Cosmological Constant from a Deformation of the Wheeler-DeWitt Equation

Understand

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.