The brightness distribution of bursting sources in relativistic cosmologies

We present analytical solutions for the integral distribution of arbitrary bursting or steady source counts as a function of peak photon count rate within Friedmann cosmological models. We discuss both the standard candle and truncated power-law luminosity function cases with a power-law density evolution. While the analysis is quite general, the specific example discussed here is that of a cosmological gamma-ray burst distribution. These solutions show quantitatively the degree of dependence of the counts on the density and luminosity function parameters, as well as the weak dependence on the closure parameter and the maximum redshift. An approximate comparison with the publicly available Compton Gamma Ray Observatory data gives an estimate of the maximum source luminosity and an upper limit to the minimum luminosity. We discuss possible ways of further constraining the various parameters.