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. 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:• 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 dH3

2/• 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. gs

2 » 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 gs

6

• 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?