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Astron. Astrophys. 362, 840-844 (2000)

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4. Discussion and conclusion

In CS we identified a subclass of the LTB models with a Big-Bang of "delayed" type which solves the standard horizon problem without need for any inflationary phase. In this preliminary approach, the observer was assumed located sufficiently near the symmetry center of the model as to justify the "centered earth" approximation.

Here, we report a further analysis of the properties of the DBB model to show that this model solves the horizon problem even with an off-center observer. The model is thus relieved of a prescription that could be considered as "unnatural".

The model is also provided with a new free parameter, the spatial location [FORMULA] of the earth in the universe, which accounts for the large scale inhomogeneities observed in the CMBR temperature anisotropies. The measured dipole and quadrupole moments of these anisotropies set bounds on the correlated values of this [FORMULA] parameter and of the local deviation of the model from homogeneity, accounted for by the slope of the Big-Bang function. A possible cosmological part of these large scale features seen in the CMBR, if once observationally identified, would select an even narrower curve in the parameter space of the model, as shown in SC.

It is of the utmost importance to stress that, as was the case with a centered observer, these results hold for any universe arbitrarily locally close to the FLRW [FORMULA] asymptotic model. The only requirements to be fulfilled are conditions (3) which are obviously compatible with an almost "flatness" of the Big-Bang function up to comoving shells arbitrarily far out the [FORMULA] shell where the observer is located. The properties of the light-cones are preserved as long as this function does not reduce to a mere constant. For instance, the subclass retained in SC, with [FORMULA], reduces to a FLRW model for b equal to zero, but fulfills the conditions (3) for b as small as one wishes, provided b does not vanish. No bound can therefore be a priori inferred on the observer location, as, according to SC, an arbitrarily small value of b corresponds to an arbitrarily large value of [FORMULA], and conversely 4.

A point worth discussing here is the validity of this claim as regards the almost Ehlers-Geren-Sachs (AEGS) theorem (Stoegger et al. 1995). This theorem states that "if all fundamental observers measure the cosmic background radiation to be almost isotropic in an expanding universe region, then that univere is locally almost spatially homogeneous and isotropic in that region." The U region considered by the AEGS authors is "the region within and near our past light cone from decoupling to the present day". It is easy to see that small b DBB models fulfill the AEGS prescription, as they can remain "close" to FLRW models for shells located between the center and an arbitrarily large value of the comoving radial coordinate, including the AEGS region. But the further away part of these small b DBB models infinitely diverges from homogeneity. On the contrary, the AEGS theorem does not apply to large b DBB models, implying an observer close to the center. The founding assumption of this theorem, namely the local Copernican principle applied to the U region, is not retained in this case. As was discussed in CS, such a choice is perfectly compatible with all available observational data and scientifically grounded principles.

It is also interesting to note that, contrary to the inflationary assumption which restores causality between the different points seen in the CMBR, but only temporarily, the DBB model provides a permanent solution to the horizon problem, whatever the position of the observer on his world line.

In the prospect of future observational tests of the large scale (in)homogeneity of the universe, the development of other interesting inhomogeneous models must be regarded as an important issue. However, this presented result is only a first improvement in the release of the simplifying assumptions (retained in CS) for a preliminary study of the properties induced by a "delayed Big-Bang". Other analyses are still needed, among which the release of the spatial spherical symmetry of the model and of the dust approximation should be considered as priorities.

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© European Southern Observatory (ESO) 2000

Online publication: October 30, 2000