de Sitter space and Holography

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An observer moving along a timelike geodesic sees a thermalbath of particles when the scalar field is in the vacuum state.de Sitter space is naturally associated with a temperature.One way to see this:Consider an observer sitting in south pole. In this caseP(X,X ′ ) = −cosh t − t′l= − cosh τ lOn the other hand the Green function is a function of PG(P(X,Y )) = G(cosh τ l )The Green function is periodic in imaginary time under τ →τ + 2πil and therefore is thermal Green function and thetemperature in given by the inverse of the periodT dS = 12πlOne can also associate entropy which is the same as blackhole and is given byS = A4Gwhere A is the area of the horizon.28
Why dS is difficult?1) dS space is inconsistent with supersymmerty: there is nosupergroup that includes the isometries of dS space and hasunitary representation.2) We have not been able to embed it in string theory (up toKKLT model).3) Horizon is observer dependent: difficult to see where thequantum microstate we would like to count are in fact supposedto be.29
Page 1 and 2: de Sitter space and HolographyThird
Page 3: 1. Historical review and motivation
Page 7 and 8: 5. Technologies:There are a number
Page 9 and 10: Let us know study different coordin
Page 11 and 12: Conformal coordinates: T, θ i , i
Page 13 and 14: Planer (Inflationary) coordinates:
Page 15 and 16: The corresponding metric isdS 2 =
Page 17 and 18: It is easy to see thatX 0 + X d =
Page 20 and 21: 1.2 Causal structure (Penrose diagr
Page 22 and 23: IINorth PoleOSouth PoleNorth PoleOS
Page 24 and 25: The entire region of the dS space i
Page 26 and 27: For example• In static coordinate
Page 30 and 31: 3. dS/CFT correspondenceFrom what w
Page 32 and 33: In d dimensions the Einstein equati
Page 34 and 35: One can generalize it for a general
Page 36 and 37: • One can always decompose the me
Page 38 and 39: Consider the Brown-York stress tens
Page 40 and 41: Using the definition of Brown-York
Page 42 and 43: Using this diffeomorphism one may s
Page 44 and 45: lim dtdtr→∞∫I ′ dφdφ ′
Page 46 and 47: dS static patch (spatial)dg =0 g =1
Page 48 and 49: • Lower dimensional Plank mass is
Page 50 and 51: One can use AdS/CFT correspondence
Page 52 and 53: Under this conformal map one has:
Page 54 and 55: Conformal AnomalyAdS/CFT instructs
Page 56 and 57: • Naively one would think that gr
Page 58: This talk is based on the following

de Sitter space and Holography

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