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There are between 90 and 254 stable nuclei all the way up to element number 82. In discussions and graphs about big bang nucleosynthesis nothing above lithium is even mentioned. It's a pretty safe bet that none of the heavier elements have been observed in reasonably primordial gases, since the implications would be profound enough to require mention in even popular level books about the big bang.

That said, has anyone bothered to perform searches for all of the heavier elements? As in, do we have explicit experimental upper limits on the concentrations of some or all of these heavier elements, or just a more qualitative, "No evidence seen for anything else"?

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Good question! Normally, the lack of heavy elements is taken as an indicator that something was made from (close-to-primordial) gas.

So an answer could be to ask what are the lowest abundances ever measured with respect to hydrogen.

I am not completely up to date with the current record holders, but stars with iron abundances that are 5 orders of magnitude less than in the Sun have been found (Norris et al 2013). This corresponds to A(Fe)$\sim 2$ on the usual logarithmic scale where hydrogen has A(H)=12.

The constraints on other iron-peak elements are similar. Alpha elements like O, Mg are usually enhanced in very metal poor stars, so the constraints are an order of magnitude higher.

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After astronomers observed the collision of two neutron stars back in June of 2013, a theory emerged that posits that most (all?) of the elements heavier than iron were synthesized in neutron star-neutron star or black hole-neutron star collisions. There is an article in Smithsonian that has a decent explanation.

It's my understanding that this theory has yet to gain widespread acceptance, though the authors seem to make a pretty convincing argument in favor of it. Time and further observations may seal the deal or not.

Edit: Adding some addition references: from Physics.org. And here is the paper the article cites. And from Nova.

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    $\begingroup$ I think maybe you should read the actual paper. arxiv.org/abs/1306.3960 It doesn't say this at all, nor half of what is said in the Smithsonian piece. $\endgroup$
    – ProfRob
    Commented Jan 13, 2017 at 8:03
  • $\begingroup$ From the PDF, "First, the inferred ejecta mass coupled with the (albeit poorly known) rate of compact object mergers, suggests that such mergers are likely to be the primary site for the r-process... From Wikipedia, "The r-process is a nucleosynthesis process that occurs in core-collapse supernovae (see also supernova nucleosynthesis) and is responsible for the creation of approximately half of the neutron-rich atomic nuclei heavier than iron." $\endgroup$
    – BillDOe
    Commented Jan 13, 2017 at 21:02
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    $\begingroup$ So, only half the elements heavier than Fe are created by the r-process; we have little idea what the merger rates for neutron stars is, or the creation rate of neutron star binaries, so the claim that this must be the dominant process is untenable. The r-process must certainly be at work in supernovae, the question is whether they can be responsible for all r-process elements or whether some other contribution is needed to create elements around the third r-process peak (basically gold, iridium, platinum and osmium). The paper doesn't even mention gold. $\endgroup$
    – ProfRob
    Commented Jan 13, 2017 at 23:38

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