Recent evidence appears to link gamma–ray bursts ( GRBs ) to star–forming regions in galaxies at cosmological distances .
If short–lived massive stars are the progenitors of GRBs , the rate of events per unit cosmological volume should be an unbiased tracer ( i.e .
unaffected by dust obscuration and surface brightness limits ) of the cosmic history of star formation .
Here we use realistic estimates for the evolution of the stellar birthrate in galaxies to model the number counts , redshift distribution , and time–delay factors of GRBs .
We present luminosity function fits to the BATSE \log N - \log P relation for different redshift distributions of the bursts .
Our results imply about 1 - 2 GRBs every one million Type II supernovae , and a characteristic ‘ isotropic–equivalent ’ burst luminosity in the range 3 - 20 \times 10 ^ { 51 } ergs s ^ { -1 } ( for H _ { 0 } = 65 { km s ^ { -1 } Mpc ^ { -1 } } ) .
We compute the rate of multiple imaging of background GRBs due to foreground mass condensations in a \Lambda –dominated cold dark matter cosmology , assuming that 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 model .
We show that the expected sensivity increase of Swift relative to BATSE could result in a few strongly lensed individual bursts detected down to a photon flux of 0.1 { cm ^ { -2 } s ^ { -1 } } in a 3–year survey .
Because of the partial sky coverage , however , it is unlikely that the Swift satellite will observe recurrent events ( lensed pairs ) .