Field Mixing in Curved Spacetime and Dark Matter

Abstract

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.

Quantum Field Theory of Neutrino Mixing in Spacetimes with Torsion

“…As far as minimally coupled Dirac fields are concerned, the information about torsion is stored in the axial vector field, T µ (x). Since we are specifically interested in the effects of torsion on Dirac fields, we assume that spacetime curvature is absent (although the most general case can be treated in a similar fashion, see, e.g., [65,[101][102][103][104][105][106]), so that the covariant derivatives in (5) are replaced with standard derivatives and the gamma matrices reduce to the flat ones. Under these assumptions, the Dirac equation becomes…”