Deuterium
Deuterium is in some ways the opposite of helium-4 in that while helium-4 is very stable and very difficult to destroy, deuterium is unstable and easy to destroy. Because helium-4 is very stable, there is a strong tendency on the part of two deuterium nuclei to combine to form helium-4. The only reason BBN does not convert all of the deuterium in the universe to helium-4 is that the expansion of the universe cooled the universe and cut this conversion short before it could be completed. One consequence of this is that unlike helium-4, the amount of deuterium is very sensitive to initial conditions. The denser the universe is, the more deuterium gets converted to helium-4 before time runs out, and the less deuterium remains.
There are no known post-Big Bang processes which would produce significant amounts of deuterium. Hence observations about deuterium abundance suggest that the universe is not infinitely old, in accorance with the Big Bang theory.
During the 1970s, there were major efforts to find processes that could produce deuterium. The problem was that while the concentration of deuterium in the universe is consistent with the Big Bang model as a whole, it is too high to be consistent with a model that presumes that most of the universe consists of protons and neutrons.
This inconsistency between observations of deuterium and observations of the expansion rate of the universe, led to a large effort to find processes that could produce deuterium. After a decade of effort, the consensus was that these processes are unlikely, and the standard explanation now used for the abundance of deuterium is that the universe does not consist mostly of baryons and that dark matter makes up most of the mass of the universe.
The reason deuterium is hard to produce is that deuterium is very fragile whereas helium-4, which is produced by the collision of two deuterium nuclei, is very stable. Hence any process which could produce deuterium would tend to also destroy the deuterium to produce helium-4. The reason the Big Bang could produce small amounts of deuterium is that the universe was only hot enough to sustain nuclear fusion for three minutes, and this short period of time allowed for very small amounts of deuterium to avoid being burned into helium-4.
It is very hard to come up with another process that would produce deuterium via nuclear fusion. What this process would require is that the temperature be hot enough to produce deuterium, but not hot enough to produce helium-4, and that this process immediately cools down to non-nuclear temperatures after no more than a few minutes. Also, it is necessary for the deuterium to be swept away before it reoccurs.
Producing deuterium by fission is also difficult. The problem here again is that deuterium is unstable, and that collisions between atomic nuclei are likely to either result in the absorption of the nuclei, or in the release of free neutrons or alpha particles. During the 1970s, attempts were made to use cosmic ray spallation to produce deuterium. These attempts proved unsuccessful at producing deuterium, but they were unexpectedly successful at producing other light elements.
Non-standard BBN
In addition to the standard BBN scenario there are numerous non-standard BBN scenarios. These should not be confused with non-standard cosmology in the at non-standard BBN scenario assumes that the big bang occurs, but insert additional physics in order to see how this affects elemental abundances. These pieces of addition physics include relaxing or removing the assumption of homogenity or inserting new particles such as massive neutrinos.
There are have been motivations for researching non-standard BBN. The first, which is largely of historical interest, is to resolve inconsistencies between BBN predictions and observations. This has proved to be of limited usefulness in that the inconsistencies were resolved by better observations, and in most cases trying to change BBN resulted in abundances that were more inconsistent with observations rather than less. The second, which is largely the focus of non-standard BBN in the early 21st century, is to use BBN to place limits on unknown or speculative physics. For example, standand BBN assumes that no exotic hypothetical particles were involved in BBN. One can insert a hypothetical particle (say a massive neutrino) and see what has to happen before BBN predicts abundances which are very different from observations. This has been usefully done to put limits on the mass of a stable tau neutrino.
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