Abstract
Photons and neutrinos are the most abundant particles in the Universe. Neutrinos played a very important role in the evolution of the Universe. Modern high precision cosmological data allow to obtain strong bounds on neutrino properties. In this section we will discuss neutrino decoupling in the Early Universe, the Big Bang nucleosynthesis and the number of the light neutrinos, the limit on the sum of the neutrino masses which can be inferred from the large-scale structure of the Universe and Cosmic Microwave Background radiation data. We will also consider supernova neutrinos.
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Notes
- 1.
From isotropy it is obvious that \(g_{0i}=0, i=1,2,3\).
- 2.
1 pc= 3.26 light years=3.26 \(\mathrm{c}\cdot\mathrm{year}\).
- 3.
We take into account that in the units \(\hbar=c=1\) the Fermi constant is equal to \(G_{F}\simeq 1.026\cdot 10^{-5} \frac{1}{m^{2}_{p}}\).
- 4.
We assumed the normal neutrino mass spectrum. It is obvious that in the case of the inverted spectrum this conclusion is also valid.
- 5.
In fact, we have \(\frac{\rho_{c}}{\frac{1}{3}n_{\nu}}=\frac{1.054\cdot 10^{4}\mathrm{eV} \mathrm{cm}^{-3} h^{2}}{112 \mathrm{cm}^{-3}}\simeq 94 h^{2} \mathrm{eV}.\)
- 6.
The temperature of the nucleosynthesis can be estimated from the condition \( \bar n_{\gamma}\lesssim n_{N}\), where \(\bar n_{\gamma}\!\simeq\!e^{-\frac{\varepsilon_{D}}{kT}} n_{\gamma}\) is the number of γ’s above the threshold of the reaction (11.133). From this condition we have \(kT \simeq -\frac{\varepsilon_{D}}{\ln \eta}\simeq 0.1\) MeV.
- 7.
In the early Universe baryons and photons can be treated as a fluid. The combination of effects of gravity and pressure of radiation creates longitudinal acoustic oscillations in the photon-baryon fluid. The sound wave can be decomposed into a superposition of modes with different wave numbers \(k\simeq \frac{1}{\lambda}\). The wave length λ corresponds to an observable angle θ. As follows from (11.170), the observed peaks are relevant to characteristic distances.
- 8.
This corresponds to the general theory of the supernova explosion: neutrinos are produced in about 10Â s after core collapse and visible light is produced later after the shock reaches the surface of the star.
- 9.
The calculation of the parameter η requires the numerical solution of the Boltzmann equation for leptogenesis. Approximately we have \(\eta\simeq \frac{10^{-3}\mathrm{eV}}{ \tilde{m}_{1}}\).
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© 2011 Springer-Verlag Berlin Heidelberg
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Bilenky, S. (2011). Neutrino and Cosmology. In: Introduction to the Physics of Massive and Mixed Neutrinos. Lecture Notes in Physics, vol 817. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14043-3_11
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DOI: https://doi.org/10.1007/978-3-642-14043-3_11
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