Lorentz Symmetry in QFT on Quantum Bianchi I Space-Time

TL;DR

This paper develops a quantum scalar field theory on Bianchi I loop quantum cosmology geometry, showing that Lorentz symmetry is preserved in the effective description without backreaction effects.

Contribution

It demonstrates that the effective geometry derived from quantum Bianchi I space-time does not induce Lorentz-violation in scalar field dispersion relations when backreaction is neglected.

Findings

No Lorentz-violation when backreaction is ignored.

Effective metric differs from classical Bianchi I geometry.

Preliminary backreaction analysis suggests minimal impact on Lorentz symmetry.

Abstract

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.