de Sitter space and Holography

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