Integral Hilbert spaces and the dynamics of loop quantum cosmos

Janek Kozicki; Tomasz Pawłowski

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arXiv · 2608.02798

Integral Hilbert spaces and the dynamics of loop quantum cosmos

Janek Kozicki·Tomasz Pawłowski

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Abstract

Polymer quantization program applied in Loop Quantum Gravity/Cosmology leads to nonseparable Hilbert spaces. Commonly, one sidesteps this problem by singling out and working with a separable superselection sector. This is however often no longer accessible in more involved models beyond isotropic ones. In an alternative approach one builds a separable Hilbert space as an integral over all available sectors. Here we test the dynamics following from the latter on the example of a flat isotropic Universe admitting negative cosmological constant and a massless scalar field. There, numerical evolution of (initially) semiclassical states shows that there is no relevant difference in their long term semiclassicality properties in comparison to those in a single sector approach. Further, the older (problem-specific) numerical methods are compared against an application of more common and more efficient standard tools (eigen library).

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Janek Kozicki, Tomasz Pawłowski. 2026-08-03. Integral Hilbert spaces and the dynamics of loop quantum cosmos. https://arxiv.org/abs/2608.02798

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