Third Quantization of Brans-Dicke Cosmology

TL;DR

This paper explores the third quantization of a Brans-Dicke cosmological model, analyzing universe creation, number density, and quantum fluctuations, revealing a Planckian distribution and finite fluctuation limits during cosmic expansion.

Contribution

It introduces the third quantization framework to a Brans-Dicke model and computes universe creation rates and quantum fluctuations, providing new insights into quantum cosmology.

Findings

Universe creation number density has a Planckian form.

Quantum fluctuations tend to a finite limit during expansion.

The model's uncertainty relations are explicitly calculated.

Abstract

We study the third quantization of a Brans-Dicke toy model, we calculate the number density of the universes created from nothing and found that it has a Planckian form. Also, we calculated the uncertainty relation for this model by means of functional Schr"odinger equation and we found that fluctuations of the third-quantized universe field tends to a finite limit in the course of cosmic expansion.