Deformation of the Wheeler-DeWitt Equation

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.

arXiv comment8 pages, 0 figures, accepted for publication in Int. J. Mod. Phys. A

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• Minimal and maximal lengths from position-dependent noncommutativity
• Emergent Universe with particle production
• Deformation of Second and Third Quantization
• Discreteness of time in the evolution of the universe
• Constraints on Operator Ordering from Third Quantization
• Quantum Cosmology with Dynamical Vacuum in a Minimal-Length Scenario
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• Frustration of resonant preheating by exotic kinetic terms
• Lorentzian Vacuum Transitions with a Generalized Uncertainty Principle
• Traversable Wormholes in Distorted Gravity
• Gauge Theories on de Sitter Spacetime