Lensing and high-z supernovae surveys

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Abstract
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 on surveys predicated on measuring standard candle brightnesses. We re-analyze recent results from the high-z supernovae team (Riess et al. 1998), taking lensing into account in the analysis. 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 drooping towards higher values of matter density, Omega_m (or correspondingly, lower values of the cosmological constant, Omega_Lambda). For example, neglecting lensing, the Omega_m=0.5, Omega_Lambda=0.5 model is more than 2 sigma away from the best fit. When lensing effects are included, this cosmology is at 1 sigma.

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