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 s...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 <em>V</em>. A minimum <em>V</em> = <em>V</em><sub>min</sub> for that purpose is determined. Fermions can not exist for <em style="white-space:normal;">V</em><span style="white-space:normal;"> < </span><em style="white-space:normal;">V</em><sub style="white-space:normal;">min</sub>. 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.展开更多
文摘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 <em>V</em>. A minimum <em>V</em> = <em>V</em><sub>min</sub> for that purpose is determined. Fermions can not exist for <em style="white-space:normal;">V</em><span style="white-space:normal;"> < </span><em style="white-space:normal;">V</em><sub style="white-space:normal;">min</sub>. 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.
