be the measurements that will lead to new information on the detailed mechanisms that governs the SN explosions.

In the first of three papers I investigate the host galaxy of the first SN Ia found in the Cosmic Assembly Near-IR Deep Extragalactic Legacy Survey (CANDELS) SN search. From long slit spectroscopy using the Xshooter spectrograph and broadband photometry I determine the gasphase metallicity, stellar mass and stellar age for this z = 1.55 host galaxy. I am also able to rule out the presence of any AGN though emission-line ratios. The host is classified as a highly star forming, low mass, low metallicity galaxy. It is a clear outlier in star formation and stellar mass compared to most low redshift (z < 0.2) SNe, but consistent with intermediate (0.2 < z < 1.0) and high (z > 1) redshift SNe. This is mainly due to the change in specific star-formation rate as a function of redshift. This can potentially impact the use of high redshift SN Ia as standard candels.

In the second paper I investigate one of the high redshift SN Ia hosts found in the Subaru Deep Field (SDF) SN search. The SDF SN search relies heavily on photometric redshifts and transients previously identified as active galactic nuclei (AGN) to reproduce the cosmic SN rate. Due to the small number statistic, especially at high redshift, catastrophic redshift outliers and miss-identified transients can bias the inferred SN rate. The host galaxy of the SDF transient was observed with the Xshooter spectrograph. I confirm the photometric redshift of z = 1.55 and from emission-line ratios I can also rule out AGN activity. I found a young host galaxy with high star-formation rate and sub-solar metallicity.

In the last paper I analyze the full high redshift (z > 1) SN host sample from the CANDELS and CLASH SN search. I determine the stellar properties of each host by fitting the broad-band photometry using the GalMC SED-fitting code. I try to constrain the slope of the delay-time distribution (DTD) by assuming a simple two-bin form, known as the A+B model. This simple model predicts that the DTD slope is constant if the ratio of the two parameters A/B / sSFR. I find that the A/B-ratio is consistent with this relation out to redshift z ⇠ 2. From the assumption that the DTD slope is constant I propose a new form of the A+B model.