Non-linear (loop) quantum cosmology

TL;DR

This paper models inhomogeneous quantum cosmology using non-linear equations derived from many-body interactions, revealing how quantum corrections can accumulate coherently in large regions, offering new insights and tests for loop quantum gravity.

Contribution

It introduces a non-linear minisuperspace equation approach to inhomogeneous quantum cosmology, enabling manageable analysis of complex gravitational dynamics.

Findings

Quantum corrections can arise from tiny local contributions adding coherently.

Non-linear and non-local equations open new avenues for mathematical and computational research.

The approach provides a framework for testing loop quantum gravity effects.

Abstract

Inhomogeneous quantum cosmology is modeled as a dynamical system of discrete patches, whose interacting many-body equations can be mapped to a non-linear minisuperspace equation by methods analogous to Bose-Einstein condensation. Complicated gravitational dynamics can therefore be described by more-manageable equations for finitely many degrees of freedom, for which powerful solution procedures are available, including effective equations. The specific form of non-linear and non-local equations suggests new questions for mathematical and computational investigations, and general properties of non-linear wave equations lead to several new options for physical effects and tests of the consistency of loop quantum gravity. In particular, our quantum cosmological methods show how sizeable quantum corrections in a low-curvature universe can arise from tiny local contributions adding up coherently in large regions.