Expansion-sensitive coupling of a local quantum system in de Sitter cosmology

When a local quantum system couples to a quantum field in a cosmological spacetime, the time dependence of the coupling strength is conventionally taken to reflect the design of the local quantum system but not to depend on the large-scale structure of the Universe. In this paper, we consider a novel coupling that incorporates additional time dependence that reflects the cosmological expansion, as motivated by structures that appear in quantum cosmology. We focus on a conformal scalar field in a de Sitter Friedmann-Lemaître-Robertson-Walker cosmology with flat but compact spatial sections in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mn>3</a:mn> <a:mo>+</a:mo> <a:mn>1</a:mn> </a:math> dimensions, and a comoving Unruh-DeWitt detector: the novel coupling posits the detector to couple to the scaled scalar field that appears in the conformally related static spacetime. We survey the differences between the conventional and novel coupling, for detectors that couple to the full field and detectors that couple only to specific field modes, and for detectors with proper time internal dynamics and detectors with conformal time internal dynamics. We also briefly discuss noncompact spatial sections and single-mode detectors with discontinuous time dependence. We find that the novel coupling tends to enhance the deexcitation peaks in the detector’s response, particularly for single-mode detectors.