Discrete fuzzy de Sitter cosmology

Abstract

We analyze the spectrum of time observable in noncommutative cosmological model introduced in [5], defined by $(\rho ,s=\frac{1}{2})$ 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 $\ell \sqrt{\frac{3}{4}\left(\frac{1}{4}+{\rho }^2\right)}$, which resolves the big bang singularity. An immediate consequence of the model is a specific breaking of the original symmetry at the Planck scale.

22 pages, 1 figure

References in corpus (5)

• Improved Z -> gamma gamma decay in the renormalizable gauge sector of the noncommutative standard model
• Gravity and the Structure of Noncommutative Algebras
• Bouncing Unitary Cosmology I: Mini-Superspace General Solution
• Fuzzy de Sitter Space
• Integrable Minisuperspace Models with Liouville Field: Energy Density Self-Adjointness and Semiclassical Wave Packets

Cited by in corpus (5)

• Asymptotic freedom for $\lambda {\varphi }_{\star }^4$ QFT in Snyder-de Sitter space
• The Snyder-de Sitter Scalar ${\phi }_{\star }^4$ Quantum Field Theory in D=2
• Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model
• Laplacian on fuzzy de Sitter space
• Search for footprints of quantum spacetime in black hole QNM spectrum