Cosmology 4: The Details of the Big Bang

Some Problems For Cosmology Are:

  1. Why is the universe matter?
    2. It would be much easier to have a universe which was equally matter and anti-matter. As well, universe is electrically neutral, we think! Why?)

  2. Why is the universe large and flat?
    It could naturally be very much smaller, and there is no reason to have Ω=1 (this is the "Why the hell" question!)

  3. Why is the universe all the same temp?
    (the horizon problem) Bits of it have never communicated.

  4. Where and what is the dark matter?
    (the "what the hell" problem)

  5. Why is the universe 75%H and 25% He?
    (I.e., what did it start as and how did it evolve?)

  6. When did structure form?
    (I.e., were the seeds that made the galaxies there at t = 0, or did they form much later?)

  7. Why are there so many γ's for each proton?
    The entropy problem.

  8. Do we really understand gravity/GR?

A Brief History of the Universe

the standard big bang model

Note that our understanding of this is limited. Assume that thermodynamics works (i.e. even though we may not know exactly how particles interact, the numbers of each are fixed via rate equations.)
eg. O2 + 2H2 <-?-> 2H2O is complex, but as long as we know the energy (Q-value) given out in the process, we can calculate equilibrium. Rates ∝ cross-sections, which can be measured.

Thermal Equilibrium

Energy/particle E = ³/2kT for a gas.

k = 1.38×10-23 J/K (so molecule at room temp has energy of about 1/40 eV) . Normally we think of ³/2 kT as being the kinetic energy of an atom, but once it exceeds the rest mass of the particle, then we can create and destroy that particle at will.

For T >> mec², Number of electrons ≈ Number of photons≈ number of positrons ≈ Number of Neutrinos .....etc for all lighter mass particles.

A somewhat more subtle effect occurs with neutrons and protons:

At very high temps, can create anti-protons (p-) as readily as γ's.
p, p̄, n, n̄ (anti-neutrons), are all in thermal equilibrium.

As universe cools, we will lose p̄ and n̄, but p & n will stay in equilibrium via n + ν <- > p + e- (we normally see only n⇒ p + e- + ν, but the density of ν's and e's was so enormous...)

However, the masses of the n and p are not exactly the same:

"mass" of neutron = 939.6 MeV
"mass" of proton = 938.3 MeV
so ΔE = 1.3 MeV

This means that there is a slight preference to have p's
Number of n's/Number of p's = e(-ΔE/kT)

Early Universe in detail: (a simple model)

  1. 10-44s

    Can't run clock back any earlier since quantum gravity dominates the early universe.

    We can find "numbers" made of G, ħ(Plancks constant) and c (speed of light) with dimensions of time, mass and length.

    Planck time. 

    τ = (Għc-5)1/2   =   5.4×10-44 s

    Planck length. 

     l = (Għc-3)1/2   =   3×10-33 m

    Planck mass/energy. 

    m = (c5h/2πG)1/2   =   1.2×1019 GeV

    Normally we think of gravity as being "caused" by matter, but (e.g.) near a black hole, the field is so strong that the effects of the gravitational energy produce changes in the gravitational field.

    For t < 10-44s, gravitational effects of gravity >>>> stronger than matter. We have no theory here.

  2. 10-30 s, E ≈ 1020 eV

    The universe was matter-antimatter symmetric: a number of models give some particles 

    X₀ ⇒ p-e+  (anti-matter)
X₀ ⇒ p+e-  (matter)
    at slightly different rates. At this stage, there were 109+1 electrons (protons) for every 109 positrons (anti-protons).

  3. 10-6 s, E ≈ 1 GeV
    Free quarks turn into protons and neutrons.

    From here on, all the particles are the ones we would recognise today. Roughly equal numbers of
    p, p̄, n, n̄, e+, e-, ν, ν̄, γ, μ+ ,μ-

  4. 10-5 s, E≈ 100 MeV

    p̄, n̄, and μ's drop out of equilibrium and disappear.

    Down to 1 proton/108 γ's

    Electrons and positrons still in equilibrium.

    Neutrons and protons are almost exactly in balance, except that n is slightly heavier.

  5. 1s, E ≈ 1MeV

    No longer enough ν's to keep n's in equilibrium. After this, they just decay.

    n -> p + e- + ν̄

    with a half life τ = 864 s: i.e.
     Nn = N₀ exp(-t/τ)

    Electrons and positrons can no longer be created.
    e+ + e- => γ + γ
    means that γ's now have a higher temperature than ν's as well.

    He could exist, but D is still unstable.

  6. 3 mins, T ≈ 9×108 K or E ≈ 100 keV

    D becomes stable, n + p -> d + γ (Note: this doesn't occur in stars. There are no free n's.)

    Then all remaining n's become cooked to He, via.

    d + d -> ³He + n,  d + ³He -> ⁴He + p

    I.e., the universe has to drop to T ≈ 109K before n's can make heavier nuclei.

Amount of ⁴He depends crucially on how long the universe takes to cool.

Time taken depends on the density of γ's and ν's, so we can run rate equations to get predictions...

Note that all the action takes place at around 3 mins.
However, this is not unique: it assumes a certain density of protons.

(Roughly, the more protons, the more neutrons so the more He.)

Hence we can run these equations for different numbers of protons.

We have several predictions out of this:

Proportion of He ≈ .1 ⇒.3, whatever we do.

Can measure ⁴He, D, ³He, and with great difficulty 7Li, and we know the number of γ's now.

And the result is..........

All the measurements are consistent and predict a number for the density of protons ≈ .1 m-3.

ΩB ≈ .06--.1

Note the value Li ≈ 10-10 H is a minimum. It is very hard to fiddle this either way.

Finallysome speculations and fantasies