Concern Regarding "A Non-Inflationary Solution to the Entropy Problem of Standard Cosmology."

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We discuss the entropy and the size/homogeneity/horizon problems in power-law expanding universes with one scale initial conditions. We set the minimal scale Λ= 10²⁵ GeV at which a non-inflationary solution is possible and show that the radiation dominated epoch alone technically is not able to explain the issue. An earlier paper on the subject, [1], attempts a multidimensional scenario. We review the scenario of the paper [1] in an effective four dimensional Einstein frame. We find that during contraction of extra dimensions, the residual bulk energy density is important and leads to a scaling solution. The existence of this scaling solution is a new result. We provide a numerical example which demonstrates the evolution of the scale factor and the extra dimensions. In the whole, the validity of the effective field theory calculations at the scale of Λ= 10²⁵ GeV is under question and, hence, the final conclusion regarding the possibility of a non-inflationary solution is preliminary.