Quantum back-reaction in a universe with positive cosmological constant

TL;DR

This paper develops systematic semiclassical methods using moments to analyze quantum back-reaction effects in a universe with a positive cosmological constant, providing high-order computational tools and applying them to cosmological models.

Contribution

It introduces a systematic approach to derive semiclassical approximations for quantum systems with one degree of freedom using moments and computer algebra, applied to cosmology.

Findings

High-order equations of motion computed for quantum systems

Demonstrated quantum back-reaction effects in cosmological models

Provided convergence analysis of the semiclassical approximation

Abstract

Semiclassical techniques have proven to be a very powerful method to extract physical effects from different quantum theories. Therefore, it is expected that in the near future they will play a very prominent role in the context of quantum gravity. In this work we develop systematic tools to derive semiclassical approximations for any quantum theory with one degree of freedom. In our approach, the wave function is decomposed in terms of an infinite set of moments, which encode the complete quantum information of the system. Semiclassical regimes can then be properly described by truncation of this infinite system. The use of efficient computer algebra tools allows us to compute the equations of motion up to a very high order. In this way, we can study very precisely the quantum back reaction of the system as well as the convergence of the method with the considered order. Finally, these tools are applied to the particular case of a homogeneous universe filled with a massless scalar field and positive cosmological constant, which provide interesting physical results.