STM-D-0932Paper2009Published and peer-reviewed

On de Sitter radiation via quantum tunneling

Grigory E. Volovik

Abstract and summary · read the original at the source

In one page

Grigory Volovik, of the Low Temperature Laboratory in Helsinki and the Landau Institute in Moscow, takes a question about the whole universe and tests it against liquid helium. Our cosmos expands, and that expansion draws a horizon around every observer much as a black hole draws one around itself. The usual tunnelling calculation gives both horizons the same temperature. Volovik argues the two cases are not alike. A black hole picks out a preferred frame — it sits still while the vacuum flows past it — and that broken symmetry is what lets the vacuum decay. Expanding empty space, de Sitter space, has no preferred frame at all, so the pure vacuum has nothing to decay into and stays stable. Put a detector in it, though, and the picture changes. He uses the simplest detector there is, a single atom, and finds it torn apart at exactly the rate a thermal bath would manage at twice the Hawking temperature. The radiation belongs to the detector, not to the horizon.

Why it matters hereChapter 2 holds that the vacuum is a real medium carrying real energy, and this is the cleanest published argument for why that energy does not simply leak away — de Sitter space is stable because of its symmetry. Chapter 5 supplies the method, since Volovik reads gravity off the flow of a superfluid, and chapter 13 gains a distinction worth keeping: radiation that decays the vacuum is a different thing from radiation that only lights up a detector.

What it claims

01A black-hole horizon and a cosmological horizon are described by the same flowing-fluid metric, and the semiclassical tunnelling calculation gives them the same form of answer: a thermal exponent set by the gradient of the flow velocity at the horizon, which for an expanding de Sitter universe is h-bar times the Hubble rate divided by two pi.Section 2, Hawking temperature and tunneling exponent, Eq. (1) through Eq. (8)
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02An atom sitting at rest in a de Sitter background is ionised by the expansion at a rate equal to the exponential of minus pi times the ionisation potential divided by the Hubble rate — which is exactly thermal activation at an effective temperature of h-bar times the Hubble rate divided by pi, twice the Hawking temperature of the horizon. The tunnelling barrier lies far inside the horizon, so the effect owes nothing to the horizon at all.Section 3, Detector in de Sitter background, Eq. (9) through Eq. (14)
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03Two kinds of radiation must be kept apart. The first is real emission that decays the vacuum and happens whether or not anyone is watching — Hawking radiation from a black-hole horizon, Zeldovich-Starobinsky radiation from the ergoregion of a rotating one, phonons from a supersonic flow in a superfluid. The second is caused by the detector’s own interaction with the vacuum, excites the detector and leaves the vacuum intact — the Unruh effect. Volovik’s conclusion is that de Sitter space supports only the second kind.Section 3, the two classes set out in the closing paragraphs
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04De Sitter spacetime is invariant under a modified translation that shifts position and boosts velocity together, so there is exactly one comoving vacuum, the same inside and outside the cosmological horizon. With no second reference frame to tunnel between, the prefactor multiplying the tunnelling exponent vanishes and the pure vacuum does not radiate — which is why no relaxation of the cosmological constant is forced by this process.Section 4, de Sitter background vs black hole background, Eq. (16) and the paragraphs following it
Published and peer-reviewed
05Condensed matter supplies the mirror image of the factor of two. Where emitting a single quasiparticle would violate mass conservation, two must tunnel together, and this co-tunnelling doubles the exponent — an effective Hawking temperature half the nominal one, against the doubled temperature the de Sitter detector sees.Section 4, the co-tunnelling paragraph
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06What to watch: applied to a black hole, the same argument says the second reference frame is supplied by the singularity at the centre, so the emission rate should depend on how strongly the vacuum fields couple to it. If that coupling is weak or forbidden by a symmetry, the prefactor shrinks, the hole is a grey body rather than a black one, and the area law for its entropy is open again — a question the analogue-horizon experiments are positioned to inform.Section 5, Discussion, the paragraphs on the prefactor and the grey body
What to watch

Read it · abstract

Abstract

We discuss why the tunneling picture does not necessarily lead to Hawking radiation from the de Sitter horizon. The experience with the condensed matter analogs of the event horizon suggests that the de Sitter vacuum is stable against Hawking radiation. On the other hand, the detector immersed in the de Sitter background will detect the radiation, which looks thermal, with the effective temperature twice as large as the Hawking temperature associated with the cosmological horizon.

Grigory E. Volovik, Low Temperature Laboratory, Helsinki University of Technology, and Landau Institute for Theoretical Physics, Moscow. International Journal of Modern Physics D 18, issue 9, pages 1227 to 1241, 2009. Author version arXiv:0803.3367, revised 29 January 2009.

(Abstract only. The author version is free to read on arXiv — see the rights note for why no further text is reproduced here.)

On this site: Volovik’s book-length statement of the superfluid-vacuum programme, The Universe in a Helium Droplet, is at /library/stm-6ee45bd8be; Unruh’s 1981 paper that opened analogue horizons to the laboratory is at /library/stm-dcc76e413a; and the question of where the partner particle goes is taken up at /library/stm-a0c0727ca5.

The way in

https://doi.org/10.1142/s0218271809015035The published article is closed at the publisher. The author version is on arXiv as arXiv:0803.3367 version 6, dated 29 January 2009, and that is the copy the summary and every locator below were written from. The arXiv abstract page records the arXiv non-exclusive distribution licence, which is not a Creative Commons licence, and no Creative Commons statement appears in the paper itself, so only the author’s own abstract is reproduced here. REGISTRY NOTE: the registry and the skeleton carried the title and the author name set in capitals — ON DE SITTER RADIATION VIA QUANTUM TUNNELING, G. E. VOLOVIK — which is the publisher’s house styling; the sheet uses normal case and the author’s full name as it appears on the paper, Grigory E. Volovik, of the Low Temperature Laboratory at Helsinki University of Technology and the Landau Institute for Theoretical Physics, Moscow.

How to cite it

Grigory E. Volovik (2009) On de Sitter radiation via quantum tunneling. doi:10.1142/s0218271809015035

Where it sits in the curriculum

What the vacuum is The vacuum as a quantum fluid The unified picture