  Here we present some critical discussions about the systematic uncertainty by
dust extinction in the recent cosmological results of high-redshift Type Ia
supernovae. First we argue that the currently available data do not robustly
exclude the cosmologically significant extinction either by the reddening check
or the dispersion argument because of the observational uncertainties, even in
the case of ordinary dust that reddens. Then we discuss two theoretical
possibilities that high-z supernovae have larger extinction and hence they are
fainter than local supernovae: the intergalactic dust and host galaxy
evolution. Optical and near-infrared observations for a large number of
supernovae with improved photometric accuracy are required to reject these
possibilities and derive a compelling cosmological result.
