Gravitational lensing of high-redshift Type Ia supernovae: a probe of medium-scale structure

The dispersion in the peak luminosities of high-redshift Type Ia supernovae will change with redshift because of gravitational lensing. This lensing is investigated with an emphasis on the prospects of measuring it and separating it from other possible sources of redshift-dependent dispersion. Measuring the lensing-induced dispersion would directly constrain the power spectrum of density fluctuations on smaller length-scales than are easily probed in any other way. The skew of the magnification distribution is related to the bispectrum of density fluctuations. Using cold dark matter models it is found that the amount and quality of data needed are attainable in a few years. A parametrization of the signal asa power law of the angular size distance to the supernova is motivated by these models. This information can be used in detecting lensing, detecting other systematic changes in supernovae and calculating the uncertainties in cosmological parameter estimates.