Quantum cosmology of a classically constrained nonsingular Universe

TL;DR

This paper develops a quantum cosmological model of a nonsingular universe, addressing the challenges of classical trajectory parameterization using semiclassical methods and emphasizing the importance of Lagrangian formulation.

Contribution

It advances the quantum cosmology of nonsingular universes by deriving the Hamilton-Jacobi equation under semiclassical approximation and clarifying the role of Lagrangian formalism.

Findings

Hamilton-Jacobi equation derived in semiclassical regime

Parameterization of classical trajectories requires Lagrangian formalism

Addresses nontrivial task of trajectory parameterization in constrained systems

Abstract

The quantum cosmological version of a nonsingular Universe presented by Mukhanov and Brandenberger in the early nineties has been developed and the Hamilton Jacobi equation has been found under semiclassical (WKB) approximation. It has been pointed out that, parameterization of classical trajectories with semiclassical time parameter, for such a classically constrained system, is a nontrivial task and requires Lagrangian formulation rather than the Hamiltonian formalism.