Historical research guide · 0932 · 2009
On de Sitter radiation via quantum tunneling
Grigory E. Volovik
In one minute
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.
Connection
Chapter 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.
From the source
A 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)
An 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)
Two 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
De 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
Condensed 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
What 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
The way in
https://doi.org/10.1142/s0218271809015035How to cite it
Grigory E. Volovik (2009) On de Sitter radiation via quantum tunneling doi:10.1142/s0218271809015035