2019/06/18 by Wojciech Kamiński, Wojciech Kaminski, Kaminski, Wojciech
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories #gr-qc
paper · pdf · doi:10.48550/arxiv.1906.07554
14 pages
arxiv created 2019/06/18 · openalex publication_date 2019/06/18 · arxiv updated 2019/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.