Chirality of tensor perturbations for complex values of the Immirzi parameter

TL;DR

This paper extends the analysis of tensor perturbations in a de Sitter background using Ashtekar variables to include all complex Immirzi parameters, revealing gamma-dependent effects on vacuum fluctuations and potential observational signatures.

Contribution

It generalizes previous work restricted to imaginary gamma to all complex values, analyzing effects on graviton states, vacuum energy, and fluctuations, with implications for quantum gravity observations.

Findings

Gamma-dependent chiral asymmetry in vacuum fluctuations for imaginary gamma

Vacuum energy and fluctuations are affected by the real part of gamma

Potential measurable effects in CMB polarization experiments

Abstract

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