The origin of matter-antimatter asymmetry is one of the most important outstanding problems at the interface of particle physics and cosmology. Gravitational leptogenesis (baryogenesis) provides a possible mechanism through explicit couplings of spac
etime curvature to appropriate lepton (or baryon) currents. In this paper, the idea that these strong equivalence principle violating interactions could be generated automatically through quantum loop effects in curved spacetime is explored, focusing on the realisation of the discrete symmetries C, CP and CPT which must be broken to induce matter-antimatter asymmetry. The related issue of quantum corrections to the dispersion relation for neutrino propagation in curved spacetime is considered within a fully covariant framework.
The effect of gravitational tidal forces on renormalized quantum fields propagating in curved spacetime is investigated and a generalisation of the optical theorem to curved spacetime is proved. In the case of QED, the interaction of tidal forces wit
h the vacuum polarization cloud of virtual e^+ e^- pairs dressing the renormalized photon has been shown to produce several novel phenomena. In particular, the photon field amplitude can locally increase as well as decrease, corresponding to a negative imaginary part of the refractive index, in apparent violation of unitarity and the optical theorem. Below threshold decays into e^+ e^- pairs may also occur. In this paper, these issues are studied from the point of view of a non-equilibrium initial-value problem, with the field evolution from an initial null surface being calculated for physically distinct initial conditions and for both scalar field theories and QED. It is shown how a generalised version of the optical theorem, valid in curved spacetime, allows a local increase in amplitude while maintaining consistency with unitarity. The picture emerges of the field being dressed and undressed as it propagates through curved spacetime, with the local gravitational tidal forces determining the degree of dressing and hence the amplitude of the renormalized quantum field. These effects are illustrated with many examples, including a description of the undressing of a photon in the vicinity of a black hole singularity.
The effect of vacuum polarization on the propagation of photons in curved spacetime is studied in scalar QED. A compact formula is given for the full frequency dependence of the refractive index for any background in terms of the Van Vleck-Morette ma
trix for its Penrose limit and it is shown how the superluminal propagation found in the low-energy effective action is reconciled with causality. The geometry of null geodesic congruences is found to imply a novel analytic structure for the refractive index and Green functions of QED in curved spacetime, which preserves their causal nature but violates familiar axioms of S-matrix theory and dispersion relations. The general formalism is illustrated in a number of examples, in some of which it is found that the refractive index develops a negative imaginary part, implying an amplification of photons as an electromagnetic wave propagates through curved spacetime.
