Why is Big Bang Nucleosynthesis favored over Stellar Nucleosynthesis?

We know that a hot soup of plasma as it cools (as space expands) can produce light elements if the baryon-photon ratio is just right and the space expands quickly enough so that the neutrons and protons fall out of equilibrium - a theory advocated by Ralph Alpher. We also know that Deuterium and Helium can be produced by fusion of hydrogen atoms in stars, a theory advocated by Fred Hoyle. The internet is full of articles that tell us that BBN is one of the pillars of Cosmology, but I can't find a single one that says why it's favored over Stellar Nucleosynthesis.

Please explain the reason/evidence for preferring BBN over Stellar nucleosynthesis for the production of light elements.

• isn't it just basically "the ratio of heavy elements to helium is too low for stellar nucleosynthesis"? Mar 29, 2021 at 20:48
• @JerrySchirmer - It could be, if the statement is followed by "because..." and then an explanation of why it's too low. This is the part that seems to be missing from the public documents available. Mar 29, 2021 at 21:04
• Wait, how does this paper have only 305 citations!? I mean, it's a great paper, and the author list just kills it! ui.adsabs.harvard.edu/abs/1948PhRv...73..803A/abstract Mar 29, 2021 at 21:09
• @KyleOman: you'd expect that with Hans Bethe being the second author on that! Mar 29, 2021 at 21:41

Deuterium and lithium are generally destroyed by nuclear reactions inside stars. They fuse at lower temperatures (about $$10^6$$ K and $$3\times 10^6$$ K for D and 7Li respectively) than the $$>10^7$$ K it takes to convert hydrogen into helium.