Spectral properties of the quantum Mixmaster universe
arXiv:1703.08462 · doi:10.1103/PhysRevD.96.043521
Abstract
We study the spectral properties of the anisotropic part of Hamiltonian entering the quantum dynamics of the Mixmaster universe. We derive the explicit asymptotic expressions for the energy spectrum in the limit of large and small volumes of the universe. Then we study the threshold condition between both regimes. Finally we prove that the spectrum is purely discrete for any volume of the universe. Our results validate and improve the known approximations to the anisotropy potential. They should be useful for any approach to the quantization of the Mixmaster universe.
Version accepted by Phys. Rev. D
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Cited by in corpus (7)
- Critical evaluation of common claims in loop quantum cosmology
- Quantum Mixmaster as a model of the Primordial Universe
- Integrable Toda system as a quantum approximation to the anisotropy of Mixmaster
- Quantum approach to a Bianchi I singularity
- Quantum formalism on the plane: POVM-Toeplitz quantization, Naimark theorem and linear polarisation of the light
- Tunneling dynamics of an oscillating universe model
- Semiclassical study of the Mixmaster model: the quantum Kasner map