Author(s)

Angelo Plastino^1,2,3, Mario Carlos Rocca^1,2,4, Gustavo Ferri⁵

¹Departamento de Física, Universidad Nacional de La Plata, La Plata, Argentina.
²Consejo Nacional de Investigaciones Científicas y Tecnológicas (IFLP-CCT-CONICET)-C. C. 727, La Plata, Argentina.
³SThAR-EPFL, Lausanne, Switzerland.
⁴Departamento de Matemática, Universidad Nacional de La Plata, La Plata, Argentina.
⁵Fac. de C. Exactas-National University La Pampa, Peru y Uruguay, Santa Rosa, La Pampa, Argentina.

We study the dependence of the of microstates number (for free fermions-bosons) 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 = 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 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.

Microstates’s Number Ω, Fermions, Bosons

Plastino, A. , Rocca, M. and Ferri, G. (2020) Pauli Principle, Inflation and Simple Statistical Treatment of Free-Fermions. Journal of High Energy Physics, Gravitation and Cosmology, 6, 443-449. doi: 10.4236/jhepgc.2020.63034.