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Thermal History of the Universe

Cosmology and the Origin of Life

Starting the Thermal Countdown: From the weird to the semi-understandable:

At very early times:

Quantum Fluctuations should produce strange hadronic pairs all of which probably have decayed back into photons. However, this is a possibility that some very heavy particles created in this era still exist (source of "Dark Matter")? quarks were present the could not form a proton because the quarks can not be found together. Its the free quark episode and we don't understand what the physics would be.
Very early times are defined as follows:

Temp = 10³²; time = 10^-43 seconds
At this time Gravity and the Strong Force have the same magnitude. That is:

1/R² is very large because R is ridiculously small
This means:

particle creation directly from the gravitational field
particle size > Horizon (what does that mean?)
all the energy of the Universe could have been in the form of one particle
We don't understand any of this physics

At a slightly later time things are a bit more understandable:

Temp = 3x10¹⁵ ; time = 10^-11 seconds
At this time Gravity and the Strong force now have separated but the Weak force and the Electrostatic Force still have the same magnitude.
When these forces are decoupled the Universe is said to go through a phase transition. The symmetry is broken in a specific manner so that the forces have now separated and are defined by a characteristic ratio of their strengths. This defines the physics of our Universe.

Important Simplification in the Early Universe: Thermal Equilibrium:

Only the temperature of the universe is important
The condition of the Universe at any epoch does not depend on what happened at earlier times

MATH ALERT!!
Unfortunately we now have to do this:

The Universe is expanding
The density in the universe is its mass divided by its volume
since the volume is increasing then the density goes down
the volume depends on the radius so we have:

The density of photons decreases just like the matter density so it goes as

Now here is the important part: Not only does the photon density of the Universe decrease with time, the average energy per photon also decreases because the Universe is expanding and cooling: Therefore we have the following

When the radiation energy density exceeds the matter density the universe is said to be RADIATION DOMINATED
When the matter energy density exceeds the radiation density the universe is said to be MATTER DOMINATED
As we will see later, when the universe is radiation dominated gravity is effectively unimportant (or at least its effects are greatly diminished)
MOST IMPORTANT POINT:

because the radiation energy density decreases with the expansion of the universe more rapidly than the matter energy density --> the universe will always end up in a matter dominated phase. This is is illustrated here:

Remember the ratio of photons to baryons in the Universe now is one billion to one.
Hence, at early times when the Univere was hot and the average energy per photon was large -> the universe has to be radiation dominated!
Remember, the threshold for particle creation only depends on the temperature. If the rest mass energy () of a particle is higher than the average energy of a photon that particle can't be created.

Watch the animation
In this animation:

shaded particles represent anti-matter
blue particles are the most massive and form only at the highest temperatures
red particles have intermediate mass
green particles are the least massive and thus can form at all the indicated temperatures

Epoch #1:

time = 0.01 seconds
temperature = 100 billion degrees (much hotter than the inside of any star)

Constituents of the Universe at this time are:

Protons, neutrons, electrons and neutrinos
a billion photons for each proton, neutron, and electron

matter and energy exist in thermal equilibrium

At this time the Universe is still so dense that it is opaque to neutrinos.
Remember the opacity analog:

A Renegade Roo
So we can have

anti-neutrino+proton<---->neutron+anti-electron
neutrino + neutron <------> proton + electron

The above process keeps the # of protons and the # of neutrons in the early Universe constant. This is extremely important and will result in a testable prediction later.
Remember, a free neutron (one that is not bound in an atomic nucleus) will decay into a proton + electron (+ anti-neutrino) in about 900 seconds. AT t=0.01 seconds, none of the neutrons have decayed. Since all of matter has a neutron component, the Universe must find a way to prevent neutrons from decaying. Fortunately it did, but that's later.
During this epoch, the proton-to-neutron ratio is 1.0
Epoch #2:

time = 0.11 seconds
temperature = 30 billion degrees

Since neutrons are slightly heavier than protons (by the mass of an electron) then the n --> p cycle in the previous neutrino reaction is favored over the p --> n cycle
Now we have 62% protons and 38% neutrons where at 0.01 seconds we had 50% protons and 50% neutrons. The proton-to-neutron ratio is 62/38 or 1.6
Epoch #3:

time =1.1 seconds
temperature = 10 billion degrees (still hotter than centers of stars)
Headline News:
NEUTRINOES DECOUPLE --> they no longer interact with any other matter in the Universe but instead "freely stream" to fill the Universe. This predicts that in addition to the microwave background there should also be a neutrino background.
A neutrino background would be impossible to directly detect but, if neutrinos have mass, then we have already indirectly detected it via its gravitational effects (more on this later).
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