Thankyou for previous answer. I believe 'we' feel we know nucleosynthesis quite well in stars. Are we as confident about the processes in the Big Bang? I have read the heavier elements need the high pressures and temperatures of stars and supernovas. Surely the Big Bang had more extreme conditions than this. Why didnt the Big Bang produce the heavier elements? Thankyou.
The Big Bang didn't produce elements heavier than helium in significant amounts because you need a large amount of helium (in terms of helium nuclei per volume of space, which is related to density, but also to the percentage of atoms that are helium atoms) and temperatures in excess of 100 million degrees to drive the triple-alpha process that turns helium into carbon, and temperatures several times that to support further nucleosynthesis. Hydrogen could be turned into helium at temperatures as low as a few million degrees (though the process isn't very efficient at temperatures well below ten million degrees), so during the very early stages of the Big Bang, when the Universe was still (relatively) small and the temperature very high, hydrogen rapidly turned into helium, to the tune of about 1/4 of the total mass. But as the Universe expanded it rapidly cooled, and there was never a time when you had really high temperatures and large amounts of helium. So other than a few odds and ends that are mostly intermediate products of the proton-proton cycle (such as deuterium) you get nothing else, and even for those only very tiny amounts. Significant further nucleosynthesis only occurs in the cores of stars that have extremely high central densities and temperatures well in excess of 100 million degrees.
You could of course suppose that the initial Universal expansion might have gone pretty slowly, allowing more time for things to stay hot, and as a result to allow some additional nucleosynthesis. But if that had happened, the amount of "trace" elements such as deuterium would have been strongly affected. By measuring the amount of such materials in the present Universe we can establish a maximum overall density for the Universe at the time the original stage of nucleosynthesis ended. And that proves the impossibility of creating any significant amounts of anything other than helium in the Big Bang itself.
This was in fact one of the reasons that the Cosmic Fireball theory was rejected for quite a long time after its proposal in the early 1930's. It just could not explain the present composition of the Universe. (Though an even more significant one was that estimates of the expansion speed back then were far too high, giving the Universe a maximum age that was less than the age of the Solar System, which was of course impossible.) It was only when the modern theory of nucleosynthesis in stars was developed (I believe in the early 50's, but I'd have to look that up) that the idea of a start that only involved hydrogen and helium became acceptable (and of course, as better estimates of the expansion rate began to give 'ages' for the Universe far greater than that of the Solar System).