A standing problem in neutrino physics is the consistent and universal definition of oscillating neutrino states as coherent superpositions of massive neutrino states. This problem is solved in a quantum field theoretical framework of neutrino mixing developed in analogy with the Nambu-Jona-Lasinio model for the dynamical generation of nucleon masses. The massive neutrino states are Bogoliubov quasiparticles and their vacuum is a condensate of "Cooper pairs" of massless flavour neutrinos. Their superpositions as oscillating neutrino states have intrinsic quantum coherence by construction. In this quantization framework, the standard phenomenological flavour neutrino states and oscillation probability formula are validated in the ultrarelativistic approximation.

We compute the gravitational wave spectrum from a tachyonic preheating transition of a Standard Model-like SU(2)-Higgs system. Tachyonic preheating involves exponentially growing IR modes, at scales as large as the horizon. Such a transition at the electroweak scale could be detectable by LISA, if these non-perturbatively large modes translate into non-linear dynamics sourcing gravitational waves. Through large-scale numerical simulations, we find that the spectrum of gravitational waves does not exhibit such IR features. Instead, we find two peaks corresponding to the Higgs and gauge field mass, respectively. We find that the gravitational wave production is reduced when adding non-Abelian gauge fields to a scalar-only theory, but increases when adding Abelian gauge fields. In particular, gauge fields suppress the gravitational wave spectrum in the IR. A tachyonic transition in the early Universe will therefore not be detectable by LISA, even if it involves non-Abelian gauge fields.

Making use of a dimensionally-reduced effective theory at high temperature, we perform a nonperturbative study of the electroweak phase transition in the Two Higgs Doublet model. We focus on two phenomenologically allowed points in the parameter space, carrying out dynamical lattice simulations to determine the equilibrium properties of the transition. We discuss the shortcomings of conventional perturbative approaches based on the resummed effective potential — regarding the insufficient handling of infrared resummation but also the need to account for corrections beyond 1-loop order in the presence of large scalar couplings — and demonstrate that greater accuracy can be achieved with perturbative methods within the effective theory. We find that in the presence of very large scalar couplings, strong phase transitions cannot be reliably studied with any of the methods.