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⁡(𝑧) and angular diameter distance 𝐷𝐴⁡(𝑧) 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 𝐷𝐴 are best complemented at moderate to low redshift (𝑧≲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 ∼5% level for 𝐷𝐴⁡(𝑧) and 𝐻⁡(𝑧) in several redshift bins. This, in turn, implies errors of 𝜎⁡(𝑤)=0.03–0.05 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∼1 or as far as redshift follow-up is available. We find that the expected constraints are at the 𝜎⁡(𝑤)=0.04–0.08 level, comparable to those of galaxies and complementary in redshift coverage.