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At what extent could be sure that no heavier elements than helium could be produced, if we know that matter in universe today is about 25% composed on helium, why could be so sure that the kind of reaction He-He-He diden't took place?

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The triple alpha process requires very high densities, very high (but not too high) temperatures, and a good amount of time. Large stars have all three. In particular, they have millions of years during which the very rare triple alpha process can proceed.

The temperatures in the very early universe were extremely high, too high to create anything more complex than protium. By the time the universe had cooled enough so that it could produce deuterium (and thence helium), its density and temperature had already dropped too low for the triple alpha process to proceed. All of this happened in a few hundred seconds. Compare that with the millions of years during which large stars burn helium.

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    $\begingroup$ I have to make what will be a silly comment to most readers here. Hopefully everybody here realizes that a supernova (where elements are created) is a high energy expansion of matter IN space whereas the Big Bang was an expansion OF space. $\endgroup$ – Jack R. Woods Mar 1 '18 at 17:58

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