Understanding the Optimal Redshift Range for the Supernovae Hubble Diagram

The supernovae Hubble diagram traces the expansion history of the universe, including the influence of dark energy. Its use to probe the cosmological model can fruitfully be guided by heuristic study of the features of the model curves. By relating these directly to the physics of the expansion we can understand simply the optimal redshift range for supernovae observations, requiring a survey depth of z=1.5-2 to distinguish evolution in dark energy properties.