Causal patch complementarity is the conjecture that in de Sitter space with a positive cosmological constant, the states within the causal patch are sufficient to fully describe the universe with the rest of the universe outside encoded within the stretched horizon a Planck length thickness on the inside of the cosmological horizon.

However, it is not at all clear if it applies to metastable phases. In the inflationary slow roll phase, for example, our universe passed through at least 60 e-foldings in a de Sitter phase with a tiny cosmological horizon before rolling into our phase and expanding into the universe we see today. The catch is once inflation ended, observers will be able to simultaneously observe information streaming in from many many causal patches (during the inflationary phase) in all directions. How can this be compatible with causal patch complimentarity? Are all these information not independent of each other in principle? Maybe because for the Bunch-Davies state, most of the apparent entropy between causal patches are really entanglement entropy?

In string theory, all phases with positive cosmological constant have to be metastable at best because the only truly stable phases have to be supersymmetric and supersymmetry is incompatible with a positive cosmological constant. This includes our current phase. Let's assume for the sake of argument our observable universe eventually decays into a thermal equilibrium at the de Sitter temperature and remains that way for an exponentially long time before a quantum fluctuation leads to a tunneling into a new stable supersymmetric phase with a zero cosmological constant. Exponentially many e-foldings would have happened in our phase before that fateful tunneling. In a Penrose diagram, the "hat" describing the new phase will be exponentially smaller in size compared to our de Sitter phase in the Penrose diagram coordinates. So, an observer in the "hat" will be able to observe exponentially many causal patches simultaneously.

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    $\begingroup$ Hi Alexander, and welcome to Physics Stack Exchange! Excellent question (and unfortunately out of my field, so I suspect I will not be able to provide an answer, but I hope somebody does). We're making a push to have our question titles be actual questions so I edited yours accordingly. If the title I put in isn't accurate, feel free to improve it. $\endgroup$
    – David Z
    Commented Jan 3, 2012 at 18:02
  • $\begingroup$ Great question. I have some guesses but I would love to hear someone's answer that has a confident logical argument beneath it. $\endgroup$ Commented Jan 3, 2012 at 22:00

2 Answers 2


Leonard Susskind, the originator of causal patch complimentarity has lately refined it to "horizon complimentarity". According to horizon complimentarity, a horizon is associated with each point on future conformal infinity, which may be built up from a union of null and spacelike segments with future tips and the like at their intersections. For each point on future conformal infinity, the horizon is defined to be the boundary of its past set a la Hawking and Penrose. It is possible for a horizon to span exponentially many causal patches in some cases. Unlike causal patches which are defined in terms of apparent horizons, this new definition is teleological and globally topological. Not that Susskind could prove horizon complimentarity any more than he could prove causal patch complimentarity.

  • $\begingroup$ You can't prove horizon complementarity any more than you can prove deBroglie's rules: horizon complimentarity is the foundational ingredient of black hole dynamics. The only activity I can associated to "proving" it in this case would mean finding the explicit map between external and internal degrees of freedom in a black hole, and this is a difficult active area (it must work for AdS/CFT to work). It is unlikely that what you describe about Susskind is accurate, because the past-boundary using TIPs and the like is not something that Susskind would use to define anything. $\endgroup$
    – Ron Maimon
    Commented Jan 4, 2012 at 6:43

Your point of view is mixing global and local pictures. You are assuming that inflation produced many disconnected patches, and then the universe is seeing more and more of these patches with time as our visible horizon rolls out. This is the global view, but you assume that in the local view this is still what's going on.

In the local view, inflation homogenized space inside the causal patch, then when inflation ended, it ended by slow roll at the center, but it didn't really end on the edges, since time goes slower there, and the slow roll didn't happen yet. The horizon moves out as the slow roll ends--- but the "now" slice in a causal patch is defined along a past-light-cone from some point, not along a global time slice. So if you go close enough to the cosmological horizon, you find inflation is still going on, and still slow-rolling to produce new stuff the same way it produced everything else. The slow-roll region is moving away from us at near the speed of light, and the slow-roll only ends once the cosmological horizon stands still in the far future, when the cosmological constant takes over, and then the slow-roll region gets swallowed by the cosmological horizon and inflation ends for good.

The reason we get a uniform universe is because we started with a uniformized de-Sitter during inflation. It is not necessary to think that it is because new universe is coming into view (although you can think this without contradiction--- all that's going on there is that you allow a global time-slice to do a slow-roll over a global coordinate so wide that our causal patch will never exceed it. This is only positivistically annoying, it's mathematically equivalent to the causal patch picture at least classically).

The answer is really simple--- the causal patch picture just generates the universe dynamically all the time, it doesn't generate it all at once everywhere, and then lets us see more.


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