# Quantum Cosmology with many fluids and the choice of cosmological time

## TL;DR

This paper quantizes a primordial universe model with five fluids to determine which fluid best defines cosmological time, comparing quantum solutions with classical ones and exploring quantum tunneling phenomena.

## Contribution

It introduces a quantum cosmological model with multiple fluids and analyzes the suitability of each as a time variable using spectral and finite difference methods.

## Key findings

- Vacuum case shows a tunneling transition from quantum to classical phase.
- Quantum solutions are obtained and compared with classical solutions.
- The vacuum fluid provides a unique tunneling mechanism.

## Abstract

In this work we propose the quantization of a cosmological model describing the primordial universe filled with five barotropic fluids, namely: radiation, dust, vacuum, cosmic strings and domain walls. We intend to identify which fluid is best suited to provide phenomenologically the temporal variable in accordance with the observable universe. Through the Galerkin spectral method and the finite difference method in the Crank-Nicolson scheme (vacuum case), the quantum cosmological solutions are obtained and compared. We, also, compare the quantum cosmological solutions with the corresponding classical ones. The vacuum case is especially interesting because it provides a tunneling transition mechanism from the quantum to the classical phase and the possibility of calculating quantum tunneling probabilities.