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Advisor(s)
Abstract(s)
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 Uq(h4) and Uq(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 10−3eV , 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 S2
q
or, alternatively, a fuzzy sphere S2F which explicitly exhibits features of the holographic principle. The corresponding
number of fundamental cells equals the dimension of the Hilbert space and hence, the
Description
Keywords
Cosmological constant problem Quantum cosmology Quantum groups Holographic principle