A&A 369, 729-735 (2001)

DOI: 10.1051/0004-6361:20010174

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

**B. F. Roukema**

^{1, 2}^{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 (~10*h*^{-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 *z*=3 would
distinguish an hyperbolic
or a spherical
universe from a flat
one to
confidence.

**Key words:**cosmology: observations

**--**cosmology: theory

**--**galaxies: clusters: general

**--**large-scale structure of Universe

**--**quasars: general

**©**

*ESO 2001*