Lensing and high-z supernova surveys
  Gravitational lensing causes the distribution of observed brightnesses of standard candles at a given redshift to be highly non-gaussian. The distribution is strongly, and asymmetrically, peaked at a value less than the expected value in a homogeneous Robertson-Walker universe. Therefore, given any small sample of observations in an inhomogeneous universe, the most likely observed luminosity is at flux values less than the Robertson-Walker value. This paper explores the impact of this systematic error due to lensing upon surveys predicated on measuring standard candle brightnesses. We re-analyze recent results from the high-z supernova team (Riess et al. 1998), both when most of the matter in the universe is in the form of compact objects (represented by the empty-beam expression, corresponding to the maximal case of lensing), and when the matter is continuously distributed in galaxies. We find that the best-fit model remains unchanged (at Omega_m=0, Omega_Lambda=0.45), but the confidence contours change size and shape, becoming larger (and thus allowing a broader range of parameter space) and dropping towards higher values of matter density, Omega_m (or correspondingly, lower values of the cosmological constant, Omega_Lambda). These effects are slight when the matter is continuously distributed. However, the effects become considerably more important if most of the matter is in compact objects. For example, neglecting lensing, the Omega_m=0.5, Omega_Lambda=0.5 model is more than 2 sigma away from the best fit. In the empty-beam analysis, this cosmology is at 1 sigma. 
Daniel E. Holz (University of Chicago)