The Large Scale Structure Peak as a Comoving Standard Ruler

Abstract

Estimates of the curvature parameters Ω0 (density parameter) and Δ0 (cosmological constant) can be made geometrically by use of either a standard candle or a standard ruler. Just as supernovae of Type Ia appear to provide a good empirical standard candle, it now appears observationally justified to use the peak in the power spectrum of density perturbations at L ≍ 130±10h-1 Mpc as an empirical standard rod. It will be shown that voids of this size are traced by quasars in a homogeneous catalogue near the South Galactic Pole at z ˜ 2 and that the large scale structure peak of the catalogue constrains the value of Ω0 to 0.1 < Ω0 < 0.45 (68% confidence), independently of Δ0. Combination with the supernovae Ia data is sufficient to show that the observable Universe is almost flat. In other words, the combination of a standard ruler and a standard candle detected in two presently available data sets is sufficient to show that the Universe is nearly flat, independently of any microwave background data or any other data analyses.