Feynman spectral action of the wave operator on asymptotically de Sitter spaces
Abstract
In this paper, we investigate the wave operator g on non-trapping (at all energies) even asymptotically de Sitter spaces. We construct a Feynman operator on the conformal extension of asymptotically de Sitter spaces and give a proof of uniform microlocal estimates for the Feynman operator in this setting. This enables the study of the Lorentzian "spectral" zeta functions in asymptotically de Sitter and the construction of a "spectral" action of the Feynman propagator.
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