Parametrization of dark-energy properties: A principal-component approach

Considerable work has been devoted to the question of how best to parametrize the properties of dark energy, in particular, its equation of state w. We argue that, in the absence of a compelling model for dark energy, the parametrizations of functions about which we have no prior knowledge, such as w(z), should be determined by the data rather than by our ingrained beliefs or familiar series expansions. We find the complete basis of orthonormal eigenfunctions in which the principal components [weights of w(z)] that are determined most accurately are separated from those determined most poorly. Furthermore, we show that keeping a few of the best-measured modes can be an effective way of obtaining information about w(z).