Since the accelerating expansion of the Universe was discovered by observing distant Type Ia supernovae (SNe Ia), SNe Ia have been playing an important role in constraining the unknown cause behind the observed cosmic acceleration, or what we refer to as dark energy.

In order to obtain robust cosmological constraints from SN Ia data, we have applied Markov Chain Monte Carlo (MCMC) to SN Ia light curve fitting. We develop a method for sampling the resultant probability density distributions (pdf) of the SN Ia light curve parameters in the MCMC likelihood analysis to constrain cosmological parameters, and validate it using simulated data sets. Applying this method to the Joint Lightcurve Analysis (JLA) data set of SNe Ia, we find that sampling the SN Ia light curve parameter pdf's leads to cosmological parameters closer to that of a flat Universe with a cosmological constant, compared to the usual practice of using only the best fit values of the SN Ia light curve parameters.

On the other front, SN classification and redshift estimation using photometric data only have become very important for the Large Synoptic Survey Telescope (LSST), given the large number of SNe that LSST will observe and the impossibility of spectroscopically following up all the SNe. We investigate the performance of a SN classifier that uses SN colors to classify LSST SNe with the Random Forest classification algorithm. Our classifier results in an AUC of 0.98 which represents excellent classification. We are able to obtain a photometric SN sample containing 99% SNe Ia by choosing a probability threshold. We estimate the photometric redshifts (photo-z) of SNe in our sample by fitting the SN light curves using the SALT2 model with nested sampling. We obtain a mean bias (⟨zphot−zspec⟩) of 0.012 with σ(zphot−zspec1+zspec)=0.0294 without using a host-galaxy photo-z prior, and a mean bias (⟨zphot−zspec⟩) of 0.0017 with σ(zphot−zspec1+zspec)=0.0116 using a host-galaxy photo-z prior. Assuming a flat ΛCDM model with Ωm=0.3, we obtain Ωm of 0.305±0.008 (statistical errors only), using the simulated LSST sample of photometric SNe Ia (with intrinsic scatter σint=0.11) derived using our methodology without using host-galaxy photo-z prior.

The methodology developed in this dissertation will be useful in the use of SN Ia data for precision cosmology and help boost the power of SNe from the LSST as cosmological probes.