We present a quantum field theoretical approach to the vacuum neutrino oscillations in curved space, we analyze the nontrivial interplay between quantum field mixing and field quantization in curved space and derive new oscillation formulas. We compute the formulas explicitly in the spatially flat Friedmann–Lemaitre–Robertson–Walker metrics for universes dominated by a cosmological constant and by radiation. We evaluate the transition probabilities in the Schwarzschild black hole metric, and we show that the Hawking radiation affects the oscillations of neutrinos. We show that our results are consistent with those of previous analyses when the quantum mechanical limit is considered.

We analyze fermion mixing in the framework of field quantization in curved spacetime. We compute the expectation value of the energy-momentum tensor of mixed fermions on the flavor vacuum. We consider spatially flat Friedmann-Lemaître-Robertson-Walker metrics, and we show that the energy-momentum tensor of the flavor vacuum is diagonal and conserved. Therefore, it can be interpreted as the effective energy-momentum tensor of a perfect fluid. In particular, assuming a fixed de Sitter background, the equation of state of the fluid is consistent with that of dust and cold dark matter. Our results establish a new link between quantum effects and classical fluids, and indicate that the flavor vacuum of mixed fermions may represent a new component of dark matter.

We propose a new possible detection strategy to reveal the fermion–fermion interaction mediated by axions and axion-like particles, based on interferometric measurement of neutron beams. We consider an interferometer in which the neutron beam is split in two sub-beams propagating in regions with differently oriented magnetic fields. The beam paths and the strength of the magnetic fields are set in such a way that the phase difference depends only on the axion-induced interaction. The resulting phase difference is directly related to the presence of axions. Our results show that such a phase might represent, in the future, a tool to probe the existence of axions and axion-like particles or a fifth force with interferometry.

An extensive review of recent results concerning the quantum field theory of particle mixing in curved spacetime is presented. The rich mathematical structure of the theory for both fermions and bosons, stemming from the interplay of curved space quantization and field mixing, is discussed, and its phenomenological implications are shown. Fermionic and bosonic oscillation formulae for arbitrary globally hyperbolic spacetimes are derived and the transition probabilities are explicitly computed on some metrics of cosmological and astrophysical interest. The formulae thus obtained are characterized by a pure QFT correction to the amplitudes, which is absent in quantum mechanics, where only the phase of the oscillations is affected by the gravitational background. Their deviation from the flat space probabilities is demonstrated, with the aid of numerical analyses. The condensate structure of the flavor vacuum of mixed fermions is studied, assessing its role as a possible dark matter component in a cosmological context. It is shown that the flavor vacuum behaves as a barotropic fluid, satisfying the equation of the state of cold dark matter. New experiments on the cosmic neutrino background, as PTOLEMY, may validate these theoretical results.