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 $w(z)$.