Limitations in using luminosity distance to determine the equation-of-state of the universe

Supernovae searches have been been suggested as a method for determining precisely the current value and time-variation of the equation-of-state, w, of the dark energy component responsible for the accelerated expansion of the universe. We show that the method is fundamentally limited by the fact that luminosity distance depends on w through a multiple integral relation that smears out information about w and its time-variation. The effect degrades the resolution of w that can be obtained from current data. Even if the luminosity distance were to be measured to one per cent accuracy out to red shift z=2, the uncertainty in the current value of w would exceed 40% and no useful information would be obtained about the time-variation and, consequently, the future fate of the universe