Deformation of the Wheeler-DeWitt Equation

TL;DR

This paper explores how deforming the Wheeler-DeWitt equation with minimal length and maximum momentum leads to a modified quantum cosmology that naturally avoids the big bang singularity.

Contribution

It introduces a deformed second quantized canonical commutation relation and derives a modified Wheeler-DeWitt equation with implications for singularity avoidance.

Findings

Big bang singularity is naturally avoided in the modified theory.

Deformation leads to a generalized second quantization framework.

Modified Wheeler-DeWitt equation incorporates minimal length and maximum momentum constraints.

Abstract

In this paper, we will analyse the consequences of deforming the canonical commutation relations consistent with the existence of a minimum length and a maximum momentum. We first generalize the deformation of first quantized canonical commutation relation to second quantized canonical commutation relation. Thus, we arrive at a modified version of second quantization. A modified Wheeler-DeWitt equation will be constructed by using this deformed second quantized canonical commutation relation. Finally, we demonstrate that in this modified theory the big bang singularity gets naturally avoided.