# Operator Ordering Ambiguity and Third Quantization

## TL;DR

This paper investigates how operator ordering ambiguities in the Wheeler-DeWitt equation affect quantum fluctuations in the universe, using third quantization to identify parameter ranges that produce realistic fluctuation behavior across different cosmological models.

## Contribution

It introduces a method to constrain operator ordering ambiguity via quantum fluctuations analysis within a third quantized framework, applicable to multiple cosmological models.

## Key findings

- Quantum fluctuations are suppressed with universe expansion for a wide range of parameters.
- Similar parameter ranges yield consistent fluctuation behavior across different models.
- The approach constrains operator ordering ambiguity in quantum cosmology.

## Abstract

In this paper, we will constrain the operator ordering ambiguity of Wheeler-DeWitt equation by analyzing the quantum fluctuations in the universe. This will be done using a third quantized formalism. It is expected that the early stages of the universe are dominated by quantum fluctuations. Furthermore, it is also expected that these quantum fluctuations get suppressed with the expansion of the universe. We will show that this desired behavior of quantum fluctuations could be realized by a wide ranges of the factor ordering parameters. We will examined two different cosmological models, and observe that a similar range of factor ordering parameters produces this desired behavior in both those cosmological models.