Probing the limits of the semiclassical Einstein equation

Abstract

In the context of semiclassical gravity, the semiclassical Einstein equation is often invoked when backreaction of quantum matter/fields on the spacetime is at stake. It is expected to hold when quantum fluctuations are small. Yet, it is routinely used to justify the central role of the expectation value of the stress-energy tensor of quantum fields, whose fluctuations formally diverge. Here we propose a new way to probe the limits of this approximation by exploiting peculiar nonlinearities of gravity. As a proof of principle, we construct a controlled, analytically tractable setting where the incoherent mixture of weak-gravity states drives the system into a strong-gravity regime. By selecting a branch-degenerate observable, one can compare predictions of quantum and semiclassical gravity, potentially delimiting the validity of the latter.