Graviton noise:the Heisenberg picture

Abstract: We study the geodesic deviation equation for a quantum particle in a linearized quantum gravitational field. Particle's Heisenberg equations of motion are treated as stochastic equations with a quantum noise. We explore the stochastic equation beyond its local approximation as a differential. We discuss the squeezed states resulting from an inflationary evolution. We calculate the noise in the thermal and squeezed states.