Light Propagation in Inhomogeneous Universes. V. Gravitational Lensing of Distant Supernovae

Abstract

We use a series of ray-tracing experiments to determine the magnification distribution of high-redshift sources by gravitational lensing. We determine empirically the relation between magnification and redshift, for various cosmological models. We then use this relation to estimate the effect of lensing on the determination of the cosmological parameters from observations of high-z supernovae. We found that, for supernovae at redshifts z<1.8 the effect of lensing is negligible compared to the intrinsic uncertainty in the measurements. Using mock data in the range 1.8<z<8, we show that the effect of lensing can become significant. Hence, if a population of very-high-z supernovae was ever discovered, it would be crucial to fully understand the effect of lensing, before these SNe could be used to constrain cosmological models. We show that the distance moduli m-M for an open CDM universe and a LCDM universe are comparable at z>2. Therefore if supernovae up to these redshifts were ever discovered, it is still the ones in the range 0.3<z<1 that would distinguish these two models.