Quantum Cosmology will need to become a Numerical Subject

TL;DR

This paper explores the quantum origins of cosmic structure formation using toy models and numerical methods, aiming to understand the complex terms in the Halliwell-Hawking model of quantum cosmology.

Contribution

It introduces a qualitative analysis of the Halliwell-Hawking model through toy models and variational principles, emphasizing the need for numerical approaches.

Findings

Toy models provide tractable insights into complex quantum cosmology terms.

Variational principles are essential for anchoring the analysis.

Numerical methods are necessary for solving the resulting equations.

Abstract

The inhomogeneous fluctuations that underlie structure formation - galaxies and CMB hotspots - might have been seeded by quantum cosmological fluctuations, as magnified by some inflationary mechanism. The Halliwell-Hawking model for these, as a lower-energy semiclassical limit, is expected to be shared by many theories. E.g. an O((H/m_pl)^2) suppression of power at large scales results from this. This model contains/suppresses very many terms; we want a qualitative understanding of the meaning of these terms and of different regimes resulting from different combinations of them. I study this with toy models that have tractable mathematics: minisuperspace and, especially, relational particle mechanics. In the present Seminar, I consider in particular averaged terms with some lessons from Hartree-Fock approach to Atomic and Molecular Physics. One needs to anchor this on variational principles; treating the subsequent equations is a numerical venture.