EARLY COSMIC DENSITIES AS MOTHER NATURE'S THORN IN THE FLESH OF COSMOLOGISTS
We all know Mother Nature's gradualist ways and have coined phrases for them: "Rome was not built in a day"; "a journey of a thousand miles starts with a step", "little drops of water make a mighty ocean", etc. Unfortunately, some cosmologists would prefer that the universe become wealthy overnight. The universe is now 1052kg rich (i.e. about 1069J) and they want to force this wealth, our current mass estimate into the very beginning (time zero), the Planck epoch and the other early times. Of course, Mother Nature has resisted this get-rich-quick attitude and has inflicted such versions of our Big bang model with riddles, like the flatness and singularity problems for example.
In this post, I quote from Steven Weinberg's popular book, The First Three Minutes,
"As the explosion continued the temperature dropped ...but the temperature continued to drop, finally reaching one thousand million degrees (109K) at the end of the first three minutes. It was then cool enough for the protons and neutrons to begin to form nuclei, starting with the nucleus of heavy hydrogen (or deuterium), which consists of one proton and one neutron".
Cosmologists generally admit uncertainty of what the scenario is at time zero, less uncertainty at the Planck epoch but some confidence of the situation at three minutes because knowing what the binding energies of nuclei are, the ambient energies that must be present at three minutes to enable their formation (nucleo-synthesis) can be deduced. For example, the binding energy of the nucleus of heavy hydrogen (deuterium) and that of helium are 2.2 MeV and 28.3 MeV respectively with the corresponding temperatures permitting stability being ~1010K and 1011K. These quantitative values are not controversial.
We can therefore say with confidence that if the ambient energies and temperatures at the end of the first three minutes are above their binding energy values, hydrogen and helium nuclei cannot form. For example, at 1012K energies are too high and only a quark-gluon plasma can be stable. See Wikipedia: Chronology of the universe, and also hyperphysics website for reference to the timelines.
Now, there are formulae that help us relate the energy density within a given volume to the temperature using blackbody radiation laws. See for sample reference, "Radiation Energy Density". Same formulae are used to estimate the 1032K temperature at the Planck epoch from the Planck density.
From the foregoing, if cosmologists decide to be greedy and accumulate all our current material wealth within three minutes, i.e. ~1052kg (~1069J), given the standard model expansion rate, our universe will be about 5.4 x 1010m radius (with volume ~ 6.6 x 1032m3), giving us an energy density of ~1036J/m3, (~1019kg/m3) at this time. This energy density translates to temperatures about 6.6 x1012K and ambient energies of ~669 MeV, which is so much higher than can permit the formation of nuclei for deuterium (binding energyAttachment #1: Cover.pdf
