ar X iv : a st ro - p h / 96 08 06 8 v 1 1 3 A ug 1 99 6 FERMILAB - Pub - 96 / 067 - A Weak Lensing and the Measurement of q

On-going projects to discover Type Ia supernovae at redshifts z ∼ 0.3 − 1, coupled with improved techniques to narrow the dispersion in SN Ia peak magnitudes, have renewed the prospects for determining the cosmic deceleration parameter q0. We estimate the expected uncertainty in the Hubble diagram determination of q0 due to weak lensing by structure in the universe, which stochastically shifts the apparent brightness of distant standard candles. Although the results are sensitive to the density power spectrum on small scales, the induced flux dispersion σm < ∼ 0.04Ω 1/2 m,0 mag for sources at z ≤ 0.5, well below the “intrinsic” spread of nearby SN Ia magnitudes, σM ≃ 0.2 mag. Thus, density inhomogeneities do not significantly impact the current program to measure q0, in contrast to a recent claim. If, however, light-curve shape and other calibrators can reduce the effective intrinsic spread to 0.1 mag at high z, then weak lensing could increase the observed spread by 30 % in an Ωm,0 = 1 universe for SNe at z > ∼ 1. Subject headings: cosmology: large-scale structure of the universe, supernovae