Synchronised neutrino oscillations from self interaction and associated applications

A recent revival of interest in synchronised oscillations due to neutrino–neutrino forward scattering in dense gases has led to two interesting applications with notable outcomes: (i) cosmological bounds on neutrino–antineutrino asymmetries are improved owing to flavour equilibration prior to the onset of big bang nucleosynthesis, and (ii) a neutron-rich environment required for rprocess nucleosynthesis is shown to be always maintained in a supernova hot bubble irrespective of flavour oscillations, contrary to results from previous studies. I present in this talk a pedagogical review of these works. 1. THE NEUTRINO–NEUTRINO FORWARD SCATTERING SAGA It is well known that neutrino oscillations in a medium are affected by the presence of other particles. A familiar example is oscillations in the sun: Extra interaction channels available exclusively to the electron neutrino induce for it an excess “effective” mass through coherent forward scattering on the ambient electrons [1].1 Depending on the electron number density, this excess serves as a refractive index for the oscillating neutrino system, modifies the oscillation frequency and amplitude from their vacuum values, and is responsible for such phenomenon as the Mikheyev–Smirnov–Wolfenstein (MSW) effect [3] and, with it, the large mixing angle (LMA) solution to the solar neutrino problem [4]. In certain astrophysical and cosmological settings, neutrinos form a gas so dense that forward scattering of neutrinos on the neutrinos themselves may constitute a significant source of refraction [5, 6]. Furthermore, such scattering differs markedly from scattering on other fermions, since in the former instance it is possible for the “beam” and “background” neutrinos to exchange flavour via the neutral current. The net outcome is a set of “on-” and “off-diagonal” refractive indices that are dependent on the state of every other neutrino in the gas, thereby rendering the evolution of the whole ensemble highly nonlinear. In the very earliest works incorporating the refractive index from neutrino–neutrino forward scattering, the off-diagonal refractive indices were erroneously left out. This was rectified by Pantaleone in 1992 [7]. Shortly after, the implications of these “self in1 This statement assumes that νe oscillates into νμ and/or ντ . If a sterile neutrino is involved, then neutral current scattering of νe on the surrounding electrons and nucleons will also contribute to the excess [2]. Note that we shall not be considering sterile neutrinos in this talk. teractions” for a multi-momentum gas were investigated extensively by Samuel [8], who discovered in his numerical studies that when a certain critical density is reached, the gas begins to exhibit self-maintained coherence (a.k.a. synchronisation) when decoherence is a priori expected. This interesting effect went unexplained for almost a decade, and was recently reexamined by Pastor, Raffelt, and Semikoz [9], who succeeded in giving it a clean and physical interpretation on which I shall elaborate in this talk. The result of Ref. [9] has since been extended and applied to the only two environments in which self interactions are expected to play a dominant role: the early universe, and a core collapse supernova. In the first setting, synchronised oscillations are investigated in the context of relic neutrino–antineutrino asymmetries in the epoch preceding big bang nucleosynthesis (BBN). Independent studies by several groups have demonstrated that if the neutrino oscillation parameters are indeed those inferred from the solar and atmospheric neutrino data, then the asymmetries in the νμ and the ντ sectors must be equilibrated with that in the νe sector prior to BBN, and be subject to the same stringent constraints on the νe asymmetry derived from uncertainties in the primordial 4He abundance [10, 11, 12] (see also Ref. [13]). In the second case, self interactions modify in an unexpected way the flavour evolution of both neutrinos and antineutrinos in the hot bubble region above a nascent neutron star a few seconds after core bounce [14]. This impinges directly on the success or otherwise of r-process nucleosynthesis, which is believed to take place in this setting. In this talk, I shall present a pedagogical review of these works, starting with the interpretation of synchronised oscillations in Sec. 1, and then moving on to the applications in Secs. 2 and 3. The material used here is drawn largely from Refs. [9], [10], [11], [12], and [14]. If you the reader happen to the author of one of these works, please pardon me for quoting you almost verbatim in some places. 1.1. Equations of motion 1.1.1. Density matrix formalism We begin with a simple two-flavour system. In order to understand the synchronisation phenomenon, it is convenient to work with bilinears of the neutrino wave function (and hence density matrices), since, as we shall see, the neutrino self interaction potential appears also in this form. For a group of neutrinos with momentum p, the density matrix at time t in the flavour basis is defined as ρ(p, t) ≡ ( ραα ραβ ρβα ρββ ) . = 1 N0(p) ∑ i |ψi(p, t)〉〈ψi(p, t)| = 1 N0(p) ∑ i ( |ai(p, t)|2 ai(p, t)bi (p, t) ai (p, t)bi(p, t) |bi(p, t)|2 )