The volume operator in loop quantum cosmology

Abstract

We show that for basically all states, the evolution of the expectation value of the volume operator in Wheeler-DeWitt and various homogenous isotropic loop quantum comology (LQC) models ($k=0$, coupled to massless scalar field and without cosmological constant) is ill-defined. The expectation value of the volume operator become instantonously infinite during the evolution. The effect is produced by a very long tail in the volume spectrum, that is however semiclassically small and beyond reach of numerical simulations (that is why it went unnoticed so far). This is not necessarily problem of theory but rather it suggests that one should be extremely careful with unbounded observables.

14 pages

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Cited by in corpus (5)

• Critical evaluation of common claims in loop quantum cosmology
• Dressed metric predictions revisited
• Challenges in recovering a consistent cosmology from the effective dynamics of loop quantum gravity
• On the evolution of the volume in Loop Quantum Cosmology
• Cosmic tango between the very small and the very large: Addressing CMB anomalies through Loop Quantum Cosmology