1997 - 2000 activity report
Theoretical cosmology
Topology of the universe
General relativity allows to determine the local geometry of the universe but give no information about its global topology. Thus the universe is usually described by Friedmann-Lemaître models whose spatial sections are assumed to be simply-connected (meaning that every closed loop can be continuously contracted to a point). But nothing prevents to use multi-connected models. These multi-connected universes can be classified according to topological criteria and to whether or not they satisfy physical criteria such as compliance with causality (Lachièze-Rey, 1996). A lot of work has been carried out in recent years to constrain the topology of the universe. In a multi-connected space, a single distant source (cluster or quasar) provides several ghost images. A test, known as « crystallographic method », has been developed, simulated, implemented and discussed (Lehoucq et al., 1996). It is based on the fact that topological images of a given source are linked by the holonomies of space, which are also isometries. In the histogram plotting the number of pairs versus their separations, the characteristic distances of a multi-connected universe should appear as sharp spikes. Applied to a real catalog this method is able to fix a lower bound, equal to 600 h-1 Mpc, on the characteristic size of our universe if it is flat and multi-connected. As this test is not suitable to negative curvature models (Lehoucq et al., 1999) another method has been developed, based on the search for correlated pairs of objects (Uzan et al., 1999) ; here, again, restrictive limits were obtained. In addition, the robustness of the various tests was examined with respect to observational uncertainties, such as peculiar velocities, redshift uncertainties and non completeness of catalogs (Lehoucq et al., 2000). The main limitation of present 3D catalogs is the small volume they covered but future surveys, as the Sloan Digital Sky Survey, will significantly improve both the redshift cut-off and the sky coverage.
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Figure 10: Cristallographic method applied to the Bury catalog of clusters leads to no peak in the pair separation histogram. This gives a lower bound on the size of a multi-connected universe. |
In a multi-connected model, topology influences the characteristics and the development of the fields. This work has concerned the calculation of the fundamental modes and states of the quantum fields. This should apply to estimations of the cosmological constant, as the energy of the vacuum in a quantified field in multi-connected space, and to the origin and development of fluctuations of matter in the universe caused by the fluctuations of such a field, as well as to the observation signatures in the anisotropies of the cosmological diffused background.
Nature of the cosmological constant and scalar field
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We can add new forces in general relativity equations. The simplest type consists in adding a scalar field to the normal gravitational field. We do not know the classic equivalent to these fields or their precise nature, but they could play an important role in cosmological theories. They provide a natural explanation for the existence of a cosmological constant that is not equal to zero, which remains an ad hoc hypothesis in the context of standard general relativity. It may also be noted that, in cosmological theories of the Kaluza-Klein type, as in cosmic cord theories, a scalar field can have a stabilizing role (Mbelek and Lachieze-Rey, 2001, a). A scalar field can produce effects, which have, so far, been attributed to black matter. For example, a scalar field can show the flat rotation curves of spiral galaxies. This is also a natural explanation for the abnormal acceleration of the Pioneer in its movement at the boundary of the solar system (Mbelek, Lachieze-Rey, 2001, b).
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| DSM/DAPNIA/Service d'Astrophysique | mise à jour : 15/10/2001 |
| Theoretical cosmology | © CEA 2001 - Tous droits réservés |
