Monday, January 05, 2015

Instability of Quantum de Sitter Spacetime

New paper! We show that quantum effects (in particular, the horizon temperature originally discovered by Gibbons and Hawking) modify the geometry of de Sitter spacetime.
Instability of Quantum de Sitter Spacetime (

Chiu Man Ho, Stephen D. H. Hsu

Quantized fields (e.g., the graviton itself) in de Sitter (dS) spacetime lead to particle production: specifically, we consider a thermal spectrum resulting from the dS (horizon) temperature. The energy required to excite these particles reduces slightly the rate of expansion and eventually modifies the semiclassical spacetime geometry. The resulting manifold no longer has constant curvature nor time reversal invariance, and back-reaction renders the classical dS background unstable to perturbations. In the case of AdS, there exists a global static vacuum state; in this state there is no particle production and the analogous instability does not arise.


Sean Carroll said...

Sorry Steve, I don't buy it. :) It's true that particle detectors in dS detect a thermal bath of particles. But such particle detectors are, by construction, out-of-equilibrium systems. In the actual dS vacuum, there are no such detectors hanging around, and correspondingly there is no thermal bath violating the symmetries of dS. There is just the vacuum state itself, whose energy-momentum tensor is perfectly dS invariant. See:

steve hsu said...

Looks like we are in for a long conversation :-) I think I know where we disagree, but it will take some time to write it up in comprehensible form -- I'll send you an email. I don't think you need "out of equilibrium detectors" for the system to evolve away from the stationary state you consider. The state of the universe we describe (QFT modes thermalized; gravitational back reaction changes geometry slightly) has higher entropy than the stationary one (yours), and there are nonzero quantum amplitudes connecting the two. So in an Everett description I think most of the measure (probability) is concentrated on the former. More later ...

PS I noticed in the original Gibbons-Hawking paper on dS temperature that Hawking promises to address some of the issues you tackle in your paper in a forthcoming publication (ref. 16; see discussion in left column of p.2751). AFAIK ref. 16 never appeared! So it's definitely a tricky question ...

G. W. Gibbons and S. W. Hawking, Phys. Rev. D 15, 2738 (1977)

Sean Carroll said...

In semiclassical QFT, the energy-momentum tensor is dS invariant, full stop. But the real world is certainly tricky, because gravitational backreaction is the whole point, so semiclassical QFT isn't necessarily up to the task. You would have to convince me that quantum gravity somehow breaks dS invariance -- which is always possible, I suppose, though I don't see why it would happen. Looking forward to talking, and always willing to be convinced!

(You might be interested in some of the papers in our references, esp. the ones on the quantum no-hair theorem.)

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