Cosmological memory effect in scalar-tensor theories

The cosmological memory effect is a permanent change in the relative separation of test particles located in a FLRW spacetime due to the passage of gravitational waves. In the case of a spatially flat FLRW spacetime filled with a perfect fluid in general relativity, it is known that only tensor perturbations contribute to the memory effect while scalar and vector perturbations do not. In this paper, we show that in the context of scalar-tensor theories, the scalar perturbations associated to the scalar graviton contribute to the memory effect as well. We find that, depending on the mass and coupling, the influence of cosmic expansion on the memory effect due to the scalar perturbations can be either stronger or weaker than the one induced by the tensor perturbations. As a byproduct, in an appendix, we develop a general framework which can be used to study coupled wave equations in any curved spacetime region which admits a foliation by time slices.