Chiral vacuum fluctuations in quantum gravity

TL;DR

This paper explores chiral vacuum fluctuations in quantum gravity using Ashtekar variables, revealing a parity asymmetry in graviton fluctuations that could be observed through cosmic microwave background polarization.

Contribution

It introduces a novel quantum gravity framework showing chiral vacuum fluctuations and their potential observational signatures, dependent on the Immirzi parameter.

Findings

Right and left gravitons have different vacuum fluctuations.

Vacuum asymmetry depends on the Immirzi parameter and Hamiltonian ordering.

Potential observational imprint on cosmic microwave background polarization.

Abstract

We examine tensor perturbations around a deSitter background within the framework of Ashtekar's variables and cousins parameterized by the Immirzi parameter $\gamma$. At the classical level we recover standard cosmological perturbation theory, with illuminating insights. Quantization leads to real novelties. In the low energy limit we find a second quantized theory of gravitons which displays different vacuum fluctuations for right and left gravitons. Nonetheless right and left gravitons have the same (positive) energies, resolving a number of paradoxes suggested in the literature. The right-left asymmetry of the vacuum fluctuations depends on $\gamma$ and the ordering of the Hamiltonian constraint, and it would leave a distinctive imprint in the polarization of the cosmic microwave background, thus opening quantum gravity to observational test.