Thermal equilibrium in de Sitter space

Physics

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Theory Of Quantized Fields, Boson Systems, Particle-Theory And Field-Theory Models Of The Early Universe

Scientific paper

Thermal-equilibrium quantum states are constructed for free scalar fields in (N+1)-dimensional de Sitter space. The states are described by density matrices of ``thermal'' form, satisfying the von Neumann equation associated with the appropriate functional Schrödinger equation. These solutions exist only for fields with mass and/or curvature coupling corresponding to conformal invariance. The temperature associated with such a state obeys the classical red-shift law. States exist with any temperature value at any given time; the zero-temperature limit is the Euclidean vacuum state. The total field energy of a thermal state above that of the Euclidean vacuum is finite and positive. This excitation energy consists of one contribution which red-shifts classically, but it can also contain a contribution which grows in time as the radius of the space.

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