We use the redshift distribution of type-Ia supernovae ( SNe ) discovered by the Supernova Cosmology Project to constrain the star formation history ( SFH ) of the Universe and SN Ia progenitor models .
Given some of the recent determinations of the SFH , the observed SN Ia redshift distribution indicates a long ( \mathrel { \raise 1.29 pt \hbox { $ > $ } \mkern - 14.0 mu \lower 2.58 pt \hbox { $ \sim$ } } 1 h ^ { -1 } Gyr ) mean delay time between the formation of a stellar population and the explosion of some of its members as SNe Ia .
For example , if the Madau et al .
( 1998 ) SFH is assumed , the delay time \tau 
is constrained to be \tau \geq 1.7 ( \tau \geq 0.7 ) h ^ { -1 } Gyr at the 95 \% ( 99 \% ) 
confidence level ( CL ) .
SFHs that rise at high redshift , similar to those advocated by Lanzetta et al .
( 2002 ) , are inconsistent with the data at the 95 \% CL unless \tau > 2.5 h ^ { -1 } Gyr .
Long time delays disfavor progenitor models such as edge-lit detonation of a white dwarf accreting from a giant donor , and the carbon core ignition of a white dwarf passing the Chandrasekhar mass due to accretion from a subgiant .
The SN Ia delay may be shorter , thereby relaxing some of these constraints , if the field star formation rate falls , between z = 1 and the present , less sharply than implied , e.g. , by the original Madau plot .
We show that the discovery of larger samples of high- z SNe Ia by forthcoming observational projects should yield strong constraints on the progenitor models and the SFH .
In a companion paper , we demonstrate that if SNe Ia produce most of the iron in galaxy clusters , and the stars in clusters formed at z \sim 2 , the SN Ia delay time must be lower than 2 Gyr .
If so , then the Lanzetta et al .
( 2002 ) SFH will be ruled out by the data presented here .