Effects of Weak Gravitational Lensing from Large-Scale Structure on the Determination of q₀

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.