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Supernova 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.
Maor et al. (2001) studied this question.