A geometric measure of dark energy with pairs of galaxies

Observations indicate that the expansion of the Universe is accelerating, which is attributed to a ‘dark energy’ component that opposes gravity. There is a purely geometric test of the expansion of the Universe (the Alcock–Paczynski test), which would provide an independent way of investigating the abundance (Ω(X)) and equation of state (W(X)) of dark energy. It is based on an analysis of the geometrical distortions expected from comparing the real-space and redshift-space shape of distant cosmic structures, but it has proved difficult to implement. Here we report an analysis of the symmetry properties of distant pairs of galaxies from archival data. This allows us to determine that the Universe is flat. By alternately fixing its spatial geometry at Ω(k)≡0 and the dark energy equation-of-state parameter at W(X)≡-1, and using the results of baryon acoustic oscillations, we can establish at the 68.3% confidence level that and -0.85>W(X)>-1.12 and 0.60<Ω(X)<0.80.