Asymptotic freedom and entropy in a perpetually oscillating universe

A model of a perpetually oscillating universe is considered. In this model the universe, when contracting to Planck dimensions, transforms from the Friedmann to the De Sitter phase with one and the same $\text{Λ ～}\text{1}\text{l}{}^2{}_{\mathrm{<mtext>P</mtext><mtext>1</mtext>}}$, irrespective of the value of the total bare mass of the Friedmann universe.