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I was thinking about this paper (https://arxiv.org/abs/1405.0298) where the authors argue that there wouldn't be dynamical quantum fluctuations in a De Sitter space as fluctuations would be static once all perturbative radiation escapes the horizon (in the case that the Universe has a finite dimensional Hilbert space or has no cosmological horizon like in a classical Minkowski spacetime).

They also argue that once perturbative radiation leaves the horizon then there would be only two non-perturbative processes: quantum down tunneling or up tunneling. However, up tunneling is supressed because quantum fluctuations become static and there would be no "measuremente device" to make them dynamical (the eigenstates would not decohere into separate outcomes of the wavefunction)

But in their argument the universe is static because all perturbative radiation abandons the cosmological horizon. However, there would still be electrons, and they could arrange into interacting systems like Wigner crystals. A local system of interacting electrons is not perturbative radiation, besides, the universe would become static if there was nothing that would interact within it, but if we leave a system of interacting electrons (like a Wigner crystal) then it does not become static in the first place as there is already a system of interacting things

Basically, my point is: even if all perturbative radiation exited the horizon, and protons decayed, there would still be electrons, and if there are electrons within the universe, then there would be a non-zero probability that some of them in some place begin interacting, even forming structures like a Wigner crystal, and these interactions could avoid quantum fluctuations from being static, as they can cause the decoherence of a quantum system. So there is a small caveat or exception in their model...

Does this make any sense?

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There is no assumption of proton decay in that article. Moreover, the time scale for proton decay (if it is finite at all) is known to be much longer than the time scales discussed in that article. So electrons are not special in this picture, and you could worry about the presence of matter more generally.

However, matter exits the horizon on the same time scale as the radiation. Within an arbitrary patch of space, you do not need have to wait very long before the matter and radiation densities are negligible. Both decay exponentially in time.

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  • $\begingroup$ you're right, but I was assuming that there was proton decay, so that is why I was talking about electrons. But even if matter densities decay within a patch, there would still be some matter inside the horizon. So, even if the likelihood is very small, couldn't there be a non-zero probability that this happens and matter (e.g. electron arrangements such as Wigner crystals) could impede quantum fluctuarions from becoming static (as the article claims)? @Sten $\endgroup$
    – vengaq
    Commented May 6 at 9:54
  • $\begingroup$ In the asymptotic future, there is matter, but it is only present in an asymptotically vanishing fraction of the causal patches. So indeed there remains the possibility for dynamics related to the matter, but they are exponentially less frequent than vacuum fluctuations would be, which is why the article focuses on the vacuum fluctuations. $\endgroup$
    – Sten
    Commented May 7 at 18:55
  • $\begingroup$ okay so the thing is that because matter would be so scarce making fluctuations dynamical (instead of static) in the paper would be a highly rare event, so they don't really consider it; is that correct? @Sten $\endgroup$
    – vengaq
    Commented May 7 at 23:29
  • $\begingroup$ Yeah, that's my understanding $\endgroup$
    – Sten
    Commented May 8 at 0:15

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