Stephen Shenker LindeFest March 8, 2008 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 nongravitational QM system

AdS/CFT “Cold” Boundary

These descriptions have taught us a great deal about quantum gravity 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..

Now, ten years later I’m entranced by…

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

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: Status Report… 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

Coarse grain to symmetric torus

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

Long handle takes more bubbles, more powers of gs

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

Expansion may be convergent!?

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?