Excluded by History: The Vacuum Density Each Cosmic Epoch Tolerates, From Nucleosynthesis to Recombination

Because radiation dilutes as the universe expands while a vacuum density does not, every epoch known to have been radiation dominated places an upper bound on the vacuum density: it cannot exceed the radiation density of that epoch. This paper computes those bounds for nucleosynthesis, matter-radiation equality, and recombination. Nucleosynthesis, at a temperature of 1 MeV, tolerates at most 1.40 x 10^35 times the observed density of 2.52 x 10^-47 GeV^4. Inverting the calculation, an electroweak-scale vacuum density would have dominated the expansion below 28.51 GeV, and a QCD-scale estimate below 0.02657 GeV, both far above the nucleosynthesis temperature and therefore both excluded by the observed history of the early universe. The paper computes from stated assumptions and reports no measurement.