On the Semiclassical Approach to Quantum Cosmology

TL;DR

This paper examines the semiclassical approach to quantum cosmology using scaled relational particle models, focusing on the interaction between heavy and light degrees of freedom and the implications for understanding cosmic inhomogeneities.

Contribution

It provides a detailed analysis of the semiclassical time approach in relational models, considering backreaction effects and the role of expectation values, advancing the theoretical framework of quantum cosmology.

Findings

Heavy-light interaction acts as an emergent-time dependent perturbation.

Small but non-negligible backreaction influences emergent time.

Expectation values may require treatment similar to Hartree-Fock methods.

Abstract

The emergent semiclassical time approach to resolving the problem of time in quantum gravity involves heavy slow degrees of freedom providing via an approximately Hamilton-Jacobi equation an approximate timestandard with respect to which the quantum mechanics of light fast degrees of freedom can run. More concretely, this approach involves Born-Oppenheimer and WKB ansatze and some accompanying approximations. In this paper, I investigate this approach for concrete scaled relational particle mechanics models, i.e. models featuring only relative separations, relative angles and relative times. I consider the heavy-light interaction term in the light quantum equation - necessary for the semiclassical approach to work, firstly as an emergent-time dependent perturbation of the emergent-time-dependent Schrodinger equation for the light subsystem. Secondly, I consider a scheme in which the backreaction is small but non-negligible, so that the l-subsystem also affects the form of the emergent time. I also suggest that the many terms involving expectation values of the light wavefunctions in both the (unapproximated) heavy and light equations might require treatment in parallel to the Hartree--Fock self-consistent approach rather than merely being discarded; for the moment this paper provides a counterexample to such terms being smaller than their unaveraged counterparts. Investigation of these ideas and methods will give us a more robust understanding of the suggested quantum-cosmological origin of microwave background inhomogeneities and galaxies.