Abstract
At the time of nucleosynthesis, the primordial fireball consisted of electrons, protons, neutrons, photons and neutrinos.
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Notes
- 1.
These relations hold during the radiation era. While we won’t derive these equations here (see the Appendix), we will outline how the dependence on time emerges. The energy density is proportional to the inverse fourth power of the scale factor, \(\rho \propto a(t)^{ - 4}\); the temperature scales as the inverse scale factor, \(T \propto a(t)^{ - 1}\); and the scale factor is proportional to the square root of time, \(a\left( t \right) \propto \sqrt t\) (found by solving Friedman’s equation during the radiation era). Thus, \(\rho \propto t^{ - 2}\), and \(T \propto t^{{ - \frac{1}{2}}}\).
- 2.
When we say a particle has mass m, we usually refer to its rest mass.
- 3.
The quark names have no meaning other than serving to distinguish the different quark particles. For example, “up” and “down” have nothing to do with direction.
- 4.
The spiral curves in opposite directions for positively and negatively charged particles, and its radius depends on the particle’s energy. Physicists use these properties to analyze high-energy collisions, like the one shown in Fig. 14.3.
- 5.
This picture of spontaneous magnetization applies only to very small magnets. When a large piece of iron is cooled below the Curie temperature, it splits into a number of domains with different directions of magnetization.
- 6.
More precisely, leptons cannot be distinguished from other leptons and quarks from other quarks, but quarks can be distinguished from leptons, since only quarks can interact through the exchange of gluons.
- 7.
Steven Weinberg, Abdus Salam and Sheldon Glashow shared the 1979 Physics Nobel prize for this work.
- 8.
Frank Wilczek, David J Gross and H. David Politzer won the 2004 Physics Nobel prize for their work on quantum chromodynamics.
- 9.
Max Planck pointed out that the only quantity with dimension of energy that can be constructed out of the fundamental constants G, c and \(\hbar\) is: \(E = \sqrt {\frac{{c^{5} \hbar }}{G}} \sim 10^{19} \;{\text{GeV}}\). This is the Planck energy.
- 10.
We introduced the two-vacuum model of Fig. 14.7 to illustrate the Standard Model of particle physics, but we emphasize that this is just a schematic illustration. The Higgs field of the Standard Model has three independent components, and the vacuum structure is more complicated. In fact, the Standard Model does not predict any vacuum defects. If any defects are formed, they are likely to come from higher-energy symmetry breakings.
- 11.
One consequence of this is that protons are not absolutely stable and can decay via processes like \(p^{ + } \to e^{ + } \gamma \gamma\). The expected proton lifetime is much greater than the age of the universe, but proton decay can in principle be observed by watching a huge number of protons. However, all attempts to observe it so far have failed and have led only to the upper bound of 1034 years on the proton lifetime.
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Perlov, D., Vilenkin, A. (2017). The Very Early Universe. In: Cosmology for the Curious. Springer, Cham. https://doi.org/10.1007/978-3-319-57040-2_14
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DOI: https://doi.org/10.1007/978-3-319-57040-2_14
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