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2. Observions and cosmological parameters

2.1. What the CMB does actually tell us?

2.1.1. The curvature of space

The detection of fluctuations on small angular scale, mainly by the Saskatoon experiment (Netterfield et al, 1995) more than 7 years ago provided a first convincing piece of evidence for a nearly flat universe (Linewaever et al., 1997; Hancock et al., 1998; Lineweaver and Barbosa, 1998), or more precisely evidence against open models which were currently favored at that time. This conclusion is now firmly established thanks to high precision recent measurements including those of Boomerang, Maxima and DASI (de Bernardis et al;, 2000; Hanany et al., 2000; Halverson et al., 2002): open models are now entirely ruled out: Omegat > 0.92 at 99% C.L., it should be noticed that upper limit on Omegat are less stringent, Omegat < 1.5 at 99% C.L., unless one add some prior, for instance on the Hubble constant.

Figure 1

Figure 1. On this picture the likelihood contours from the CMB constraints are given: dashed lines, when projected provide the 68%, 95%, 99% confidence intervals, while shade area correspond to the contours on two parameters. The likelihood is maximized on the other parameters. This diagram illustrates several aspects of constraints that can be obtained from CMB: flatness of the universe follows from the fact that Omegat > 0.92 at 99% C.L., but H0 is very poorly constrained. Indeed CMB allows to severely tighten the model parameters space, but can leave us with indetermination on specific individual parameter because of degeneracies. See Douspis et al., (2001) for further details.

The most recent measurements of CMB anisotropies, including those obtained after this conference by Archeops (Benoît et al., 2002a), provide a remarkable success of the theory: the detailed shape of the angular power spectrum of the fluctuations, the theoretical predictions of the Cl curve, is in excellent agreement with the observational data. This success gives confidence in the robustness of conclusions drawn from such analyses, while alternative theories, like cosmological defects (Durrer et al, 2002) are almost entirely ruled out as a possible primary source of the fluctuations in the C.M.B. This gives strong support for theories of structures formation based the gravitational growth of initial passive fluctuations, the gravitational instability scenario, a picture sketched nearly seventy years ago by G. Lemaître (1933). At the same time this implies that conclusions on cosmological parameters from CMB have to be considered as robust: the spectacular conclusion that the universe is nearly flat space (1) is a major scientific result of modern science which is certainly robust and is very likely to remain as one of the greatest advance of modern Cosmology.

2.1.2. A strong test of General Relativity

Contrarily to a common conception, General Relativity (GR) is weakly tested on cosmological scales: the expansion of the Universe can be described in a Newtonian approach, while departure from the linear Hubble diagram are weak, and therefore does not provide strong test of GR. Actually the observed Hubble diagram is used to fit the amplitude of the cosmological constant, i.e. ones assumes (a non-standard version of!) GR and fits one of the parameter, therefore this does not constitute a test of the theory. However, the Cl curve of CMB fluctuations provides an interesting test of GR on such scales: the angular distance to the CMB accordingly to RG is such that:

Equation 3 (3)

(t0 being the present age of the universe, and tlss the age of the universe at the last scattering surface (lss) from where the C - l curve is produced). This means that the angular distance to the CMB is of the same order than the one to the Virgo cluster! Therefore the Cl curve can be obtained only within a theory where photons trajectories are essentially those predicted by GR.

1 It is sometimes believed that a space cannot be "nearly" flat, because mathematically space is flat or not. This is not true in Cosmology where there is a natural scale which is c/H0. Stating that the Universe is nearly flat means that its curvature radius Rc is much larger than this scale. Back.

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