Astron. Astrophys. 362, 840-844 (2000) 3. Solving the horizon problemAn inspection of Eqs. (1) and (4), as done in CS, shows that the shell-crossing singularity surface is null: it cannot be crossed by any ingoing null geodesic. The solution of the horizon problem, for an off-center observer in a DBB model, can thus proceed from its representation using a Penrose-Carter conformal diagram (see Fig. 3) ^{2}.
The light-like character of the shell-crossing surface forces all matter to be causally connected at , and any finite region to have been in causal contact at some . The horizon problem is thus solved permanently in this model, a priori , for any location of the observer ^{3}. It is worth emphasizing that if the inflationary assumption also solves the horizon problem, it does so only temporarily. In effect, if one considers the horizon problem in a standard FLRW universe, as sketched in Fig. 4, the Big-Bang surface is space-like. It thus implies the existence of a limiting point L, in the history of the observer O, beyond which the observer sees, on the last-scattering surface, some no causally connected points. The current observer, being located above L, is confronted with this horizon problem.
The solution proposed by the inflationary assumption is presented in Fig. 5. Adding an inflationary phase in the early history of the universe amounts to adding a slice of de Sitter space-time betwen the Big-Bang and the last-scattering, thus postponing the limit L when the observer can see non-causally connected points in the CMBR. Inflation thus solves the horizon problem, but only temporarily.
© European Southern Observatory (ESO) 2000 Online publication: October 30, 2000 |