How to distinguish a nearly flat Universe from a flat Universe using the orientation independence of a comoving standard ruler

Abstract

Several recent observations using standard rulers and standard candles now suggest, either individually or in combination, that the Universe is close to flat, i.e. that the curvature radius is about as large as the horizon radius (\sim 10h^{-1}Gpc) or larger. Here, a method of distinguishing an almost flat universe from a precisely flat universe using a single observational data set, without using any microwave background information, is presented. The method (i) assumes that a standard ruler should have no preferred orientation (radial versus tangential) to the observer, and (ii) requires that the (comoving) length of the standard ruler be known independently (e.g. from low redshift estimates). The claimed feature at fixed {\em comoving} length in the power spectrum of density perturbations, detected among quasars, Lyman break galaxies or other high redshift objects, would provide an adequate standard candle to prove that the Universe is curved, if indeed it is curved. For example, a combined intrinsic and measurement uncertainty of 1% in the length of the standard ruler $\llss$ applied at a redshift of $z=3$ would distinguish an hyperbolic $(Ω_m=0.2,Ω_Λ=0.7)$ or a spherical $(Ω_m=0.4,Ω_Λ=0.7)$ universe from a flat one to 1-P > 95% confidence.