Pauli Principle, Inflation and Simple Statistical Treatment of Free-Fermions

Abstract

We study the dependence of the of microstates number (for free fermionsbosons) as a function of the volume-size in quantum statistics and fermions, and show then that fermions can not be accommodated in arbitrarily small volumes V. A minimum V = Vmin for that purpose is determined. Fermions can not exist for min V < V . This fact might have something to do with inflation. More precisely, in order to accommodate N fermions in a Slater determinant, we need a minimum radius, which is a consequence of the Pauli principle. This does not happen for bosons. As a consequence, extrapolating this statistical feature to a cosmological setting, we are able to “predict” a temperature-value for the final-stage of the inflationary period. This value agrees with current estimates.