Gravitational wave signals in an Unruh-de Witt detector

Abstract

We firstly generalize the massive scalar propagator for gravitational waves propagating on Minkowski space obtained recently in Ref. [1]. We then use this propagator to study the response of a freely falling Unruh-de Witt detector to a gravitational wave backg round. We find that a freely falling detector completely cancels the effect of the deformation of the invariant distance induced by the gravitational waves, such that the only effect comes from an increased average size of scalar field vacuum fluctuations, the origin of which can be traced back to the change of the surface in which the gravitational waves fluctuate. When resummed over classical graviton insertions, gravitational waves generate cuts on the imaginary axis of the complex ∆τ -plane (where ∆τ = τ − τ denotes the difference of proper times), and the discontinuity accross these cuts is responsible for a continuum of energy transitions induced in the Unruh-de Witt detector. Not surprisingly, we find that the detector's transition rate is exponentially suppressed with increasing energy and the mass of the scalar field. What is surprising, however, is that the transition rate is nonanalytic function of the gravitational field strain. This means that, no matter how small is the gravitational field amplitude, expanding in powers of the gravitational field strain cannot approximate well the detector's transition rate. We present numerical and approximate analytical results for the detector's transition rate both for nonpolarized and for selected polarized monochromatic, unidirectional, gravitational waves.