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 ( \Lambda CDM , 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 Navarro-Frenk-White profiles on group/cluster scales , and are distributed in mass according to the Press-Schechter theory , then about one every 12 SNe at z \sim 1 will be magnified by \Delta m \geq 0.1 mag ( SCDM ) .
The detection rate of SN Ia with magnification \Delta m \geq 0.3 is estimated to be of order a few events yr ^ { -1 } deg ^ { -2 } at maximum B -light and I _ { AB } \leq 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 .
While the time delay between the images is shorter than 3 days ( 30 days ) in \sim 25 \% ( 50 % ) of the cases ( SCDM ) , a serious bias against the detection of small-separation events in ground-based surveys is caused by the luminosity of the foreground lensing galaxy .
Because of the flat K -correction and wide luminosity function , Type II SNe dominate the number counts at I _ { AB } > 25 and have the largest fraction of lensed objects .
The optimal survey sensitivity for Type Ia ’ s magnified by \Delta m \geq 0.75 mag is I _ { AB } \approx 23 .
Magnification bias increases their incidence by a factor of 50 in samples with I _ { AB } \leq 22 , dropping to a factor of 3.5 at 24 mag .
At faint magnitudes the enhancement is larger for SN II .