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Weak gravitational lensing by large-scale structure affects the determination of the cosmological deceleration parameter q0. We find that the lensing induced dispersions on truly standard candles are 0.04 and 0.02 mag at redshift z = 1 and z = 0.5, respectively, in a COBE-normalized cold dark matter universe with Ω0 = 0.40, Λ0 = 0.6, H = 65 km s-1 Mpc-1, and σ8 = 0.79. It is shown that one would observe q0 = -0.395−0.095+0.125 and q0 = -0.398−0.077+0.048 (the error bars are 2 σ limits) with standard candles with zero intrinsic dispersion at redshift z = 1 and z = 0.5, respectively, compared to the truth of q0 = -0.400. A standard COBE normalized Ω0 = 1 CDM model would produce three times as much variance and a mixed (hot and cold) dark matter model would lead to an intermediate result. One unique signature of this dispersion effect is its non-Gaussianity. Although the lensing induced dispersion at lower redshift is still significantly smaller than the currently best observed (total) dispersion of 0.12 mag in a sample of type Ia supernovae, selected with the multicolor light curve shape method, it becomes significant at higher redshift. We show that there is an optimal redshift, in the range z ~ 0.5-2.0 depending on the amplitude of the intrinsic dispersion of the standard candles, at which q0 can be most accurately determined.
Wambsganß et al. (Sat,) studied this question.