Why didn't the Big Bang create heavy elements? In the case of a supernova explosion it is possible to create heavy elements through fusion. Supernovae have a tremendous amount of energy in a very small volume but not as much energy per volume as there was in our early universe. So, what is the major difference? Why didn't the Big Bang create heavy elements?
 A: Heavy elements couldn't form right after the Big Bang because there aren't any stable nuclei with 5 or 8 nucleons. 
 Source: Wikipedia (user Pamputt)
In the Big Bang nucleosynthesis, the main product was $^4He$, because it is the most stable light isotope: 20 minutes after the Big Bang, helium-4 represented about 25% of the mass of the Universe, and the rest was mostly $^1H$. There was only 1 nucleus of deuterium and helium-3 for each $10^5$ protons, and 1 nucleus of $^7Li$ for each $10^9$ protons.
Given these abundances, the most probable reactions to yield heavier elements would be $^1H + {}^4He$ and $^4He + {}^4He$, but neither produces stable nuclei. So instead we have only $^2H + {}^7Li \to {}^9Be$ and $^4He + {}^7Li \to {}^{11}B$. This reactions are extremely unlikely, since lithium was so scarce. It is predicted that one of these nuclei was form for $10^{16}$ protons. Abundance of the previous elements and cooling of the universe prevented the formation of even heavier elements.
On the other hand, in the first stars carbon formed in the triple alpha process, which is only possible with the density and helium abundance found in stars, and takes a lot of time. Subsequent nuclear fusions create heavier elements up to iron, and the energy released in the supernova explosion allows the synthesis of even heavier elements.
References
Alain Coc, Jean-Philippe Uzan, Elisabeth Vangioni: Standard big bang nucleosynthesis and primordial CNO Abundances after Planck JCAP10(2014)050 arxiv:1403.6694
A: 
In the case of a supernova explosion it is possible to create heavy
  elements through fusion. Supernovae have a tremendous amount of energy
  in a very small volume but not as much energy per volume as there was
  in our early universe. So, what is the major difference? Why didn't
  the Big Bang create heavy elements?

I just want to point out, too much energy hurts the building of elements process, it doesn't help.   
http://www.physicsoftheuniverse.com/topics_bigbang_timeline.html

Nucleosynthesis, from 3 minutes to 20 minutes: The temperature of the
  universe falls to the point (about a billion degrees) where atomic
  nuclei can begin to form as protons and neutrons combine through
  nuclear fusion to form the nuclei of the simple elements of hydrogen,
  helium and lithium. After about 20 minutes, the temperature and
  density of the universe has fallen to the point where nuclear fusion
  cannot continue.

So, over a billion degrees, protons and neutrons are too energetic to bind.   Under a billion, they can begin to fuse and you begin to get hydrogen fusion into deuterium and helium.
But, there's a problem, 
https://en.wikipedia.org/wiki/Big_Bang_nucleosynthesis

As the universe expands, it cools. Free neutrons and protons are less
  stable than helium nuclei, and the protons and neutrons have a strong
  tendency to form helium-4. However, forming helium-4 requires the
  intermediate step of forming deuterium. Before nucleosynthesis began,
  the temperature was high enough for many photons to have energy
  greater than the binding energy of deuterium; therefore any deuterium
  that was formed was immediately destroyed (a situation known as the
  deuterium bottleneck). Hence, the formation of helium-4 is delayed
  until the universe became cool enough for deuterium to survive (at
  about T = 0.1 MeV); after which there was a sudden burst of element
  formation. However, very shortly thereafter, at twenty minutes after
  the Big Bang, the universe became too cool for any further nuclear
  fusion and nucleosynthesis to occur. At this point, the elemental
  abundances were nearly fixed

A: This question is answered in detail by the so-called "Big Bang Nucleosynthesis", the theory about the creation of the nuclei in the early Universe. Almost out of nothing, it allows one to determine that 75% of the nuclear mass was coming in hydrogen, 25% in helium, and some small traces of lithium appeared, too.
Even though Gamow used to think that all elements could have been created in the Big Bang, Alpher and Herman quickly showed otherwise. The reason why the heavier elements can't be created in the Big Bang is that elements with masses above 56 require neutron capture to be created.
Supernovae are a great environment for neutron capture. However, after the Big Bang, the density of neutrons goes down as the Universe expands; and after much more 10 minutes, the lifetime, the neutrons decay away. There isn't enough time to create the heavier elements.
So we're left with the composition created without processes like neutron capture. And those favor the energetically optimized nuclei such as the light three. The issue is really that it's not quite "high temperature" that is needed for the creation of heavy nuclei. The high temperature is "good" for the creation of energetically wasteful bound state; but it is also "good" for their destruction. The Big Bang is a process in which the temperature is going down so at the end, the energetically thrifty bound states (with higher binding energy) dominate.
