Chiral vacuum fluctuations in quantum gravity

We examine tensor perturbations around a deSitter background within the framework of Ashtekar's variables and cousins parameterized by the Immirzi parameter $γ$. 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 $γ$ 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.

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