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

¹ Inter-University Centre for Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, Pune, 411 007, India
² DARC/LUTH, Observatoire de Paris-Meudon, 5 place Jules Janssen, 92195 Meudon Cedex, France

Received: 25 October 2000
Accepted: 30 January 2001

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 (~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 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 in the length of the standard ruler L applied at a redshift of would distinguish an hyperbolic or a spherical universe from a flat one to confidence.