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Emergent Space-Time and and Induced Gravity

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

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Emergent Space-Time and and Induced Gravity

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

  2. 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.

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

  4. Strings versus Cosmology String theory indicates that • Space-time is emergent • Gravity is induced • 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?

  5. 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”

  6. I: A Model for de Sitter space

  7. Observer complementarity Every eternal observer has complete knowledge about the quantum state of the Universe. 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.

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

  9. 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

  10. lightcone time matrices II: The Matrix Big Bang weakly coupled strings

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

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

  13. III: The Black Hole Farey Tail

  14. Extremal Black Hole Near horizon geometry:

  15. 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:

  16. Partition function obeys An Exact Asymptotic Formula Then we have

  17. cigar Thermal AdS3 vs. BTZ Periodic identification

  18. SL(2,Z) orbit of AdS Black Holes Different euclidean black holes distinguished by non-contractible cycle: Euclidean action Maldacena, Strominger AdS3/CFT2

  19. Black holes Farey tail: Z(t)=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

  20. IV: A Heretic View on Cosmology

  21. Standard Big BangModel

  22. observer past lightcone Early Universe

  23. 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?

  24. 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.

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

  26. The End

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