Chiral vacuum fluctuations in quantum gravity

In this paper we investigate cosmological tensor modes in terms of the Ashtekar variables of loop quantum gravity, for complex values of the Immirzi parameter. While, on-shell, the classical Hamiltonian reduces to the usual expression found in cosmological perturbation theory, the quantum Hamiltonian displays significant differences. We can find a physical Fourier space Hamiltonian in terms of graviton creation and annihilation operators, after selecting out the non-physical modes through the inner product which itself is determined by the reality conditions. We are left with the usual graviton modes but with a chiral asymmetry in the the vacuum energy and fluctuations. The latter depends on gamma (in particular it vanishes for purely real gamma) and on the ordering of the 2-point function. Such an effect would leave a distinctive imprint in the polarisation of the cosmic microwave background, thus finally engaging quantum gravity in meaningful experimental test.