2015/10/31 by Remo Garattini, Mir Faizal
Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Constant (computer programming) #Cosmological constant #Cosmological constant problem #Cosmology #Cosmology and Gravitation Theories #Dark energy #Eigenvalues and eigenvectors #Equation of state #Friedmann–Lemaître–Robertson–Walker metric #Mathematical physics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Superspace #Supersymmetry #Theoretical physics #gr-qc #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2016.02.023
published as Nucl. Phys. B905, 313 (2016) · 11 pages, 0 figures, Accepted in Nucl. Phys. B
arxiv created 2016/02/23 · openalex publication_date 2016/02/27 · arxiv updated 2016/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper, we consider the Wheeler–DeWitt equation modified by a deformation of the second quantized canonical commutation relations. Such modified commutation relations are induced by a Generalized Uncertainty Principle. Since the Wheeler–DeWitt equation can be related to a Sturm–Liouville problem where the associated eigenvalue can be interpreted as the cosmological constant, it is possible to explicitly relate such an eigenvalue to the deformation parameter of the corresponding Wheeler–DeWitt equation. The analysis is performed in a Mini-Superspace approach where the scale factor appears as the only degree of freedom. The deformation of the Wheeler–DeWitt equation gives rise to a Cosmological Constant even in absence of matter fields. As a Cosmological Constant cannot exist in absence of the matter fields in the undeformed Mini-Superspace approach, so the existence of a non-vanishing Cosmological Constant is a direct consequence of the deformation by the Generalized Uncertainty Principle. In fact, we are able to demonstrate that a non-vanishing Cosmological Constant exists even in the deformed flat space. We also discuss the consequences of this deformation on the big bang singularity.