High-order quantum back-reaction and quantum cosmology with a positive cosmological constant

TL;DR

This paper develops systematic computational methods to derive high-order quantum corrections in quantum cosmology, demonstrating the evolution and convergence of quantum states with strong back-reaction effects.

Contribution

It introduces a comprehensive approach to include all quantum corrections in high-order moments within quantum cosmology models, supported by a deparameterized example.

Findings

Gaussian states evolve into new characteristic shapes

Strong convergence observed across high-order moments

Effective methods remain valid even with large quantum fluctuations

Abstract

When quantum back-reaction by fluctuations, correlations and higher moments of a state becomes strong, semiclassical quantum mechanics resembles a dynamical system with a high-dimensional phase space. Here, systematic computational methods to derive the dynamical equations including all quantum corrections to high order in the moments are introduced, together with a (deparameterized) quantum cosmological example to illustrate some implications. The results show, for instance, that the Gaussian form of an initial state is maintained only briefly, but that the evolving state settles down to a new characteristic shape afterwards. Remarkably, even in the regime of large high-order moments, we observe a strong convergence within all considered orders that supports the use of this effective approach.