de Sitter space and Holography

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Static coordinates: t,r, θ i , i = 1,...d − 2There is another way to solve the constraint in which it is<strong>de</strong>composed as followswith(−X 2 0 + X 2 d) + (X 2 1 + · · · + X 2 d−1) = l 2−X 2 0 + X 2 d = l 2 − r 2X 2 1 + · · · + X 2 d−1 = r 2which can be solved by the following parametrizationX 0= √ l 2 − r 2 sinh t lX d = √ l 2 − r 2 cosh t lX i = rω i , i = 1,....d − 116
It is easy to see thatX 0 + X d = √ l 2 − r 2 e t/l ≥ 0X 0 − X d = − √ l 2 − r 2 e −t/l ≤ 0Therefore this coordinates system can not cover whole<strong>space</strong>time. In fact it just cove quarter of it which in ourconvention is given by the following figureX 0X 0 = −X d X 0 = X dlX d17
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: The corresponding metric isdS 2 =
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 28 and 29: An observer moving along a timelike
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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