Comparison of Two-Atom Cross Spectra in de Sitter Spacetime, Uniformly Accelerated Minkowski Vacuum, and a Thermal Bath

We study the weak coupling of two identical two-level atoms to a four-dimensional massless conformally coupled scalar field and compare three settings with the same local temperature but different physical origins: comoving atoms in the Bunch--Davies vacuum of de Sitter spacetime, transversely separated uniformly accelerated atoms in the Minkowski vacuum, and static atoms in a Minkowski thermal bath. We first derive the two-atom cross spectra in the three settings and then obtain the single-atom local spectra uniformly from the zero-separation limit. When a=H and β=2π/H, the complete local Wightman kernels and local spectra are identical in all three cases. At finite separation, a genuine thermal bath produces a sinc(ΩL) spatial factor, whereas de Sitter spacetime and the transversely accelerated vacuum produce a hyperbolic geometric factor. In the long-distance limit, the cross correlations in de Sitter spacetime and the transversely accelerated vacuum decay as L^-2, whereas those in the Minkowski thermal bath decay only as L^-1. The de Sitter and transversely accelerated vacuum cross spectra coincide when a=H and the separations are instantaneously matched. For a fixed experimental setup, the physical separation between the two comoving atoms in de Sitter space evolves with cosmic expansion, whereas the pulled-back cross correlations in the uniformly accelerated and thermal Minkowski configurations are stationary.