Lensing and High-[CLC][ITAL]z[/ITAL][/CLC] Supernova 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 Letter explores the impact of this systematic error due to lensing upon surveys predicated on measuring standard candle brightnesses. We reanalyze recent results from the high-z supernova team (Riess and coworkers), 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 Ωm=0, ΩΛ=0.45), but the confidence contours change size and shape, becoming larger (and thus allowing a broader range of parameter space) and dropping toward higher values of matter density Ωm (or correspondingly, lower values of the cosmological constant ΩΛ). 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 Ωm=0.5, ΩΛ=0.5 model is more than 2 σ away from the best fit. In the empty-beam analysis, this cosmology is at 1 σ.