Abstract
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 spacetime 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.
Highlights
Been proposed to address the second Sakharov condition
First there is the question of whether the full terms arising in the effective Lagrangian, including the curvature, are invariant under the symmetries of the original theory; in particular, whether discrete symmetries present at tree level may be violated by quantum loop effects
We have studied a number of fundamental theoretical issues related to gravitational leptogenesis
Summary
We give a brief review of the main elements of the spinor formalism in curved spacetime we need in the paper (see [12, 13] for a more complete account). Lorentz transformations can only be realised locally in the tangent plane at each spacetime point. This is achieved by introducing an orthonormal basis {e(μa)}. Which preserves the relation (2.1), where M ab form a basis for the fundamental representation of the Lorentz algebra. We can write the derivative in the vierbein basis ∇X = (∇μXa) dxμ ⊗ e(a), which after a little algebra leads to the relation. We introduce the concept of a non-accelerating vierbein frame, and use this together with the relation (2.16) to show how the spin connection must vanish at the origin of such a frame and that the Dirac equation satisfies the strong equivalence principle
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