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The classical Friedmann-Lema\^itre equations are solved using a correctedversion of Planck's radiation law. The function curves of the scale parametera(t) and the variations with temperature a(T) and t(T) are given. It is shownthat a reasonable cosmological evolution is only possible in case of flatspatial slices (k=0). The initial singularity is avoided. Horizon and flatnessproblems do not exist. For low temperatures compared with the PlanckTemperatur, the equations yield the usual course of expansion of the standardFLRW model for a radiation universe with k=0 and p=u(T)/3.

The Early Universe and Planck's Radiation Law