![]() Since the effect of the neutrino mass on CMB fluctuations is indirect and appears only at the background level, one could think that by changing the value of other cosmological parameters it would be possible to cancel exactly this effect. 4 the acoustic peaks are slightly enhanced and shifted to the left in the ΛMDM case. Also, postponing the time of equality increases slightly the size of the sound horizon at recombination. This produces an enhancement of small-scale perturbations, especially near the first acoustic peak. So, when f v increases, a eq increases proportionally to −1: equality is postponed. This gives a eq = Ω r/(Ω b + Ω cdm), where Ω r stands for the radiation density extrapolated until today assuming that all neutrinos would remain massless, given by Eq. Since neutrinos are still relativistic at decoupling, they should be counted as radiation instead of matter around the time of equality (when ρ b + ρ cdm = ρ γ + ρ v). The main effect on the CMB anisotropy spectrum results from a change in the time of equality. Thus, while Ω b and Ω Λ are constant, Ω cdm is constrained to decrease as Ω v increases. ![]() Let us describe one example: we choose to maintain a flat Universe with fixed (ω b = Ω b h 2, π m = Ω m h 2, Ω Λ). However, we will see later that this situation is disfavoured by current upper bounds on the neutrino mass. This case would have more complicated consequences for the CMB, as described in. If neutrinos were heavier than a few eV, they would already be non-relativistic at decoupling. Therefore, the effect of the mass is indirect, appearing only at the level of the background evolution: the fact that the neutrinos account today for a fraction Ω v of the critical density implies some change either in the present value of the spatial curvature, or in the relative density of other species. Sergio Pastor, in Les Houches, 2007 6.4 Impact of massive neutrinos on the CMB anisotropy spectrumįor neutrino masses of the order of 1 eV (about f v ≤ 0.1) the three neutrino species are still relativistic at the time of photon decoupling, and the direct effect of free-streaming neutrinos on the evolution of the baryon-photon acoustic oscillations is the same in the ΛCDM and ΛMDM cases. And we can argue only what is the most plausible possibility. Typically models accommodate but not really explain the results. There are plenty of models, scenarios and approaches and only few simplest possibilities have been excluded so far. It is difficult to say with confidence what is correct context or domain of new physics involved. The bottom line is that new physics behind the neutrino masses and mixing has not been identified yet. At the same time, neutrinos may require something more. Some part of this new physics may be in common. Quark mass and mixing as well as neutrino mass and mixing are new physics. And in this sense they are also manifestations of physics beyond SM. The quark and lepton mass hierarchies as well as the structure of CKM mixing have no explanation in the Standard Model either. The statement requires some clarification. What is this New physics? What do we see in the window? How far beyond? Neutrino mass is considered as the first manifestation of physics beyond the standard model, as a window to new physics. The central issue of these lectures is the neutrino mass and lepton mixing, non-standard neutrino interactions. Neutrino Mass, Mixing, and Flavor Change. ![]() Reviews of Modern Physics, 87(March), 137–163. Colloquium: Majorana fermions in nuclear, particle, and solid-state physics. References for Majorana fermions: Lecture notes by Matthew Schwartz Harvard: Lecture 10 Spinors and the Dirac Equation, Lectures notes by Tong DAMPTP. These diagrams illustrate what Dirac mass and Majorana mass do to the neutrinos. 2.2 Figure 1 in arXiv:hep-ph/0211134 by Boris Kayser. The see-saw mass term in (2.1) combined with the meaning of the creation and annihilation operators, we know that Majorana mass can annihilate a neutrino or antineutrino then create a antineutrino or neutrino.įig. Neverthless, we can identify that the see-saw mechanism works already at this point. Then we can find the transformation matrix. Equation of Motion in Gravitational Field MSW Refraction, Resonance and Non-adiabacity
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