We investigate possible interactions between neutrinos and massive scalar bosons via g φ ννφ (or massive vector bosons via g V νγ µ νV µ ) and explore the allowed parameter space of the coupling constant g φ (or g V ) and the scalar (or vector) boson mass m φ (or m V ) by requiring that these secret neutrino interactions (SNIs) should not spoil the success of Big Bang nucleosynthesis (BBN). Incorporating the SNIs into the evolution of the early Universe in the BBN era, we numerically solve the Boltzmann equations and compare the predictions for the abundances of light elements with observations. It turns out that the constraint on g φ and m φ in the scalar-boson case is rather weak, due to a small number of degrees of freedom. However, in the vector-boson case, the most stringent bound on the coupling g V 6 × 10 −10 at 95 % confidence level is obtained for m V 1 MeV, while the bound becomes much weaker g V 8 × 10 −6 for smaller masses m V 10 −4 MeV. Moreover, we discuss in some detail how the SNIs affect the cosmological evolution and the abundances of the lightest elements. * arXiv:1712.04792v2 [hep-ph] 1 Apr 2018 § The BBN theory can also predict the primordial abundances of 3 He and 7 Li. However, the only data on 3 He are available for the solar system and the high-metallicity regions in our Galaxy and it is difficult to infer its primordial abundance [15]. On the other hand, the observed relative abundance of lithium is 7 Li/H| p = (1.6 ± 0.3) × 10 −10 , showing a discrepancy in the baryon density between the BBN and CMB estimates [9,17]. Since the lithium abundance remains an unresolved issue, it will not be used to draw any constraints in this work.

The ANITA experiment has observed two unusual upgoing air shower events which are consistent with the τ -lepton decay origin. However, these events are in contradiction with the standard neutrino-matter interaction models as well as the EeV diffuse neutrino flux limits set by the IceCube and the cosmic ray facilities like AUGER. In this paper, we have reinvestigated the possibility of using sterile neutrino hypothesis to explain the ANITA anomalous events. The diffuse flux of the sterile neutrinos is less constrained by the IceCube and AUGER experiments due to the small active-sterile mixing suppression. The quantum decoherence effect should be included for describing the neutrino flux propagating in the Earth matter, because the interactions between neutrinos and the Earth matter are very strong at the EeV scale. After several experimental approximations, we show that the ANITA anomaly itself is able to be explained by the sterile neutrino origin, but we also predict that the IceCube observatory should have more events than ANITA. It makes the sterile neutrino origin very unlikely to account for both of them simultaneously. A more solid conclusion can be drawn by the dedicated ANITA signal simulations.