Long-Time Asymptotics of a Bohmian Scalar Quantum Field in de Sitter Space-Time

TL;DR

This paper studies the long-term behavior of a Bohmian scalar quantum field in de Sitter space-time, showing that field modes freeze at late times and discussing implications for Boltzmann brain formation.

Contribution

It provides a detailed analysis of the asymptotic behavior of scalar quantum fields in de Sitter space within the Bohmian framework, demonstrating mode freezing and its cosmological implications.

Findings

Field Fourier coefficients approach a finite limit as time goes to infinity

Each field mode 'freezes' at late times in de Sitter space

Supports the non-formation of Boltzmann brains in the late universe

Abstract

We consider a model quantum field theory with a scalar quantum field in de Sitter space-time in a Bohmian version with a field ontology, i.e., an actual field configuration $\varphi({\bf x},t)$ guided by a wave function on the space of field configurations. We analyze the asymptotics at late times ($t\to\infty$) and provide reason to believe that for more or less any wave function and initial field configuration, every Fourier coefficient $\varphi_{\bf k}(t)$ of the field is asymptotically of the form $c_{\bf k}\sqrt{1+{\bf k}^2 \exp(-2Ht)/H^2}$, where the limiting coefficients $c_{\bf k}=\varphi_{\bf k}(\infty)$ are independent of $t$ and $H$ is the Hubble constant quantifying the expansion rate of de Sitter space-time. In particular, every field mode $\varphi_{\bf k}$ possesses a limit as $t\to\infty$ and thus "freezes." This result is relevant to the question whether Boltzmann brains form in the late universe according to this theory, and supports that they do not.