Gravitational Lensing of Distant Supernovae in Cold Dark Matter   Universes
  Ongoing searches for supernovae (SNe) at cosmological distances have recently started to provide large numbers of events with measured redshifts and apparent brightnesses. Compared to quasars or galaxies, Type Ia SNe represent a population of sources with well-known intrinsic properties, and could be used to detect gravitational lensing even in the absence of multiple or highly distorted images. We investigate the lensing effect of background SNe due to mass condensations in three popular cold dark matter cosmologies (LambdaCDM, OCDM, SCDM), and compute lensing frequencies, rates of SN explosions, and distributions of arrival time differences and image separations. If dark halos approximate singular isothermal spheres on galaxy scales and NFW profiles on group/cluster scales, and are distributed in mass according to the Press-Schechter theory, then about one every 12 SNe at z~1 will be magnified by Delta m>0.1 mag (SCDM). The detection rate of SN Ia with magnification Delta m>0.3 is estimated to be of order a few events per year per square degree at maximum B-light and I<25, a hundred time smaller than the total rate expected at these magnitude levels. In the field, events magnified by more than 0.75 mag are 7 times less frequent: about one fifth of them gives rise to observable multiple images. Because of the flat K-correction and wide luminosity function, Type II SNe dominate the number counts at I>25 and have the largest fraction of lensed objects. The optimal survey sensitivity for Type Ia's magnified by Delta m>0.75 mag is I=23. Magnification bias increases their incidence by a factor of 50 in samples with I<22, dropping to a factor of 3.5 at 24 mag. At faint magnitudes the enhancement is larger for SN II. 
Cristiano Porciani and Piero Madau