Safety in numbers: Gravitational lensing degradation of the luminosity distance-redshift relation

Observation of the expansion history of the universe allows exploration of the physical properties and energy density of the universe's various constituents. Standardizable candles such as Type Ia supernovae remain one of the most promising and robust tools in this endeavor by allowing for a direct measure of the luminosity distance-redshift curve and thereby producing detailed studies of the dark energy responsible for the universe's currently accelerating expansion. As such observations are pushed to higher redshifts, the observed flux is increasingly affected by gravitational lensing magnification due to intervening structure along the line of sight. We simulate and analyze the non-Gaussian probability distribution function of deamplification and amplification due to lensing of standard candles, quantify the effect of a convolution over many independent sources ( which acts to restore the intrinsic average [unlensed] luminosity due to flux conservation), and compute the additional uncertainty due to lensing on derived cosmological parameters. We find that, in the case of large numbers of sources, the lensing distribution along any particular line of sight can be approximated by a Gaussian with standard deviation given by sigma(eff) = 0.088z as a function of redshift z. The resulting degradation factor'' due to lensing is a factor of 3 reduction in the effective number of usable supernovae at z = 1.5 ( for sources with intrinsic flux dispersion of 10%).