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

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 $\phi (\mathbf{x},t)$ 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 ${\phi }_{\mathbf{k}}(t)$ of the field is asymptotically of the form $c_{\mathbf{k}}\sqrt{1+{\mathbf{k}}^2\exp (-2Ht)/H^2}$, where the limiting coefficients $c_{\mathbf{k}}={\phi }_{\mathbf{k}}(\infty )$ are independent of $t$ and $H$ is the Hubble constant quantifying the expansion rate of de Sitter space-time. In particular, every field mode ${\phi }_{\mathbf{k}}$ 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.

11 pages LaTeX, no figures; v2: section 5 added, and minor additions

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• Bohmian Mechanics and Quantum Field Theory
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Cited by in corpus (1)

• Classical Universe emerging from quantum cosmology without horizon and flatness problems