Path Integral of Bianchi I models in Loop Quantum Cosmology

Abstract

A path integral formulation of the Bianchi I models containing a massless scalar field in loop quantum cosmology is constructed. Following the strategy used in the homogenous and isotropic case, the calculation is extended to the simplest non-isotropic models according to the $\bar{\mu }$ and ${\bar{\mu }}^{\prime }$ scheme. It is proved from the path integral angle that the quantum dynamic lacks the full invariance with respect to fiducial cell scaling in the $\bar{\mu }$ scheme, but it does not in the ${\bar{\mu }}^{\prime }$ scheme. The investigation affirms the equivalence of the canonical approach and the path integral approach in loop quantum cosmology.

11 pages,revised version, accepted for publication in Class. Quantum Grav

References in corpus (9)

• Loop Quantization of Vacuum Bianchi I Cosmology
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