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## Future Foam

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**Future Foam**Stephen Shenker LindeFest March 8, 2008**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**AdS/CFT**• “Cold” Boundary**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**But at this time Andrei was thinking about quite a different**kind of picture…**Baby universes nucleating inside each other, wildly**bifurcating… • The extravagant pattern of eternal inflation..**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)**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)**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**But if the 2D boundary is “metrically warm” shouldn’t**it be “topologically warm” as well?**Explore this:**• Bousso, Freivogel, Sekino, Susskind, Yang, Yeh, S.S. • Status Report…**Simple idea**• “Hole” larger than Hubble radius rH then it keeps inflating and persists**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**If single bubble nucleation probability is then the**handle probability »k • Small, but nonzero. Conceptually important. • Do they exist? (Or crunch?…)**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**Try to find such a solution with flat space inside, in thin**wall limit • Asymptotic solution exists, but with short time transient**Try to understand by studying a special limit without coarse**graining**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**Asymptotic metric inside the torus**( = 0) has FRW form. • ds2 = -dt2 +t2 dH32/ • is discrete group**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**It is plausible that any single-observer description of**eternal inflation must include different topologies.**Multiple boundaries are more subtle**Maeda, Sato, Sasaki, Kodama**Horizon separates observer from second boundary**• Conjecture that this happens for general multiple boundary situation**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 + …**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”**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…**gs2 gs6**• Only the modulus (aspect ratio) of torus has changed. • Changing shape costs powers of gs**With a fixed number of bubbles, nontrivial topologies are a**small fraction of possible configurations**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 ?!**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**Another question:**• c >> 26, a “supercritical string” • gs() » exp(-(2h-2)c ) • At large higher genus surfaces should be strongly suppressed. • Bulk explanation?