Redshift sensitivities of dark energy surveys

Great uncertainty surrounds dark energy, both in terms of its physics, and the choice of methods by which the problem should be addressed. Here we quantify the redshift sensitivities offered by different techniques. We focus on the three methods most adept at constraining $w$, namely, supernovae, cosmic shear, and baryon oscillations. For each we provide insight into the family of $w(z)$ models which are permitted for a particular constraint on either $w=w_0$ or $w=w_0+w_a(1-a)$. Our results are in the form of “weight functions”, which describe the fitted model parameters as a weighted average over the true functional form. For example, we find the recent best-fit from the Supernovae Legacy Survey ($w=-1.023$) corresponds to the average value of $w(z)$ over the range $0<z<0.4$. Whilst there is a strong dependence on the choice of priors, each cosmological probe displays distinctive characteristics in their redshift sensitivities. In the case of proposed future surveys, a SNAP-like supernova survey probes a mean redshift of $z\sim 0.3$, with baryon oscillations and cosmic shear at $z\sim 0.6$. If we consider the evolution of $w$, sensitivities shift to slightly higher redshift. Finally, we find that the weight functions may be expressed as a weighted average of the popular “principal components”.