Testing classicality of gravity by gravitation decoherence

Here we discuss an influence of an external weak gravitational field on the gravitational self-decoherence effect with help of the stochastic extension of regularized Shr\"odinger-Newton equation in a curved background. We derive the master equation and demonstrate that it leads to the experimentally verifiable conclusions about applicability of the classical description of the weak gravitation field. Namely, a presence of oscillating terms in the otherwise purely exponential decay of the coherence would indicate classicality of gravity for the case.