We derive the expected Type II SN differential number counts , N ( m ) , and Hubble diagram for SCDM and LCDM cosmological models , taking into account the effects of gravitational lensing ( GL ) produced by the intervening cosmological mass .
The mass distribution of dark matter halos ( i.e . the lenses ) is obtained by means of a Monte Carlo method applied to the Press-Schechter mass function .
The halos are assumed to have a NFW density profile , in agreement with recent simulations of hierarchical cosmological models .
Up to z = 15 , the ( SCDM , LCDM ) models predict a total number of ( 857 , 3656 ) SNII/yr in 100 surveyed 4 ^ { \prime } \times 4 ^ { \prime } fields of the Next Generation Space Telescope .
NGST will be able to reach the peak of the N ( m ) curve , located at AB \approx 30 ( 31 ) for SCDM ( LCDM ) in J and K wavelength bands and detect ( 75 % , 51 % ) of the above SN events .
This will allow a detailed study of the early cosmic star formation history , as traced by SNIIe . N ( m ) is only very mildly affected by the inclusion of lensing effects .
In addition , GL introduces a moderate uncertainty in the determination of cosmological parameters from Hubble diagrams , when these are pushed to higher z .
For example , for a “ true ” LCDM with ( \Omega _ { M } = 0.4 , \Omega _ { \Lambda } = 0.6 ) , without proper account of GL , one would instead derive ( \Omega _ { M } = 0.36 ^ { +0.15 } _ { -0.12 } , \Omega _ { \Lambda } = 0.60 ^ { +0.12 } _ { -0.24 } ) .
We briefly compare our results with previous similar work and discuss the limitations of the model .