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 .