Dark energy, a cosmological constant, and type la supernovae

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). We 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.