The Minimum Scale Factor of a Spin-Driven Bounce as a Function of Spin Alignment, and the Alignment Below Which No Bounce Occurs Above the Planck Length

Reducing the alignment to f = 0.1 raises the bounce density by a factor of one hundred and changes the minimum scale factor, relative to the fully aligned case, by the factor 4.64 recorded in the results file; at f = 0.01 the corresponding scale-factor ratio is 21.54. The critical alignments at which the required bounce density reaches the Planck density are f = 3.070e-20 for a neutron fluid and f = 1.669e-23 for an electron fluid. Both critical values are extremely small, which carries the real message of the computation: for these species the classical spin bounce remains below the Planck density even for very poor alignment, and only an almost perfectly random spin ensemble pushes the required density into the quantum-gravity regime. The full-alignment bounce densities used are 5.403e+40 kg/m^3 for neutrons and 1.598e+34 kg/m^3 for electrons. The study is a computation from stated assumptions, performed by the accompanying script; it is simulated, not measured.