Pauli principle, Inflation, and simple statistical treatment of free-fermions

A. PLASTINO; M. C. ROCCA; G. L. FERRI

JOURNAL OF HIGH ENERGY PHYSICS, GRAVITATION AND COSMOLOGY

SCIENTIFIC RESEARCH PUBLISHING

Año: 2020 vol. 6 p. 443 - 449

2380-4327

We study the dependence of the of microstates number  (for free  fermions-bosons) as a function ofthe volume-size in quantum statistics andfermions, and show then that fermions can not be accommodated in arbitrarily small volumes $V$.   A minimum $V=V_{min}$ for that purpose is determined. Fermions can not exist for $V<V_{min} $. This fact might  have something to do with inflation.  More precisely, in order to accommodate $N$ fermions in a Slaterdeterminant 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 agree with current estimates.