## 5. Dependence on cosmologyBesides the standard flat = 1
cosmology (SCDM) used so far, we have also studied two additional
cosmologies; one open cosmology (OCDM) with
= 0.3 and
= 0, and one flat,
-dominated cosmology
(CDM) with
= 0.3 and
= 0.7. The most obvious effect of a
different cosmology comes from the luminosity distance,
(Eq. (5)). Changing from SCDM to
OCDM and CDM increases the distance
modulus, making the high- The cosmology also affects the volume element, given by where is the proper motion
distance, =
(1+. The luminosity distance,
, is given by Eq. (5). The change in
volume element affects the SNRs when expressed in units number of SNe
per Mpc When it comes to the Type Ia SNe, the volume element enters the calculations since the time between the formation of the progenitor star and the explosion of the SN may be a significant fraction of the Hubble time. This dependency on cosmology increases as the delay time increases. The general trend is an increased SNR for the alternative cosmologies at high redshift. Fig. 9 show the estimated number per square arcmin of core collapse and Type Ia (using = 1 Gyr) SNe in the I and K´ filters down to different limiting magnitudes for the three cosmologies, using the hierarchical model for star formation.
For the number of core collapse SNe the effect of changing cosmology is small for the reasons discussed above. Only at the very faintest magnitudes is there significant deviation between the models. At K´ = 31, the estimated rates increase by a factor 1.5 when changing from SCDM to CDM. The estimated rates of Type Ia SNe differ at faint magnitudes by up to a factor two between the cosmologies. For = 1 Gyr the intrinsic rates of the OCDM and CDM models are higher than the SCDM at redshifts 1. It is, however, necessary to reach faint magnitudes to observe this increase in the total rates. Note, however, that a Type Ia at peak magnitude has m 25 at 1. This means that using SNe seen at peak allows probing of the region where the rates start to differ between the cosmological models at more moderate limiting magnitudes. Ruiz-Lapuente & Canal (1998) discuss the use of Type Ia's to distinguish between different cosmologies. In Sect. 8 we comment on their results. The increased Type Ia rates at high © European Southern Observatory (ESO) 1999 Online publication: October 4, 1999 |