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Future Foam

Future Foam

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Future Foam

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  1. Future Foam Stephen Shenker LindeFest March 8, 2008

  2. I came to Stanford 10 years ago, entranced by Gauge/Gravity dualities • Matrix Theory, AdS/CFT • Precise descriptions of Quantum Gravity, in certain simple situations • QG holographically dual to a nongravitationalQM system

  3. AdS/CFT • “Cold” Boundary

  4. These descriptions have taught us a great deal about quantum gravity. Information is not lost in black holes,… • They have also provided a whole new set of insights into the boundary (strongly coupled) field theory

  5. But at this time Andrei was thinking about quite a different kind of picture…

  6. Baby universes nucleating inside each other, wildly bifurcating… • The extravagant pattern of eternal inflation..

  7. Now, ten years later I’m entranced by…

  8. I’m not exactly sure how to interpret this history…

  9. In most proposals for a holographic description of inflation, gravity does not decouple. • A “warm” boundary • dS/CFT (Strominger; Maldacena) • dS/dS (Alishahiha, Karch, Silverstein)

  10. FRW/CFT (Freivogel, Sekino, Susskind, Yeh) • 3+1 D bubble nucleated in dS space is holographically described by a 2D Euclidean CFT coupled to 2D gravity (Liouville)

  11. c of 2D CFT is ~S, the entropy of the ancestor dS space • The 2D CFT lives on a sphere because the domain wall is spherical

  12. But if the 2D boundary is “metrically warm” shouldn’t it be “topologically warm” as well?

  13. Explore this: • Bousso, Freivogel, Sekino, Susskind, Yang, Yeh, S.S. • Status Report…

  14. Simple idea • “Hole” larger than Hubble radius rH then it keeps inflating and persists

  15. Assume one false vacuum and one true vacuum for simplicity, no domain walls between colliding bubbles • A dynamically generated “foam” that can persist to the infinite future

  16. If single bubble nucleation probability is  then the handle probability »k • Small, but nonzero. Conceptually important. • Do they exist? (Or crunch?…)

  17. Collisions well controlled if the critical droplet size, rc , is much less than the Hubble radius, rH. • Slow, gentle collisions of low tension domain walls

  18. Coarse grain to symmetric torus

  19. Try to find such a solution with flat space inside, in thin wall limit • Asymptotic solution exists, but with short time transient

  20. Try to understand by studying a special limit without coarse graining

  21. Metric approaches flat space, with transient • Still working out details • No sign anywhere of a crunch • Existence of torus seems very likely • Higher genus cases seem plausible, but no precise analytic techniques

  22. Asymptotic metric inside the torus ( = 0) has FRW form. • ds2 = -dt2 +t2 dH32/ •  is discrete group

  23. What can a single observer see? • ds2 = -dt2 +t2 dH32/ • Modding out by  only increases causal connection • Neighboring bubbles causally connected • One observer can see everything

  24. It is plausible that any single-observer description of eternal inflation must include different topologies.

  25. Multiple boundaries are more subtle Maeda, Sato, Sasaki, Kodama

  26. Horizon separates observer from second boundary • Conjecture that this happens for general multiple boundary situation

  27. Higher topologies are (plausibly) present. Are they important? • FRW/CFT will be “plated” on different genus surfaces. • A kind of string theory. gs2»k + gs2 + gs4 + …

  28. Typical situation in string theory: • String perturbation series is only asymptotic • gs2h (2h)! , for h handles • e-1/gs , D-branes • “Strings are collective phenomena, made out of D-branes”

  29. Typical genus h amplitude • Integral over moduli space of surface • s dm e-f(m) • Volume of moduli space » (2h)! • Gives gs2h (2h)! • Here things are different…

  30. gs2 gs6 • Only the modulus (aspect ratio) of torus has changed. • Changing shape costs powers of gs

  31. Long handle takes more bubbles, more powers of gs

  32. With a fixed number of bubbles, nontrivial topologies are a small fraction of possible configurations

  33. Expansion may be convergent!?

  34. How does this work in FRW/CFT on higher genus surfaces? • One clue: c ~ S of ancestor dS vacuum • » e-S • gs» e-c • s dm e-c f(m)»s dm gsf(m) • Changing moduli costs powers of gs • Peaked at a certain value of moduli ?!

  35. Conclusions • Single observer descriptions of eternal inflation must, plausibly, contain different topologies • Summing over these topologies does not seem to require new degrees of freedom

  36. Another question: • c >> 26, a “supercritical string” • gs() » exp(-(2h-2)c ) • At large  higher genus surfaces should be strongly suppressed. • Bulk explanation?