Spinfoams, γ-duality and Parity Violation in Primordial Gravitational Waves

It is expected that the presence of the Barbero-Immirzi parameter (γ) in Loop Quantum Gravity (LQG) results in a quantum correction to the classical theory of gravity in the form of parity violation in primordial gravitational waves. In this work, we construct an effective field theory for inflation with the same amount of parity violation than the Holst action for LQG. As a consequence, the polarization of the primordial gravitational wave background depends explicitly on γ. In this manner, the observation of primordial parity violation together with the mechanism that we propose would provide a way to set an experimental bound on the value of γ, and therefore on the scale of discreteness of geometrical observables, such as the area and volume of a quantum chunk of space.