The Horizon / Causality Problem

One of the main results of scale relativity concerning the primeval Universe is its ability to solve the causality / horizon problem. Let us recall the nature of this problem.

When looking at two directions separated by a large angle, e.g. two opposite directions, we observe regions of the Universe which, for a large enough redshift, may have never been connected in the past. The problem is particularly strong concerning the microwave background radiation, due to its high isotropy (δT/T ≈ 2 x 10^-5) and its early origin (z ≈ 1000): at least twenty such independent regions would be observed in the framework of standard cosmology. Such causally disconnected regions should behave as completely independent universes, and it becomes very strange that no large fluctuation of the microwave background temperature is observed. The solution to this problem is usually searched for in the framework of inflationary cosmology. However one may remark that inflation is to some extent an ad hoc solution, in particular as concerns its cause (now unobservable scalar field , primordial black holes...), that must be postulated additionally to the presently known content of the Universe. Moreover it does not solve the problem in principle: in its framework the presently observed regions of the universe would have been causally connected in the past, but this does not remain true in the distant future.

The horizon / causality problem is simply solved in the special scale-relativity framework without needing an inflation phase, thanks to the new role played by the Planck lenth-time scale. It is identified with a limiting scale, invariant under dilations. This implies a causal connection of all points of the universe at the Planck epoch. This is due to the fact that, if one accounts for the scale-Lorentz factor, one finds that the light cones that rest on two arbitrary distant points flare when t → t_P and finally always cross themselves in their past.

Though there is no inflation in the usual sense,
since the scale factor time dependence is unchanged
with respect to standard cosmology, there is an
inflation of the light cones when t → t_P

___________________________________

Quoted from: Nottale L., 2003, Chaos Solitons and Fractals, 16, 539
"Scale-relativistic cosmology"