A PRIMORDIAL COSMOLOGICAL SCENARIO AND THE HORIZON PROBLEM

The coupling of the Einstein-Hilbert Lagrangian with a conformal field in an arbitrary even dimension leads, after reduction to four dimensi ons, to the ordinary gravity coupled non-trivially to two scalar field s. The vacuum solutions display an initial singularity, but with an in finite proper distance between any two points of the space-time. There is an initial contraction phase followed by an expansion phase. This is a kind of ''anti-Big Bang'' scenario. The coupling to a radiative f luid preserves this feature; however, the temperature of the radiative fluid is initially zero, increasing afterwards: its maximum value is related to the moment where the horizon crosses the radius of the Univ erse. The entropy in the three-dimensional space is inversely proporti onal to the volume of the internal space, and it can be very high toda y. We perform also a perturbative study of this model during the contr action phase. There is no explosive growth of the scalar perturbations .