Type Ia supernovae can, for a short period of time, reach the same brightness as an entire galaxy. They are responsible for the creation of a large fraction of all heavy elements and can be used, as standard candles, to prove that the expansion of the universe is accelerating. Yet, we do not fully understand them.

A basic picture where Type Ia supernovae are caused by thermonuclear explosions of white dwarfs is generally accepted, but the details are still debated. These unknowns propagate into systematic uncertainties in the estimates of cosmological parameters. A Monte Carlo framework, SMOCK, designed to model this error propagation, is presented. Evolution with time/distance and the nature of reddening are studied as the dominant astrophysical uncertainties.

Optical spectra of Type Ia supernovae contain a wealth of information regarding the nature of these events, and can be used both to understand supernovae and to limit the systematic uncertainties in cosmological parameter estimates. We have reduced spectra observed with the Nordic Optical Telescope and the New Technology Telescope in conjunction with the SDSS-II supernova survey, and compared spectral properties (pseudo-Equivalent Widths and line velocities) of this sample with local supernovae.We have further studied possible systematic difficulties in such comparisons between nearby and distant supernovae, caused by noise and host galaxy contamination.Taking such uncertainties into account, we find a tentative evolution in supernova properties with redshift, compatible with expected demographic changes. Correlations with light curve shape found by other studies are confirmed. A tentative correlation with light curve colour is also presented. The latter could indicate an intrinsic component of the observed reddening, i.e. independent of interstellar dust in the host galaxy.

The use of Type Ia supernovae as standardisable candles for probing cosmological parameters with high precision requires good knowledge about how the supernova light is affected along the line of sight and how the intrinsic brightness varies between objects. The work in this thesis addresses these topics.

One potential problem is if there is an evolution of the intrinsic brightness of Type Ia supernovae with redshift. To investigate this we have compared spectral features of intermediate-redshift supernovae with local ones. No redshift evolution could be detected up to z = 0.3. Correlations of the strength of some of the spectral features with supernova colour and lightcurve shape were found, in particular for the feature which primarily is a product of SiII 4130 absorption.

Another difficulty concerns dust present in the line of sight which could both dim and redden the supernovae. We investigated dust extinction in distant galaxies by comparing the colours of background quasars with what is expected for different types of dust. A wide range of fitted values of Rv, the total-to-selective extinction ratio, was found, indicating that the dust properties in other galaxies could potentially be different from the Milky Way value, Rv ~ 3.1.

The light could also be affected by an intergalactic dust population with an almost flat extinction curve. We found, using quasar observations, that any dimming larger than 0.2 magnitudes in the rest-frame B-band for a Type Ia supernova at z = 1 is ruled out. If the intergalactic dust has an extinction law similar to the one in the Milky Way, the corresponding limit would be 0.03 magnitudes.

Another problem is that if axions exist, photons could be converted to axions over large cosmological distances, in the presence of magnetic fields, leading to a dimming of distant objects. For some model parameters, a dimming as large as 0.6 magnitudes for a Type Ia supernova at z = 1 would be allowed from quasar observations.