The use of Type Ia supernovae (SNe Ia) as distance indicators is essential for studying the expansion history of the Universe and for exploring the nature of dark energy. However, a lack of understanding of the progenitor systems and the empirically derived colour-brightness corrections represent severe limitations for SNe Ia as cosmological probes. In this thesis, we study how dust along the line of sight towards SNe Ia affects the observed light over a wide range of wavelengths; from X-rays to infrared.

Unless properly corrected for, the existence of intergalactic dust will introduce a redshift dependent magnitude offset to standard candle sources and bias the cosmological parameter estimates as derived from observations of SNe Ia. We model the optical extinction and X-ray scattering properties of intergalactic dust grains to constrain the intergalactic opacity using a combined analysis of observed quasar colours and measurements of the soft X-ray background. We place upper limits on the extinction A_B(z = 1) < 0.10 - 0.25 mag, and the dust density parameter Ω_dust < 10⁻⁵ − 10⁻⁴ (ρ_grain/3 g cm⁻³), for models with R_V < 12 − ∞, respectively.

Dust in the host galaxies, and dust that may reside in the circumstellar (CS) environment, have important implications for the observed colours of SNe Ia. Using the Hubble Space Telescope and several ground based telescopes, we measure the extinction law, from UV to NIR, for a sample of six nearby SNe Ia. The SNe span a range of E(B − V ) ≈ 0.1 − 1.4 mag and R_V  ≈ 1.5 − 2.7, showing a diversity of dust extinction parameters. We present mid- and far-infrared (IR) observations for a number of SNe Ia, obtained with the Herschel Space Observatory and Spitzer Space Telescope, addressing CS dust as an explanation for “peculiar” extinction towards some SNe Ia. No excess IR emission is detected, limiting CS dust masses, M_dust < 10⁻⁵ solar masses. In particular, the timely appearance of SN 2014J in M82 - the closest SN Ia in several decades - allows for detailed studies, across an unprecedented wavelength range, of its lightcurve and spectral evolution along with the host galaxy and CS environment.

Type Ia supernovae (SNe Ia) have proven to be extremely useful for measuring cosmological distances and were used for the discovery of the accelerated expansion of the universe. Although thousands of SNe Ia have been observed to date, many questions surrounding the physics of the explosions and the nature of their progenitor systems remain unanswered. An notable property of many SNe Ia is the relation between extinction due to dust and their colour. For example SN 2014J, the nearest SN Ia in recent years, has an extinction relation which would be very unusual to observe in the Milky Way. One possible explanation to the peculiar extinction could be the presence of circumstellar (CS) dust surrounding the explosions. Incidentally, some proposed progenitor models of SNe Ia suggest that the explosions are surrounded by shells of matter, which could account for the unusual extinction.

CS gas would be ionised, if it is exposed to the intense ultraviolet (UV) radiation of a SN Ia. The research presented in this thesis focuses on the search for CS gas by observing the effects of photoionisation on absorption lines commonly detected in optical spectra. Simple models suggest that the frequently studied sodium doublet (Na I D) should significantly decrease or even disappear if the gas is in the CS environment. Conversely, the absence of variations implies that the absorbing gas clouds must be far from the explosion, in the interstellar medium (ISM). To date, few SNe Ia have been shown to have variable absorption lines, to which we have added another case with SN 2013gh. Yet, we have also shown that most observations searching for variable absorption lines have been taken at too late phases, when most CS gas will have already been ionised. Setting out to obtain the earliest possible coverage of a SN Ia with high-resolution spectra, we have been able to set strong limits on the presence of CS gas surrounding SN 2017cbv.

Along with evidence from other observational methods, these results have shown that there is little matter in the CS environments of SNe Ia, suggesting that the peculiar extinction likely results from the dust properties of their host galaxy ISM. Although the progenitor question cannot be resolved by these observations, nondetections of CS gas point to models which do not deposit large amounts of matter in their surroundings.

Type Ia Supernovae (SNe) have been used to discover the accelerated expansion of the universe but many open questions remain unanswered. These include the stellar progenitor, extinction and possible systematic trends in the supernova brightness for different host galaxy environments or cosmic time. In this thesis we attempt to address these open questions by looking at a large homogeneous sample of nearby SNe from the Palomar Transient Factory (2009-2012) and the intermediate Palomar Transient Factory (2013-2017) for which we have 265 well-observed light-curves in the R-band and 2981 spectra from a total of 2060 SNe.

In Paper I we study the global properties of the R-band light-curves, such as rise-time, stretch and intrinsic brightness at different SN phases, to examine if there are multiple populations in any of the parameters suggesting different progenitor channels. We do not find evidence supporting this. We characterize the second maximum in the R-band in Paper II and find a correlation between the time from light-curve maximum, and the "colour-stretch" parameter, a proxy for ⁵⁶Ni mass. We also found that the integrated flux under the second maximum, correlates with the transparency timescale, a proxy for total ejecta mass. Using these two relations we find that sub-Chandrasekhar double detonation models can account for the biggest fraction of the PTF/iPTF SNe light-curves properties. In Paper III we present the spectroscopic sample of PTF/iPTF and using automatic machine learning tools to explore spectral features and possible connection to photometric and host galaxy properties.

Paper IV focuses on a small sample of SNe, with multi-wavelength light-curves, to address one of the most important systematic uncertainties in supernova cosmology: extinction by dust in the line-of-sights. We found a diversity in the reddening laws as characterised by the total-to-selective extinction, R_V. Finally, Paper V looks at a strongly lensed SNIa at z=1.4  to see if there is evolution of its spectral and photometric properties over cosmic time. Both Paper IV and Paper V use the code developed for Paper III to analyse spectra.