Measuring the properties of extragalactic dust and implications for the Hubble diagram

Scattering and absorption of light by a homogeneous distribution of intergalactic large dust grains has been proposed as an alternative, non-cosmological explanation for the faintness of type Ia supernovae at zsimilar to0.5. We investigate the differential extinction for high-redshift sources caused by extragalactic dust along the line of sight. Future observations of type Ia supernovae up to zsimilar to2, e.g. by the proposed SNAP satellite, will allow the measurement of the properties of dust over cosmological distances. We show that 1% relative spectrophotometric accuracy (or broadband photometry) in the wavelength interval 0.7-1.5 mum is required to measure the extinction caused by "grey" dust down to deltam = 0.02 mag. We also argue that the presence of grey dust is not necessarily inconsistent with the recent measurement of the brightness of a supernova at z=1.7 (SN 1997ff), in the absence of accurate spectrophotometric information of the supernova.