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.