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Long-Time Asymptotics of a Bohmian Scalar Quantum Field in de Sitter Space-Time
Quantum Physics · Submitted 30 Jul 2015
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 0.60 | 0.54 | 0.04 | asserted 0.92 |
| s1 | 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. | result 0.96 | 0.93 | 0.82 | hedged possibility 0.93 |
| s2 | 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. | interpretation 0.90 | 0.82 | 0.37 | asserted 0.79 |
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The paper
Original 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.
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How the literature uses it
2 arXiv papers cite this in 3 sentences
Papers citing it · 1 sentence without a confident label
Cites it as support 1 paper
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This question is answered in [ref] , where it is derived that, in the Bohmian model defined by [ref] and [ref], the time dependence [ref] applies asymptotically at late times to every Bohmian history $φ$ and generic wave function $Ψ$.
The Bohmian Approach to the Problems of Cosmological Quantum Fluctuations · No Boltzmann brain problem · 0.97
What it cites · 6 sentences without a confident label
Uses the method or tool of 4 papers
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The quantum field theory (QFT) we use here, adopted from [ref] , can be thought of as arising by quantization of the classical field equation φ̈ + 3H φ̇ - ^-2Ht ∇^2 φ= 0
Semiclassicality and Decoherence of Cosmological Perturbations · Introduction · 0.93
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The quantum field theory (QFT) we use here, adopted from [ref] , can be thought of as arising by quantization of the classical field equation φ̈ + 3H φ̇ - ^-2Ht ∇^2 φ= 0
The Bohmian Approach to the Problems of Cosmological Quantum Fluctuations · Introduction · 0.93
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This equation of motion, adopted from [ref] , can be obtained via certain general rules [ref] for obtaining a Bohm-type equation of motion from a given Hamiltonian.
De Broglie-Bohm Guidance Equations for Arbitrary Hamiltonians · Model Setup · 0.86
Cites as background 8 papers
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Further discussion within the Bohmian approach can be found in [ref] , and within the Everettian approach in [ref] .
Why Boltzmann Brains Don't Fluctuate Into Existence From the De Sitter Vacuum · Implications for the Boltzmann Brain Problem · 0.84
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Further discussion within the Bohmian approach can be found in [ref] , and within the Everettian approach in [ref] .
The Bohmian Approach to the Problems of Cosmological Quantum Fluctuations · Implications for the Boltzmann Brain Problem · 0.84
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Extensions of Bohmian mechanics to quantum field theory use either a particle ontology [ref] or a field ontology [ref] ; we choose here the latter.
Pilot-wave theory and quantum fields · Introduction · 0.90
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