Abstract
We examine tensor perturbations around a de Sitter background within the framework of Ashtekar’s variables and its cousins parameterized by the Immirzi parameter . 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 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.
- Received 18 October 2010
DOI:https://doi.org/10.1103/PhysRevLett.106.121302
© 2011 American Physical Society