Detecting the massive bosonic zero-mode in expanding cosmological spacetimes

Abstract

We examine a quantised 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, generalising 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 de-excitation resonances towards higher values of the detector's energy gap.

The time traveler’s guide to the quantization of zero modes

“…It is known that quantization of a massless scalar field on a topologically closed spacetime and under certain boundary conditions can give rise to zero modes. A zero mode naturally arises when a massless scalar field is subject to periodic or Neumann boundary conditions, or when the background spacetime has toroidal topology in all spatial directions [26][27][28][29][30]. Zero modes are problematic because they do not admit a Fock representation, thus the physical ground state of the zero mode, and hence the full theory, is a priori ambiguous [26,27].…”