## 2. The inhomogeneous delayed big-bang modelThe main features and properties of the model are here briefly mentioned. For a more detailed presentation and a discussion of the assumptions retained, the reader is referred to CS and SC. The proposed DBB model is a subclass of the LTB flat model. Its
line-element, in comoving coordinates
() and proper time An appropriate choice of the radial coordinate The Big-Bang function, ,
verifies The physical singularity of the model - i.e. the first surface, encountered on a backward path from "now", where the energy density and the invariant scalar curvature go to infinity - is the shell-crossing surface, represented in the plane by the curve: As the energy density increases approaching this surface, radiation becomes the dominant component in the universe, pressure can no longer be neglected, and the LTB model no longer holds. The region between the Big-Bang surface and the shell-crossing one is thus excluded from the part of the model retained to describe the matter dominated region of the universe, which we discuss here. The optical depth of the universe to Thomson scattering is
approximated by a step function (see SC). The last-scattering surface
is thus defined, in the local thermodynamical equilibrium
approximation (see CS), by its temperature,
, as is the now-surface,
The value of the entropy function
is assumed to be constant with An observer located at a distance from the center sees an axially
symmetrical universe in the center direction. In the geometrical
optics approximation, the light travelling from the last-scattering
surface to this observer follows null-geodesics, which is thus
legitimate to consider in the meridional plane. The photon path is
uniquely defined by the observer's position
and the angle
between the direction from which the
light ray comes and the direction of the center of the universe,
The microwave radiation observed in the direction of this symmetry
center follows a light-cone issued from point The radial null-geodesic equation, as established in CS, is It is easy to see that, with a function
verifying conditions (3), for a fixed
If observed with an angle in the
inward direction, a light beam issued from point
The corresponding null-geodesics are solutions of the system of differential equations established in SC (in units ): with a plus sign in Eq. (6) from If one considers Eq. (6), for a fixed With taking every value between
and
, and considering the two oppposite
directions of sight, the CMBR is observed from To prove that this set of points can be causally connected, it is
sufficient to show that there is at least one forward radial
light-cone, i.e. issued from a point
including the © European Southern Observatory (ESO) 2000 Online publication: October 30, 2000 |