Two formation scenarios are investigated for type Ia supernovae in elliptical galaxies: the single degenerate scenario (a white dwarf reaching the Chandrasekhar limit through accretion of matter transferred from its companion star in a binary) and the double degenerate scenario (the inspiralling and merging of two white dwarfs in a binary as a result of the emission of gravitational wave radiation). A population number synthesis code is used, which includes the latest physical results in binary evolution and allows to differentiate between certain physical scenarios (such as the description of common envelope evolution) and evolutionary parameters (such as the mass transfer efficiency during Roche lobe overflow). The thus obtained theoretical distributions of type Ia supernova delay times are compared to those that are observed, both in morphological shape and absolute number of events. The critical influence of certain parameters on these distributions is used to constrain their values. The single degenerate scenario alone is found to be unable in reproducing the morphological shape of the observational delay time distribution, while use of the double degenerate one (or a combination of both) does result in fair agreement. Most double degenerate type Ia supernovae are formed through a normal, quasi-conservative Roche lobe overflow followed by a common envelope phase, not through two successive common envelope phases as is often assumed. This may cast doubt on the determination of delay times by using analytical formalisms, as is sometimes done in other studies. The theoretical absolute number of events in old elliptical galaxies lies a factor of at least three below the rates that are observed. While this may simply be the result of observational uncertainties, a better treatment of the effects of rotation on stellar structure could mitigate the discrepancy.