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The evolving Universe
The evolving Universe

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1.7 The hadron era

Time: 10−5 s to 100 s

Temperature: 3 × 1012 K to 109 K

Energy: 1 GeV to 300 keV

From the time that the temperature fell to about 3 × 1012 K, at about 10−5 s after the Big Bang, stable baryons (protons and neutrons) began to form from the up and down quarks that remained after the annihilation of matter and antimatter.

Figure 10

How does the mean energy per particle at 10−5 s compare with the mass energy of a proton or neutron?

Answer

Protons and neutrons have a mass energy of about 1 GeV, which is similar to the mean energy per particle in the Universe at this time.

This is why confinement of quarks became important from this time onwards. Before 10−5 s after the Big Bang, there had been sufficient energy available for up and down quarks to escape to distances significantly larger than the dimensions of a proton or neutron. After this time, no such escape was possible.

Question 11

What are the quark contents of a proton and a neutron?

Answer

A proton is composed of two up quarks and a down quark, whereas a neutron is composed of two down quarks and an up quark.

Equal numbers of up and down quarks therefore led to an equal number of protons and neutrons emerging from this process. To recap on the contents of the Universe at this time, there were about a billion photons, electrons, positrons, neutrinos and antineutrinos for every single proton or neutron in the Universe.

Question 12

Why had the electrons and positrons not yet mutually annihilated each other?

Answer

The mass energy of an electron or positron is about 500 keV, and the mean energy per particle was still much higher than the 1 MeV required to create a pair of them. So electrons and positrons were still in equilibrium with photons, undergoing both annihilation and pair creation reactions at the same rate.

As soon as baryons had formed, weak interactions took over, with protons and neutrons existing in equilibrium governed by the following processes:

So neutrons converted into protons by reacting with either positrons or electron neutrinos; protons converted into neutrons by reacting with either electron antineutrinos or electrons.

Question 13

At the quark and lepton level, how may the two reactions in Equation 3 be represented?

Answer

Bearing in mind the quark composition of a proton and a neutron, each of the reactions involve conversions between a down quark and an up quark as shown in Equations 4a and b:

We can also draw Feynman diagrams to illustrate these two processes, as shown in Figure 5. Each of the two processes may be considered as arising from the exchange of a W boson. Furthermore, each of the parts of this figure may be read either from bottom to top, or from top to bottom, depending on which way the reaction in Equation 4 progresses.

Question 14

What is the change in electric charge when a positron converts into an electron antineutrino? What is the change in electric charge when a down quark converts into an up quark? How can the exchange of a W boson, as illustrated in Figure 5a, maintain conservation of electric charge in this case?

Answer

When a positron (electric charge = +1 unit) converts into an electron antineutrino (electric charge = 0), the change in electric charge is −1 unit. When a down quark (electric charge = −1/3 unit) converts into an up quark (electric charge = +2/3 unit), the change in electric charge is +1 unit. So in Figure 5a the exchange of a W+ boson from left to right can be thought of as carrying +1 unit of electric charge away from the positron and adding it to the down quark. Alternatively, the exchange of a W boson from right to left can be thought of as carrying −1 unit of electric charge away from the down quark and adding it to the positron.

With plenty of energy available, the transitions from neutron to proton and from proton to neutron proceeded at the same rate. Since there were as many neutrinos as electrons, and as many antineutrinos as positrons, the numbers of neutrons and protons in the Universe remained equal, at least initially. However, this situation did not continue. The mass of a neutron is slightly higher than that of a proton. As a consequence of this, the reactions in which a proton converted into a neutron became slightly less likely to happen as the energy fell, because they required more energy than those in which a neutron converted into a proton. As the Universe cooled, this difference in the rates of the two processes became more pronounced, and protons began to outnumber neutrons for the first time.

Figure 5
Figure 5 (a) and (b) Feynman diagrams illustrating the reactions occurring in Equations 4a and b, respectively. No arrows are shown because each of these Feynman diagrams can be read either from bottom to top (neutron to proton conversions), or from top to bottom (proton to neutron conversions). The W boson in each case may be exchanged either from left to right or from right to left. Positrons, electron neutrinos, and up quarks will emit W+ bosons, whereas electrons, electron antineutrinos and down quarks will emit W bosons.

As the Universe cooled still further, another reaction became important for the neutrons and the protons: isolated neutrons decay into protons. This additional process, again governed by the weak interaction, added to the dominance of protons over neutrons in the Universe:

Once the Universe was 0.1 s old, the weak interactions described by the reactions in Equations 3 and 4 became too slow, and neutrinos virtually ceased to have any further interaction with the rest of the Universe - ever! The ratio of protons to neutrons continued to rise as a result of neutron decay, and was only halted when the neutrons became bound up in atomic nuclei where they became essentially immune from decay. If the typical lifetime of the neutron (about 10 minutes) were much shorter than it in fact is, then all neutrons would have decayed into protons long before they could become confined inside nuclei.

When the Universe was about 10 s old, and the mean energy per particle was about 1 MeV, a final important event for the matter contents of the Universe occurred. The remaining primordial electrons and positrons mutually annihilated, producing yet more photons, but leaving the excess one-in-a-billion electrons to balance the charges of the primordial one-in-a-billion protons and ensure that the Universe has a net electric charge of zero.