# Quantum Hamilton-Jacobi cosmology and classical-quantum correlation

## TL;DR

This paper demonstrates how classical time evolution and quantum-classical correspondence naturally emerge in quantum cosmology using the quantum Hamilton-Jacobi formalism, applied to early universe models with perfect fluid matter.

## Contribution

It introduces a framework linking quantum Hamilton-Jacobi theory to quantum cosmology, explaining the emergence of classical behavior without inflation.

## Key findings

- Classical cosmology emerges around one Planck time.
- No need for inflationary phase for universe growth.
- Quantum Hamilton-Jacobi formalism explains time evolution in quantum cosmology.

## Abstract

How the time evolution which is typical for classical cosmology emerges from quantum cosmology? The answer is not trivial because the Wheeler-DeWitt equation is time independent. A framework associating the quantum Hamilton-Jacobi to the minisuperspace cosmological models has been introduced in [1]. In this paper, we show that time dependence and quantum-classical correspondence both arise naturally in the quantum Hamilton-Jacobi formalism of quantum mechanics applied to quantum cosmology. We study the quantum Hamilton-Jacobi cosmology of spatially flat homogeneous and isotropic early universe whose matter content is a perfect fluid. The classical cosmology emerge around one Planck time where its linear size is around a few millimeter, without needing any classical inflationary phase afterwards to make it grow to its present size.