Is the BKL map an intrinsic feature of the Quantum Mixmaster Universe?
arXiv:2504.00774 · doi:10.1016/j.jheap.2025.100463
Abstract
We study the quantum Mixmaster dynamics by constructing the corresponding Wheeler-DeWitt equation as a relativistic quantum theory in a pseudo-Riemannian Mini-superspace. The transition amplitude from a Kasner regime to the next one is built via the standard S-matrix of a relativistic scattering, and mediated by a single wall potential. We provide a coherent and convincing representation of the original Misner's idea that quasi-classical states can survive arbitrarily close to the cosmological singularity. By constructing a complete set of states, we demonstrate that the quasi-classical BKL map is preserved by the resulting transition amplitude to a new state when their mean total momentum is high enough (exactly coinciding with Misner's high occupation numbers). This scheme is naturally iterated to the initial singularity without appreciable shape changes. We also clarify the role played by the state localization, and, in particular, we outline that when the incoming state is spread, the possibility of violating the Kasner map is no longer negligible. Thus, Kasner-like wave packets can approach the initial singularity.
arXiv comment8 pages, 3 figures
References in corpus (16)
- The mixmaster universe is chaotic
- Classical and Quantum Features of the Mixmaster Singularity
- A Proposal for Solving the ``Problem of Time" in Canonical Quantum Gravity
- On the Covariance of the Mixmaster Chaoticity
- Applications of a New Proposal for Solving the "Problem of Time" to Some Simple Quantum Cosmological Models
- An Overview on the Nature of the Bounce in LQC and PQM
- Inhomogeneous Quantum Mixmaster: from Classical toward Quantum Mechanics
- Quasi-Isotropization of the Inhomogeneous Mixmaster Universe Induced by an Inflationary Process
- Frame-independence of the Inhomogeneous Mixmaster Chaos via Misner-Chitre'-like variables
- Singularity-free and non-chaotic inhomogeneous Mixmaster in polymer representation for the volume of the universe
- The Big Bang and the Quantum
- Quantum Big Bounce of the isotropic Universe via a relational time
- Semiclassical solutions of generalized Wheeler-DeWitt cosmology
- Multifractality in the general cosmological solution of Einstein's equations
- Potential scattering in space: (2) Rigorous scattering probability of wave packets
- Quantum Big-Bounce as a phenomenology of RQM in the Mini-superspace