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Lorentz Symmetry in QFT on Quantum Bianchi I Space-Time

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arxiv 1207.0671 v3 pith:YVR4NJV7 submitted 2012-07-03 gr-qc

Andrea Dapor , Jerzy Lewandowski , Yaser Tavakoli This is my paper · ORCID
classification gr-qc
keywords bianchieffectivequantumbackreactionclassicalequationfieldgeometry
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We develop the quantum theory of a scalar field on LQC Bianchi I geometry. In particular, we focus on single modes of the field: the evolution equation is derived from the quantum scalar constraint, and it is shown that the same equation can be obtained from QFT on an "classical" effective geometry. We investigate the dependence of this effective space-time on the wavevector of the mode (which could in principle generate a deformation in local Lorentz-symmetry), focusing our attention on the dispersion relation. We prove that when we disregard backreaction no Lorentz-violation is present, despite the effective metric being different than the classical Bianchi I one. A preliminary analysis of the correction due to inclusion of backreaction is briefly discussed in the context of Born-Oppenheimer approximation.

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    Extended Born-Oppenheimer coupling of the EM field to quantum geometry yields chromatic dispersion of light—a prism effect proposed as an all-energy quantum-gravity probe on a quantum FLRW background.

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