Bf. Roukema, How to distinguish a nearly flat Universe from a flat Universe using the orientation independence of a comoving standard ruler, ASTRON ASTR, 369(3), 2001, pp. 729-735
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 ra
dius (similar to 10h(-1) Gpc) or larger. Here, a method of distinguishing a
n almost Bat universe from a precisely flat universe using a single observa
tional data set, without using: any microwave background information, is pr
esented. The method (i) assumes that a standard ruler should have no prefer
red orientation (radial versus tangeatial) to the observer, and (ii) requir
es that the (comoving) length of the standard ruler be known independently
(e.g. front low redshift estimates). The claimed feature at fixed comoving
length in the power spectrum of density perturbations, detected among quasa
rs: Lyman break galaxies or other high redshift objects, mould provide an a
dequate 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 L applied at a redshift of z = 3 wo
uld distinguish an hyperbolic (Omega (m) = 0.2, Omega (Lambda) = 0.7) or a
spherical (Omega (m) = 0.4, Omega (Lambda) = 0.7) universe from a flat one
to 1 - P > 95% confidence.