The Temperature at the Bounce: A Radiation-Equivalent Ceiling from the Aldred Limit

A density bound implies a temperature ceiling wherever the matter is hot enough for its energy to be counted thermally. Converting the Aldred Limit density into a radiation-equivalent temperature through u = a T^4 gives, for the neutron branch, a ceiling of 3.278e+22 K. The corresponding thermal energy per particle, 2.825e+12 MeV, is a fraction 3006319882.85 of the neutron rest energy of 939.6 MeV, so the bounce on the neutron branch is a hot but not ultra-relativistic-per-particle event in thermal terms. On the electron branch the ceiling is 7.644e+20 K and on the proton branch 3.276e+22 K. These ceilings are the temperatures a bouncing region cannot exceed if its energy density is capped by the Limit, and they set the hottest conditions any post-bounce relic was ever exposed to. Because the conversion assumes all of the energy density is thermal radiation, the figures are strict ceilings within the stated model, not estimates of an actual temperature. Computed from stated assumptions, not measured.