Limitations in Using Luminosity Distance to Determine the Equation of State of the Universe

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.