Time Evolution in Quantum Cosmology

TL;DR

This paper explores the quantum evolution of cosmological models in mini-superspace, proposing a gauge-fixed path integral approach that yields classical-like states evolving over time, challenging traditional constraints like the Wheeler-DeWitt equation.

Contribution

It introduces a gauge-fixed path integral method for quantum cosmology that constructs Hamiltonians in coherent states, showing classical states do not satisfy the Hamiltonian constraint.

Findings

Coherent states follow classical Einstein equations.

Classical states do not satisfy the Wheeler-DeWitt equation.

Predicts a pressureless dark matter component with variable energy density.

Abstract

The quantum description of time evolution in non-linear gravitational systems such as cosmological space-times is not well understood. We show, in the simplified setting of mini-superspace, that time evolution of this system can be obtained using a gauge fixed path integral, as long as one does not integrate over proper time. Using this gauge fixed action we can construct a Hamiltonian in the coherent - or classical - state basis. We show that by construction the coherent states satisfy the classical dynamical equations of General Relativity. They do not satisfy the Hamiltonian constraint. A consequence of this is that the Wheeler-DeWitt equation should not be satisfied in quantum gravity. Classical states have a natural non-trivial time evolution since they are not eigenstates of the Hamiltonian. A general feature of the unconstrained quantum theory of gravity is the prediction of a pressureless dark matter component of either sign energy density in the classical universe which may lead to novel phenomenology.