The existence of the cosmic microwave background is one of the two great
predictions of the Big Bang cosmology. The other one is the nucleosynthesis of
light elements. In the earlier stages of the expansion of
the universe, there will be an equilibrium between electrons, positrons,
protons, neutrons, and both species of neutrinos.
And the reactions would work both ways and that lasts until the temperature
drops to about 10 billion degrees or age of the universe about the second.
And simply, because the neutron's are a little heavier, there will be fewer of
them in the mix, which is why there will be asymmetry
between them and protons. So their mass inequality causes asymmetry
because of the beta decay and beta decay reactions that convert one into the
other. It requires little less energy to turn
neutron into a proton than the other way round, and so, that is the more favorite
reaction. So after the annihilation of excess
positrons, only neutrons can decay. We can again compute the ratio of
neutrons and protons using Boltzmann's formula, and indeed, initially, at very
high temperatures, there'd be slight asymmetry due to the reasons we just
described. But the asymmetry increases as the
universe expands and it finally gets frozen at the value of 0.227 when the
universe is only 10^10 degrees hot. So that's how many neutrons come out of
the equilibrium, but then they start decaying using in beta decay and have a
mean lifetime of a little less than 15 minutes.
So before they can be combined with protons into helium or other like nuclei,
the decay destroys about 24, 25% of them. By the time temperature drops to a
billion degrees, neutrons and protons can combine to form
nuclei of helium according to these reactions.
Some of those newly made nuclei of helium are then dissociated by residual photons,
but as the universe expands, they cool it off and so no more association can occur.
So by the time the universe is little less than 15 minutes old and the
temperature drops to 300 million Kelvin, all of these ratios are frozen and those
are the abundances that we will observe. Actually, the real network of reactions
is a little more complicated and here it's shown.
However the story we just went through pretty much captures the essence of it,
but people who model cosmic nuclear synthesis have to actually do the
full-blown reaction network. And the models predict how the abundances
of different nuclear species will change in time as all this is going on as shown
here. Now you can see that by the time it's all
over, say 15 minutes after the Big Bang, the lines remain flat, except of course,
for small residual number of neutrons that keep decaying.
At this point, the neutron to proton ratio has dropped to 0.14 and these
neutrons end up in the like nuclei that they're produced.
This is roughly 25% by mass and this is why there's about 25% by mass of
primordial helium. So in this way, the intrinsic mass
difference between protons and neutrons, something that comes out of particle
physics, determines the abundances of light nuclei created in the Big Bang.
Since, essentially all neutrons are tied up in helium, its abundance is not
dependent on density, but some of the other species,
they do depend on the actual baryonic density.
That the reason the reactions don't proceed beyond lithium or beryllium,
beryllium or so is the universe expands and becomes insufficiently hot and dense
to create heavier nuclei. Obviously, the heavier nuclei have higher
charges and there is a higher Coulomb barrier to be overcome.
So after helium, there is a big gap going to lithium, and then also another one
going to boron, which is what limits the abundance of those elements.
The Big Bang nucleosynthesis predicts abundances of light nuclei.
And generally, this is parameterized as the ratio of the number of baryons to
photons, which is frozen after all this is
complete. Since there is roughly a billion photons
for every baryon, usually 10^10 are units that are used
here, and this ratio is closely related to the
baryonic density according to the following simple formula.
Since this ratio is preserved after all this is complete,
we can measure it today and find out what it was in the early years,
which leads to the prediction that Omega baryons will be of the order of 4% and
that is in an excellent agreement with the completely different argument from
micro background fluctuations. Here, the predictions of the Big Bang
nucleosynthesis in plot it in one diagram.
The different bands correspond to abundances of different nuclei at the end
as a function of the baryon density. The steeper the line, the more it's
sensitive to abundance of baryons. And you can see the deuterium will work
best as a means of estimating the baryonic density in the universe.
Helium-4 does not work at all because the line is essentially flat.
The first confirmation of this is through measurement of the helium abundance.
Star-forming galaxies are used for this purpose,
and since stars synthesize helium as well as heavier elements, that should be in
proportion. So by measuring abundance of other
elements, say oxygen, and then correlating it with abundance of helium
should be a line that goes through zero if there was no primordial helium
created. However, because there was, then the
intercept on the y-axis gives you the primordial abundance of helium.
And that number is a little less than 24% is in an excellent agreement with
predictions of the Big Bang nucleosynthesis.
Remember that deuterium is the most sensitive one to the actual baryonic
density. So, measuring cosmic abundance of the
deuterium before it's processed in stars gives us a means of estimating the
baryonic density of the universe. The way this is done is through
absorption lines in spectra of quasars. The hydrogen clouds are called
Lyman-alpha forest and there will be Lyman-alpha equivalent for deuterium
line, because of its topic shift, its wave length will be little shorter than
hydrogen Lyman-alpha. So the idea is to find clouds where there is enough of
materials, so that the line is already, well saturated for hydrogen, but not
enough to cover the equivalent absorption of the material.
And of the order of dozens such systems have been measured, and from the relative
abundance of the deuterium to hydrogen in these clouds, we can infer the baryonic
density. Lithium is a little more complicated,
because it's also generated in stars, and it's subject to uncertainties in stellar
structure and evolution. And so this is why it's not really used
to constrain, constrain nucleosynthesis. However,
we note that its abundance is perfectly consistent with the predictions that
satisfy the other measurements like helium and deuterium.
And finally, all this also depends on the number of neutrino families,
because that they each have degree of freedom in the early universe,
and the Big Bang nucleosynthesis predicts that there should be only three of them,
which is in agreement from what we know from particle physics.
Next time, we'll talk about inflation.