The large scale homogeneity of the universe has been recently questioned in an increasing number of works. For instance, the controversy over whether the universe is smooth on large scale or presents an unbounded fractal hierarchy is not yet ended, and its final resolution requires the next generation of galaxy catalogs (Martinez, 1999). From another point of view, a direct test of the Cosmological Principle on our past light cone, up to redshifts approaching unity, has been recently proposed, using type Ia supernovae as standard candles (Célérier, 2000). If such tests were to exclude the universe homogeneity assumption up to such large scales, and even beyond, we would need alternative inhomogeneous models to describe its evolution.
This article is the third in a series dedicated to the study of a new cosmological application of the inhomogeneous Lemaître-Tolman-Bondi (Lemaître, 1933; Tolman, 1934; Bondi, 1947) spherically symmetrical dust models.
In a first work (Célérier & Schneider, 1998, hereafter refered to as CS), a subclass of these models which solves the standard horizon problem without need for any inflationary phase has been identified. This subclass exhibits spatial flatness and a conic Big-Bang singularity of "delayed" type. In this preliminary approach, the observer has been assumed located sufficiently near the symmetry center of the model as to justify the "centered earth" approximation. The horizon problem has thus been solved using the properties of the null-geodesics issued from the last-scattering surface and propagating in a matter dominated region of the universe, as seen from a centered observer.
However, we stressed in CS a potential difficulty, namely the observer at the center. Although such a location is not forbidden by scientific principles, it does not account for the observed large scale temperature anisotropies of the cosmic microwave background radiation (CMBR).
The dipole moment in the CMBR anisotropy is usually considered to result from a Doppler effect produced by our motion with respect to the CMBR rest-frame (Partridge 1988). In the second work of the series (Schneider & Célérier 1999, hereafter refered to as SC), we assumed that the measured CMBR dipole and quadrupole moments can have, totally or partially, a cosmological origin, and we studied to which extent they can be reproduced, in a peculiar example of our Delayed Big-Bang (DBB) class of models, with no a priori assumption of the observer's location. We have shown that this implies a relation between this location and the model parameter value, namely the increasing rate b of the Big-Bang function. The farther the observer is from the symmetry center, the smaller is the value of b.
The purpose of this present work is therefore to prove that the geometry of the DBB model is such that the horizon problem can be solved, in principle, with no a priori constraint on the location of the observer. By "in principle", we mean: provided the null-geodesics are not too distorted in the radiation dominated area, such as to prevent them from reconnecting before the Big-Bang surface. Were this not the case, it would yield a constraint on the model parameters, as discussed in CS. This allows us to generalize the previous results of CS to a model with an off-center observer, thus improving the consistency of the assumption of a possible cosmological origin of the large scale features of the CMBR temperature anisotropies.
The above property will have however to be interpreted with care, as regards the Ehlers-Geren-Sachs (1968) and almost Ehlers-Geren-Sachs (Stoegger et al. 1995) theorems, which are usually considered as robust supports for the Cosmological Principle. As was stressed in the preceding works, this Principle is not mandatory and does not apply to the DBB model. This issue is discussed below in Sect. 4.
The present paper is organised as follows: a brief reminder of the characteristics of the DBB model is given in Sect. 2. Arguments and proofs are developed in Sect. 3. The discussion and conclusion appear in Sect. 4.
© European Southern Observatory (ESO) 2000
Online publication: October 30, 2000