de Sitter space and Holography
de Sitter space and Holography de Sitter space and Holography
Plan of talk1. Historical review and motivation2. de Sitter space and its properties3. dS/CFT correspondence4. dS/dS correspondence2
1. Historical review and motivation• In 1917 the cosmological constant Λ was introduced byEinstein to get static homogeneous universe in the present ofmatter.• In 1920 Slipher’s works showed that the light from galaxieswas redshifted indicating that they are moving away from us.• In 1922 a matter dominated expanding universe withoutcosmological constant was constructed by Friedmann.• In 1923 in a letter to Weyl, Einstein says“ If there is no quasi-static world, then away withcosmological term.”• In 1927 the conclusive discovery was made by HubbleA linear expansion law relating redshift to distance whichmade Friedmann models the standard geometrical framework.3
- Page 1: de Sitter space and HolographyThird
- 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 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
Plan of talk1. Historical review <strong>and</strong> motivation2. <strong>de</strong> <strong>Sitter</strong> <strong>space</strong> <strong>and</strong> its properties3. dS/CFT correspon<strong>de</strong>nce4. dS/dS correspon<strong>de</strong>nce2
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