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arXiv · 1903.08378

Discrete fuzzy de Sitter cosmology

Maja Buric·Dusko Latas
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Abstract

We analyze the spectrum of time observable in noncommutative cosmological model introduced in [5], defined by $(ρ, s=\frac 12)\,$ representation of the de Sitter group. We find that time has peculiar property: it is not self-adjoint, but appropriate restrictions to the space of physical states give self-adjoint extensions. Extensions have discrete spectrum with logarithmic distribution of eigenvalues, $\,t_n \sim \ell\, \log\, n$+const, where $\ell$ characterizes noncommutativity and the usual assumption is $\,\ell=\ell_{Planck}$. When calculated on physical states, radius of the universe is bounded below by $\, \ell\, \sqrt{\frac 34\, \left( \frac 14 +ρ^2\right)}\, $, which resolves the big bang singularity. An immediate consequence of the model is a specific breaking of the original symmetry at the Planck scale.

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Maja Buric, Dusko Latas. 2019-07-30. Discrete fuzzy de Sitter cosmology. https://doi.org/10.1103/physrevd.100.024053

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