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:

Very early times are defined as follows:

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


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:

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: