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 $z\s im 0.5$. 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 $z\sim 2$, e.g. by the proposed SNAP satellite, will allow the measurement of the properties of dust over cosmological distances. We show that 1% {\em relative} spectrophotometric accuracy (or broadband photometry) in the wavelength interval 0.7--1.5 $\mu$m is required to measure the extinction caused by ``grey'' dust down to $\delta m=0.02$ magnitudes. 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.