Quantum deformation of quantum cosmology: A framework to discuss the cosmological constant problem

Abstract

We endorse the context that the cosmological constant problem is a quantum cosmology issue. Therefore, in this paper we investigate the $q$-deformed Wheeler-DeWitt equation of a spatially closed homogeneous and isotropic Universe in the presence of a conformally coupled scalar field. Specifically, the quantum deformed Universe is a quantized minisuperspace model constructed from quantum Heisenberg-Weyl ${\mathcal{U}}_q(h_4)$ and ${\mathcal{U}}_q(su(1,1))$ groups. These intrinsic mathematical features allow to establish that ($i$) the scale factor, the scalar field and corresponding momenta are quantized and ($ii$) the phase space has a non-equidistance lattice structure. On the other hand, such quantum group structure provides us a new framework to discuss the cosmological constant problem. Subsequently, we show that a ultraviolet cutoff can be obtained at $10^{-3}eV$, i.e., at a scale much larger than the expected Planck scale. In addition, an infrared cutoff, at the size of the observed Universe, emerges from within such quantum deformation of Universe. In other words, the spectrum of the scale factor is upper bounded. Moreover, we show that the emerged cosmological horizon is a quantum sphere $S_q^2$ or, alternatively, a fuzzy sphere $S_F^2$ which explicitly exhibits features of the holographic principle. The corresponding number of fundamental cells equals the dimension of the Hilbert space and hence, the cosmological constant can be presented as a consequence of the quantum deformation of the FLRW minisuperspace.

14 pages, to appear in Physics of Dark Universe

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• Fractional Scalar Field Cosmology
• Phase space analysis of the bouncing universe with stringy effects
• Classical and quantum bicosmology with noncommutativity
• A quantum cosmology approach to cosmic coincidence and inflation
• Fractional Einstein-Gauss-Bonnet scalar field cosmology
• Probing extra dimensions through cosmological observations of dark energy
• On the Hydrogen Atom in the Holographic Universe
• Fractional entropy of the Brown-Kuchař dust in fractional anti-de Sitter quantum gravity
• Classical Universe Arising from Quantum Cosmology
• Quantum Groups and Polymer Quantum Mechanics
• Remarks on SU_q(2) fermions