• methods: numerical;
  • supernovae: general;
  • galaxies: evolution;
  • cosmology: theory;
  • dark matter;
  • gravitational lensing

We derive the expected Type II supernova (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 haloes (i.e. the lenses) is obtained by means of a Monte Carlo method applied to the Press–Schechter mass function. The haloes are assumed to have a Navarro, Frenk & White (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−1 in 100 surveyed 4×4 arcmin2 fields of the Next Generation Space Telescope (NGST). NGST will be able to reach the peak of the N(m) curve, located at AB≈30(31) for SCDM (LCDM) in J and K wavelength bands, and detect (75 per cent, 51 per cent) 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 (ΩM=0.4, ΩΛ=0.6), without proper account of GL, one would instead derive inline imageinline image We briefly compare our results with previous similar work and discuss the limitations of the model.