Chirality of tensor perturbations for complex values of the Immirzi parameter

Abstract

In this paper we generalise previous work on tensor perturbations in a de\nSitter background in terms of Ashtekar variables to cover all complex values of\nthe Immirzi parameter gamma (previous work was restricted to imaginary gamma).\nParticular attention is paid to the case of real gamma. Following the same\napproach as in the imaginary case, we can obtain physical graviton states by\ninvoking reality and torsion free conditions. The Hamiltonian in terms of\ngraviton states has the same form whether gamma has a real part or not; however\nchanges occur for the vacuum energy and fluctuations. Specifically, we observe\na gamma dependent chiral asymmetry in the vacuum fluctuations only if gamma has\nan imaginary part. Ordering prescriptions also change this asymmetry. We thus\npresent a measurable result for CMB polarisation experiments that could shed\nlight on the workings of quantum gravity.\n