The Primeval Singularity

The new meaning attributed to the Planck-length and the Planck-time drastically changes the standard view about the primeval singularity. The first new physical law of cosmological importance is the disappearance of the zero instant from meaningful physical concepts. The evolution of the Universe does not begin any more at the instant t = 0 (i.e. log(t/t₀) = -∞ for any t₀ > 0), but instead at the Planck time t_P = l_P/c. However this new structure should not be misinterpreted: in the new theory, the Planck scale owns all the properties of the previous zero instant. This means that temperature, redshift, energy, density and all the quantities Q which were previously diverging as t^-k are now diverging toward the past when t→t_P asThe scale factor of expansion of the Universe is also submitted to a similar new constraint, since it can no longer become smaller than the Planck length l_P. Therefore the Universe starts asymptotically from the Planck scale. This solves the problem of the singularity, which did not make part of the model in the standard general relativistic approach. For example, in the hyperbolic Robertson-Walker solution with trivial topology, the Universe is infinite at any instant t ≠ 0, as small as it could be, while the spatial part of the metric vanishes at t = 0 since R(0) = 0. This kind of problem is no longer posed in the scale-relativistic framework.
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Quoted from: Nottale L., 2003, Chaos Solitons and Fractals, 16, 539
"Scale-relativistic cosmology"