On the Degeneracy Inherent in Observational Determination of the Dark Energy Equation of State

Using a specific model for the expansion rate of the Universe as a function of scale factor, it is demonstrated that the equation of state of the dark energy cannot be determined uniquely from observations at redshifts $z\lesssim{\rm a few}$ unless the fraction of the mass density of the Universe in nonrelativistic particles, $\Omega_M$, somehow can be found independently. A phenomenological model is employed to discuss the utility of additional constraints from the formation of large scale structure and the positions of CMB peaks in breaking the degeneracy among models for the dark energy.