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 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.

6 pages, 1 figure

References in corpus (4)

• Anomalous CMB polarization and gravitational chirality
• Chiral vacuum fluctuations in quantum gravity
• Superconducting loop quantum gravity and the cosmological constant
• Quantum gravity as a Fermi liquid

Cited by in corpus (8)

• Higgs inflation with the Holst and the Nieh-Yan term
• Gravitational origin of the weak interaction's chirality
• On the Relations between Gravity and BF Theories
• Loop Quantum Gravity Phenomenology: Linking Loops to Observational Physics
• Detecting chiral gravity with the pure pseudospectrum reconstruction of the cosmic microwave background polarized anisotropies
• Scalar Cosmological Perturbations from Quantum Entanglement within Lorentzian Quantum Gravity
• Linking shape dynamics and loop quantum gravity
• Statistics of the CMB polarised anisotropies