Quantum cosmology with varying speed of light: canonical approach

TL;DR

This paper explores higher-dimensional cosmology with a varying speed of light, solving the Wheeler-DeWitt equation to find classical and quantum solutions, and demonstrating good correspondence between quantum and classical trajectories.

Contribution

It provides exact solutions for a $(c$--$\Lambda$)--dominated universe in varying speed of light cosmology using a canonical approach, including wave packets and Bohmian trajectories.

Findings

Quantum and classical trajectories align well.

Wave packets exhibit good classical-quantum correspondence.

Initial conditions lead to consistent classical descriptions.

Abstract

We investigate $(n+1)$--dimensional cosmology with varying speed of light. After solving corresponding Wheeler-DeWitt equation, we obtain exact solutions in both classical and quantum levels for ($c $--$\Lambda$)--dominated Universe. We then construct the ``canonical'' wave packets which exhibit a good classical and quantum correspondence. We show that arbitrary but appropriate initial conditions lead to the same classical description. We also study the situation from de-Broglie Bohm interpretation of quantum mechanics and show that the corresponding Bohmian trajectories are in good agreement with the classical counterparts.