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

TL;DR

This paper explores a quantum-deformed cosmological model using quantum groups to address the cosmological constant problem, revealing natural ultraviolet and infrared cutoffs and a holographic structure.

Contribution

It introduces a quantum group framework for quantum cosmology that naturally incorporates cutoffs and links the cosmological constant to quantum deformation.

Findings

Ultraviolet cutoff at 10^{-3} eV scale

Infrared cutoff at the size of the observed Universe

Cosmological horizon as a quantum or fuzzy sphere

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 $S^2_q$ or, alternatively, a fuzzy sphere $S^2_F$ 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.