  We focus on uncertainties in supernova measurements, in particular of
individual magnitudes and redshifts, to review to what extent supernovae
measurements of the expansion history of the universe are likely to allow us to
constrain a possibly redshift-dependent equation of state of dark energy,
$w(z)$. focus in particular on the central question of how well one might rule
out the possibility of a cosmological constant $w=-1$. We argue that it is
unlikely that we will be able to significantly reduce the uncertainty in the
determination of $w$ beyond its present bounds, without significant
improvements in our ability to measure the cosmic distance scale as a function
of redshift. Thus, unless the dark energy significantly deviates from $w(z)=-1$
at some redshift, very stringent control of the statistical and systematic
errors will be necessary to have a realistic hope of empirically distinguishing
exotic dark energy from a cosmological constant.

Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology;High Energy Physics - Theory