<p>Type Ia supernovae can be used as distance indicators for probing the expansion history of the Universe. The method has proved to be an efficient tool in cosmology and played a decisive role in the discovery of a yet unknown energy form, dark energy, that drives the accelerated expansion of the Universe. The work in this thesis addresses the nature of dark energy, both by presenting existing data, and by predicting opportunities and difficulties related to possible future data.</p><p>Optical and infrared measurements of type Ia supernovae for different epochs in the cosmic expansion history are presented along with a discussion of the systematic errors. The data have been obtained with several instruments, and an optimal method for measuring the lightcurve of a background contaminated source has been used. The procedure was also tested by applying it on simulated images.</p><p>The future of supernova cosmology, and the target precision of cosmological parameters for the proposed SNAP satellite are discussed. In particular, the limits that can be set on various dark energy scenarios are investigated. The possibility of distinguishing between different inverse power-law quintessence models is also studied. The predictions are based on calculations made with the Supernova Observation Calculator, a software package, introduced in the thesis, for simulating the light propagation from distant objects. This tool has also been used for investigating how SNAP observations could be biased by gravitational lensing, and to what extent this would affect cosmology fitting. An alternative approach for estimating cosmological parameters, where lensing effects are taken into account, is also suggested. Finally, it is investigated to what extent strongly lensed core-collapse supernovae could be used as an alternative approach for determining cosmological parameters.</p>

Type Ia supernovae can be used as distance indicators for probing the expansion history of the Universe. The method has proved to be an efficient tool in cosmology and played a decisive role in the discovery of a yet unknown energy form, dark energy, that drives the accelerated expansion of the Universe. The work in this thesis addresses the nature of dark energy, both by presenting existing data, and by predicting opportunities and difficulties related to possible future data. Optical and infrared measurements of type Ia supernovae for different epochs in the cosmic expansion history are presented along with a discussion of the systematic errors. The data have been obtained with several instruments, and an optimal method for measuring the lightcurve of a background contaminated source has been used. The procedure was also tested by applying it on simulated images. The future of supernova cosmology, and the target precision of cosmological parameters for the proposed SNAP satellite are discussed. In particular, the limits that can be set on various dark energy scenarios are investigated. The possibility of distinguishing between different inverse power-law quintessence models is also studied. The predictions are based on calculations made with the Supernova Observation Calculator, a software package, introduced in the thesis, for simulating the light propagation from distant objects. This tool has also been used for investigating how SNAP observations could be biased by gravitational lensing, and to what extent this would affect cosmology fitting. An alternative approach for estimating cosmological parameters, where lensing effects are taken into account, is also suggested. Finally, it is investigated to what extent strongly lensed core-collapse supernovae could be used as an alternative approach for determining cosmological parameters.

This thesis aims to give an introduction to quintessence models as well ascomparing those models with the currently accepted ΛCDM model. We willconsider quintessence in a spatially flat and isotropic Universe and useregular dynamical systems on a bounded three dimensional phase spacewhere we perform numerical calculations. This enables a globalunderstanding of these models and makes it possible to give thoroughdescriptions of the dynamics. We will discuss the three different types ofquintessence: Thawing, Scaling and Tracking quintessence and comparethem with the ΛCDM model. This thesis is based on several scientific papersand contains new numerical calculations and associated analysis. / Denna kandidatuppsats syfte är att ge en första inblick i kvintessens samtatt jämföra sådana modeller med den nuvarande accepterade ΛCDMmodellen. Vi studerar kvintessens i ett rumshomogent, isotropt och plantUniversum och använder reguljära dynamiska system i ett begränsattredimensionellt fasrum där vi utför numeriska beräkningar. Detta tillåter englobal undersökning av dessa modeller och gör det möjligt att noggrantbeskriva dynamiken. Vi diskuterar de tre olika typerna av kvintessens:”Thawing”, ”Scaling” och ”Tracking” kvintessens och jämför dessa medΛCDM modellen. Uppsatsen är baserad på flertalet vetenskapliga artiklaroch innehåller nya numeriska beräkningar med tillhörande analys.