Redshifting rings of power

The cosmic microwave background (CMB) has provided a precise template for features in the linear power spectrum: the matter-radiation turnover, sound horizon drop, and acoustic oscillations. In a two-dimensional power spectrum in redshift and angular space, the features appear as distorted rings, and yield simultaneous, purely geometric, measures of the Hubble parameter $H\left(z\right)\mathrm{}$ and angular diameter distance $D_A\mathrm{}\left(z\right)\mathrm{}$ via an absolute version of the Alcock-Paczynski test. Employing a simple Fisher matrix tool, we explore how future surveys can exploit these rings of power for dark energy studies. High-z CMB determinations of H and $D_A$ are best complemented at moderate to low redshift $(z\lesssim 0.5)$ with a population of objects that are at least as abundant as clusters of galaxies. We find that a sample similar to that of the ongoing SDSS luminous red galaxy survey can achieve statistical errors at the $\sim 5\%$ level for $D_A\mathrm{}\left(z\right)\mathrm{}$ and $H\left(z\right)\mathrm{}$ in several redshift bins. This, in turn, implies errors of $\sigma \mathrm{}\left(w\right)=0.03\mathrm{}–0.05$ for a constant dark energy equation of state in a flat universe. Deep galaxy cluster surveys such as the planned South Pole Telescope survey can extend this test out to $z\sim 1$ or as far as redshift follow-up is available. We find that the expected constraints are at the $\sigma \mathrm{}\left(w\right)=0.04\mathrm{}–0.08$ level, comparable to those of galaxies and complementary in redshift coverage.