Measuring the equation of state of the universe: Pitfalls and prospects

We explore various pitfalls and challenges in determining the equation of state $\mathrm{}\left(w\right)\mathrm{}$ of the dark energy component that dominates the universe and causes the current accelerated expansion. We demonstrated in an earlier paper the existence of a degeneracy that makes it impossible to resolve well the value of w or its time derivative with supernovae data. Here we consider standard practices, such as assuming that w is constant or greater than $-1,$ and show that they also can lead to gross errors in estimating the true equation of state. We further consider combining measurements of the cosmic microwave background anisotropy and the Alcock-Paczynski test with supernovae data and find that the improvement in resolving the time derivative of w is marginal, although the combination can constrain its present value perhaps to 20% uncertainty.