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Noise kernel near the horizon of de Sitter space

The symmetric two point correlation function of the stress–energy tensor, also known as the noise kernel, for the conformally invariant scalar field is computed in the static region of de Sitter space in terms of the usual static coordinates. Its behavior near the cosmological horizon is investigated. The exact expression is then compared to an approximate expression derived using a quasi-local expansion in order to test the validity of that expansion in a static spherically symmetric spacetime containing a horizon. This gives insight into the likely range of validity of the quasi-local expansion for the noise kernel in Schwarzschild spacetime which has been previously computed.