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 dimensions, to the ordinary gravity coupled non-trivially to two scalar fields. The vacuum solutions display an initial singularity, but with an infinite 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 fluid 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 Universe. The entropy in the three-dimensional space is inversely proportional to the volume of the internal space, and it can be very high today. We perform also a perturbative study of this model during the contraction phase. There is no explosive growth of the scalar perturbations.