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Astron. Astrophys. 348, 8-16 (1999)

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Constraining curvature parameters via topology

B.F. Roukema 1,2 and J.-P. Luminet 3

1 Inter-University Centre for Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, Pune, 411 007, India (boud@iucaa.ernet.in)
2 Observatoire de Strasbourg, 11 rue de l'Université, F-67000 Strasbourg, France
3 DARC, Observatoire de Paris-Meudon, 5 place Jules Janssen, F-92195 Meudon Cedex, France (Jean-Pierre.Luminet@obspm.fr)

Received 12 November 1998 / Accepted 26 March 1999


If the assumption that physical space has a trivial topology is dropped, then the Universe may be described by a multiply connected Friedmann-Lemaître model on a sub-horizon scale. Specific candidates for the multiply connected space manifold have already been suggested. How precisely would a significant detection of multiple topological images of a single object, or a region on the cosmic microwave background, (due to photons arriving at the observer by multiple paths which have crossed the Universe in different directions), constrain the values of the curvature parameters [FORMULA] and [FORMULA]?

The way that the constraints on [FORMULA] and [FORMULA] depend on the redshifts of multiple topological images and on their radial and tangential separations is presented and calculated. The tangential separations give the tighter constraints: multiple topological images of known types of astrophysical objects at redshifts [FORMULA] would imply values of [FORMULA] and [FORMULA] preciser than [FORMULA] and [FORMULA] respectively. Cosmic microwave background `spots' identified with lower redshift objects by the Planck or MAP satellites would provide similar precision. This method is purely geometrical: no dynamical assumptions (such as the virial theorem) are required and the constraints are independent of the Hubble constant, [FORMULA]

Key words: methods: observational – galaxies: quasars: general – galaxies: clusters: general – cosmology: distance scale – cosmology: theory – cosmology: observations

Send offprint requests to: B.F. Roukema

© European Southern Observatory (ESO) 1999

Online publication: July 16, 1999