Effects of Weak Gravitational Lensing from Large-Scale Structure on the Determination of $q_0$

Weak gravitational lensing by large-scale structure affects the determination of the cosmological deceleration parameter $q_0$. 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 $\Omega_0=0.40$, $\Lambda_0=0.6$, $H=65$km/s/Mpc and $\sigma_8=0.79$. It is shown that one would observe $q_0=-0.44^{+0.17}_{-0.05}$ and $q_0=-0.45^{+0.10}_{-0.03}$ (the errorbars are $2\sigma$ limits) with standard candles with zero intrinsic dispersion at redshift $z=1$ and $z=0.5$, respectively, compared to the truth of $q_0=-0.40$ in this case, i.e., a 10\% error in $q_0$ will be made. A standard COBE normalized $\Omega_0=1$ 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 $z\sim 0.5-2.0$ depending on the amplitude of the intrinsic dispersion of the standard candles, at which $q_0$ can be most accurately determined.