Emergent Space-Time and and Induced Gravity Erik Verlinde University of Amsterdam Madrid, November 17 th, 2006 Some (Speculative) Ideas on “Strings versus Cosmology ”

Standard (inflationary) cosmology is successfull. It uses low energy effective action, and needs very little input from string theory. My personal view: Don’t be satisfied to with using low energy action, but use the complete (microscopic) string theory to challenge the basic assumptions on which standard cosmology (including inflation) is based. Strings versus Cosmology

String theory needs concrete problems Black Holes : led to important progress (AdS/CFT). drastic departure from old views. (complementarity, holography, unitarity.) Cosmology : still in its infancy, no breakthrough yet. expect drastic departure from old views. (initial conditions, inflation, multiverse.) (complementarity, holography, unitarity.) (collapse, information loss, baby universes.) Strings versus Cosmology

String theory indicates that Space-time is emergent Gravity is induced Strings versus Cosmology What does this mean for cosmology? What was the Big Bang? (if it ever happened) How does space-time emerge? Is the emergent space-time observer dependent? Is there a unitary quantum system underlying all this? Will this be at all important for observations?

Outline Part I: “ Observer complementarity ”. Parikh, EV (’04) A Model for de Sitter space Part II: “Emergent Space-Time” The Matrix Big Bang Craps, Sethi, EV (’05) Part III: “Induced Gravity” The Black Hole Farey Tail. Dijkgraaf, Moore,Maldacena, EV (’00) de Boer, Cheng, Dijkgraaf, Manschot, EV (’06) Part IV: “A Heretic View on Cosmology”

I: A Model for de Sitter space

Every eternal observer has complete knowledge about the quantum state of the Universe. Observer complementarity No quantum states correspond to physics outside the maximal causal diamant. Observers agree on probabilities for events, but not necessarily on their interpretation. Classical space-time is only an approximate notion and may be different for different observers.

Model for de Sitter space Every observer has a finite dimensional Hilbert space The probability is given by The state is de Sitter invariant and is the analogue of the S-matrix. These form a de Sitter representation. Events are described by a tensor product state

Model for de Sitter space The Hilbert space is reps of SO(d-1) forms a reps of SO(d,1). A concrete model can be made using a spinor field on the (d-1)-dim spatial sphere

II: The Matrix Big Bang

Lightlike Linear Dilaton in new lightcone coordinates Lift to M-theory: 10d metric +dilaton null singularity

/ Matrix dual of lightlike linear dilaton in DLCQ Matrix String = (1+1)d super Yang-Mills string coupling light-cone momentum forward quadrant of Milne space time dependent worldsheet metric flat world sheet coordinates /

III: The Black Hole Farey Tail

Extremal Black Hole Near horizon geometry:

Black holes in string and M-theory. M-theory on CY M2-branes wrapping 2-cycles M5-branes wrapping 4-cycles  5d black strings 4d black hole = 5d black string wrapping circle. World volume theory = 2d CFT (Maldacena, Strominger,Witten) Holographic dual to near horizon geometry:

Partition function obeys An Exact Asymptotic Formula Then we have

Thermal AdS 3 vs. BTZ Periodic identification cigar

SL(2,Z) orbit of AdS Black Holes Different euclidean black holes distinguished by non- contractible cycle: Euclidean action Maldacena, Strominger AdS 3 /CFT 2

Farey tail: Z(  )= sum over SL(2,Z) orbit of black holes contribution of each black hole geometry subleading corrections: black hole ‘dressed’ with light particle states that do not form black holes Black holes

IV: A Heretic View on Cosmology

Standard Big Bang Model

Geometry of Universe is derived from OUR OBSERVATIONS From our perspective we are in the middle of our Universe Can one interprete the cosmological data in an STATIC isotropic but non-homogenous (!) cosmological model?

brane worlds: can live in a static background. one adds “scale” as fifth dimension. Idea: We live in a static five dimensional space. The apparent expansion of the Universe is caused by the fact that for more distant objects the observed signals are coming from bigger scales.

RULE: at every time step re-throw one dice. QUESTION: What is the most likely state at the following time step? previous

The End