Cosmology Lecture 09

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  • "Frame 5:" , , . As was started in Frame 4, the major player is , with only small contributions from (p,n,). Therefore:

At this point, neutron decay becomes important ():

There isn’t much deuterium in the universe because are small and is large, so deuterium gets broken up as soon as it’s made.

Digression: The primary channel for energy generation in the center of stars is the pp chain, whereby H is fused into He. The pp chain generates about 85% of the energy in the sun. This chain goes as follows:

This generates a temperature of about in the core of the sun. The early universe, this temperature occurred about 9 days in. Back then, the dominant energy-releasing reaction was:

Why are the primary reactions different for the center of a star and the early universe? Well, in the center of a star, there aren’t so many free neutrons floating around, so the early universe reaction doesn’t work there. Also, the density of the core of a star () is much greater than the density of the early universe (). Notice that one of the reactions for the sun generates a neutrino, so these reactions involve weak interactions. We already discussed that the universe’s density was out of the realm of weak interactions after about 1 sec. Now back to our regularly scheduled program.

  • "Frame 5.5:" . Here T finally gets low enough for deuterium to persist. Nucleosynthesis begins. .
  • "Frame 6:" , , . The major players are still , with a little more p, . Free neutrons are now mostly in .

After Frame 6, the next important epoch is matter-radiation equality. After that, it’s the last scattering of off . The CMB epoch is when recombination occurs.

Frame 4 Revisited

This is the epoch of annihilation. Energy conservation dictates that (the entropy density) be conserved. Thus, the entropy is transferred into as annihilate. Since , we can calculate how much the photon gas was heated up in this epoch:

Since the neutrinos have already decoupled, they are unaffected by this heating. Therefore:

This is true even today.

Frame 5.5 Revisited

Recall that this was the epoch of nucleosynthesis. In Frame 5, there was a bottleneck where elements heavier that H could not be made because D kept being destroyed by radiation. In 5.5, that bottleneck has been lifted, and heavier elements are synthesized:

This tree continues ad infinitum. The most abundant element in the universe is , then . The abundance of can be calculated:

We can estimate that , since all other n-containing elements are rare. Thus:

We can use an estimate of .


  • depends on the baryon-to-photon ratio=. As increases, is favored over photo-dissociation, so D is more stable and the bottleneck breaks earlier, so is higher when forms. Thus would be larger.
  • depends on the lifetime of neutrons: .
  • depends on the # of species of neutrinos, . This parameter affects the energy density of the universe. A higher causes the expansion of the universe to increase, since:

This affects how many neutrons have decayed. We can establish a fitting formula for Y:

This shows, for example, that an increase in of 1 would change :