Cosmological Constant from a Deformation of the Wheeler-DeWitt Equation

TL;DR

This paper shows that deforming the Wheeler-DeWitt equation via a Generalized Uncertainty Principle naturally induces a non-zero cosmological constant, impacting early universe singularities.

Contribution

It introduces a deformation of the Wheeler-DeWitt equation that generates a cosmological constant without matter fields in a mini-superspace model.

Findings

Deformation leads to a non-zero cosmological constant.

The cosmological constant arises even in flat space.

Implications for the big bang singularity.

Abstract

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 exists 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.