Detecting the massive bosonic zero-mode in expanding cosmological spacetimes

We examine a quantized massive scalar field in (1+1)-dimensional spatially compact cosmological spacetimes in which the early time and late time expansion laws provide distinguished definitions of Fock "in"and "out"vacua, with the possible exception of the spatially constant sector, which may become effectively massless at early or late times. We show, generalizing the work of Ford and Pathinayake, that when such a massive zero mode occurs, the freedom in the respective in and out states is a family with two real parameters. As an application, we consider massive untwisted and twisted scalar fields in the (1+1)-dimensional spatially compact Milne spacetime, where the untwisted field has a massive in zero mode. We demonstrate, by a combination of analytic and numerical methods, that the choice of the massive in zero mode state has a significant effect on the response of an inertial Unruh-DeWitt detector, especially in the excitation part of the spectrum. The detector's peculiar velocity with respect to comoving cosmological observers has the strongest effect in the in vacuum of the untwisted field, where it shifts the excitation and deexcitation resonances toward higher values of the detector's energy gap.