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Currently accepted scientific theory says that all elements heavier than hydrogen, helium, and a little lithium have been created in supernova explosions.

My questions, specifically, is has anyone done the math to see if the observed amounts and the distribution of, the heavier elements in the universe agrees with the 13.7 billion year age of the universe?

With the birth, life, and death of stars at the currently observed and accepted rates... does the math work out? Can you please refer me to a resource where I can review the material or get further clarification. (I freely admit that my maths aren't up to the task, but I'm hoping for a deeper understanding of the phenomenon.)

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Non-super nova stars create elements heavier than lithium. Red giants can apparently produce up to Lead en.wikipedia.org/wiki/Supernova#Source_of_heavy_elements . –  Edward Mar 22 '11 at 13:40
    
Google "baryogenesis" and "nucleogenesis". The subject itself is too wide for a SE question. –  user346 Mar 22 '11 at 14:00
    
@Deepak Vaid: Surely you meant "nucleosynthesis", not "nucleogenesis". –  dbrane Mar 22 '11 at 15:45
    
Thanks @dbrane. That's the correct term! –  user346 Mar 22 '11 at 15:59
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Of course people have "done the math" on this. The chemical evolution of the Universe is a significant research area in astrophysics. There are tons of observations charting the evolution over time (by looking at different distances, we can measure things at different times), and tons of work on numerical models.

You could try this book for an entry point into the voluminous literature, if you're really interested. (It's about 15 years old, so there are probably more recent review articles, but your question of whether the timing can work out has been understood for far longer than that, so this book should be OK.)

Oh, and Edward's comment is quite right, although I think he should have said "iron" rather than "lead." Elements from beryllium to iron are mostly produced during "normal" stellar evolution, not supernovae; elements heavier than iron are produced in supernovae.

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I've heard iron before as well, but the wiki link says "The only other major competing process for producing elements heavier than iron is the s-process in large, old red giant stars, which produces these elements much more slowly, and which cannot produce elements heavier than lead." The wikipedia s-process article also lists Pb as the limit. I skimmed the article it cited on the claim and didn't see anything on lead. I'm not very knowledgeable on this, so it may be a wiki error. –  Edward Mar 22 '11 at 14:10
    
It's probably right. It certainly could be true that small quantities of elements in the iron-lead range are produced outside of supernovae, although my impression is that the majority is in supernovae. I suppose I could look up the reference in the Wikipedia article (which is to a reputable-looking source), but I'm not going to. –  Ted Bunn Mar 22 '11 at 14:26
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The heavy element abundances vary by space as well as time. Gas which has been contaiminated with heavy elements from supernova will have more heavy elements than gas which hasn't. Dwarf galaxies which have had low rates of star formation/death have much fewer heavy elements, and resemble the gas that existed many billions of years ago in larger galaxies. There probably are intergalactic gas clouds that have essentially primordial compostion as well. –  Omega Centauri Mar 22 '11 at 15:42
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For the lighter elements the standard model nucleosynthesis works pretty good. But all is not quite perfect in the nucleosynthesis world, particularly with lithium. Google "lithium problem" to find lots of papers on this. For example:

JCAP 0811:012 (2008), Richard H. Cyburt, Brian D. Fields, Keith A. Olive, A Bitter Pill: The Primordial Lithium Problem Worsens
http://arxiv.org/abs/0808.2818

The lithium problem arises from the significant discrepancy between the primordial 7Li abundance as predicted by BBN theory and the WMAP baryon density, and the pre-Galactic lithium abundance inferred from observations of metal-poor (Population II) stars. This problem has loomed for the past decade, with a persistent discrepancy of a factor of 2--3 in 7Li/H. Recent developments have sharpened all aspects of the Li problem.

Here's a paper suggesting that there's problems even with 4He:

Int.J.Mod.Phys.E15:1-36 (2006), Gary Steigman, Primordial Nucleosynthesis: Successes And Challenges
Summary and Conclusions:

Perhaps the $^4$He challenge to SBBN is a signal of new physics.

http://arxiv.org/abs/astro-ph/0511534

All this is good news for physicists; there jobs are safe.

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