Abstract
In this chapter the history of the universe through the first ten microseconds of its existence will be described. First, in Sect. 9.1 the Planck scale, where quantum-mechanical and gravitational effects both become important, will be defined. This sets the starting point for the theory to be described. In Sects. 9.2 and 9.3 some formulae from statistical and thermal physics will be assembled, which are needed to describe the hot dense phase, out of which the universe then evolved.
Who cares about half a second after the Big Bang; what about the half second before?
Fay Weldon quoted after Paul Davies
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Notes
- 1.
Note that Boltzmann’s constant k has also been set equal to one.
- 2.
The neutrino within the Standard Model is assumed to behave as Dirac fermion. But the nature of the neutrino is not yet settled; it may be either a Dirac or Majorana particle. A Majorana particle is a fermion that is its own antiparticle. Such type of particles were hypothesized by Ettore Majorana in 1937. If neutrinos were of Majorana type a neutrinoless double beta decay should be possible. Such a decay can be considered as two subsequent beta decays, where the produced antineutrino in the first decay will immediately transform into its (own) antiparticle, which is absorbed in the second decay. Even though many searches for Majorana-type neutrinos have been performed, such a decay mode has never been observed, and the limit for the lifetime of such a decay, e.g., of \(^{76}\mathrm{Ge}\) is \(T_{1/2} = 5.3 \times 10^{25}\) years, which is fairly long. Also sterile neutrinos, which are assumed to be hypothetical particles that interact only via gravity and not via the known interactions of the Standard Model, are not considered here. Sterile neutrinos are considered to be right-handed, and sterile antineutrinos should be left-handed. Recent results from the ICECUBE Neutrino Observatory did not find any evidence for sterile neutrinos.
- 3.
Quantum anomalies can arise if a classical symmetry is broken in the process of quantization and renormalization. The perturbative treatment of quantum field theories requires a renormalization, and this adds non-invariant counter terms to the invariant Lagrange density that one gets at the classical level.
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Grupen, C. (2020). The Early Universe. In: Astroparticle Physics. Undergraduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-27339-2_9
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DOI: https://doi.org/10.1007/978-3-030-27339-2_9
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