The First Three Minutes

Cast of characters:

1. Baryons: proton (electrical charge +1, mass 1), neutron (charge 0, mass 1.002)

2. Leptons: electron (electrical charge -1, mass 0.0005), neutrino (charge 0, mass<10^-5)

3. Photon: (charge 0, mass 0)

4. Anti-particles: Particles with exactly the same mass, opposite charge. When particle and antiparticle interact, they annihilate, Two photons emerge, total energy is conserved.

5. The anti-electron has its own name, positron.

6. Neutrinos and anti-neutrinos are very non-reactive, seldom annihilate in practice.

7. The photon is its own antiparticle.

The earliest epoch known is Inflation. It happened at cosmic time t=10^-32. Discussed later.

At t= 1 microsecond, there was an equal mix of every particle and antiparticle in the above cast. Annihilations were balanced by creations of particle pairs in collisions.

At t= .01 second (T=10¹³ K), the particle energy became too low to create a proton-antiproton pair (or neutron-anti-neutron pair), but annihilation was still possible. A tremendous drop in the baryon population occurred. When it was over, about 1 baryon was left from every 100 million baryon - anti-baryon pairs. We know this from the result--matter does exist today; antimatter is rare and short-lived. We can’t calculate the tiny asymmetry from any known principle.

n + neutrino

p + e

From .01 s<t<0.1 s, protons and neutrons (and their anti-particles) were equal in numbers. They weren’t static. They changed into one another. For example:

Notice the conservation laws in the above:

1. Charge is conserved (+1 –1 = 0 + 0)

2. Baryon number is conserved (Proton and neutron)

3. Lepton number is conserved (electron and neutrino)

p + anti-neutrino

n + positron

Another example:

(Charge +1 conserved; 1 baryon + 1 anti-lepton conserved)

From 0.1s < t< 1s the energy available is less because of cooling. In this time, the neutron-to-proton conversions are easier than the reverse, since the neutron has more mass-energy. The proton population increases and neutrons become fewer. The neutrons would vanish soon BUT:

At about t = 1s (T=10¹⁰), the temperature has dropped enough that:

1. Electrons and positrons annihilate. (Again, 1 electron in 100 million survives.)

2. Neutrinos become ineffective in causing transformations. They started streaming freely, and are still doing so.

At this point, the mix consisted of about 85% protons & 15% neutrons. In the next minute, not much happened. Protons joined with neutrons making deuterium, but then the combination would be disrupted by an energetic collision. After the first minute, it was cool enough for deuterium to be stable. The neutron fraction was down to 14% by spontaneous neutron decay. Then element building began, ending when the neutrons were used up in a couple of minutes. The paths were:

1. p + n = deuterium

2. deuterium + n = ₁H³

3. ₁H³ + n = ₂H⁴, OR

4. deuterium + p = ₂He³

5. ₂He³ + n = ₂He⁴

Some deuterium remained uncombined. The uncombined fraction would have been greater at lower density. The actual fraction, still measurable today, means that the cosmic density of ordinary matter is greater than the density in stars and visible nebulae.

Neither a proton nor a neutron can bind to a Helium nucleus. Thus the heavier elements must have been made much later in stars. The Big Bang accounts for about 99% of the mass of stars and nebulae, but not the stuff of planets like the earth or the icy giants.

The final mix of ordinary material and energy was dominated by photons and neutrinos, things that couldn’t annihilate. For every trillion photons, there exist about 300 billion neutrinos and anti-neutrinos, 75 H atoms, 6 He atoms, and a trace of deuterium. The neutrinos are very low energy and undetectable at present. The atoms are detectable; most of them are in gas lying outside of galaxies.

There is considerable evidence that most material and energy is not “ordinary”. That’s another story.