"Laboratory" description of field excitations in a hyperbolically expanding cavity

Scalar fields in a hyperbolically expanding "cavity" provide a flat-spacetime model for particle dynamics in de Sitter space. A timelike, spherically symmetric Rindler-coordinate hypersurface having de Sitter geometry describes the evolution of the expanding cavity. The field theory in the cavity corresponds to the reduction of the embedding-space theory to this coordinate hypersurface. The de Sitter particle-number eigenstates of the cavity theory are unsuitable for the embedding-space or "laboratory" description, as they yield infinite excitation energies. States for the "laboratory" description are constructed by localizing excitations in the embedding space about the world tube of the cavity. Adjusted states approximate a free-particle spectrum with additive excitation energies for a wide range of parameters. While the time dependence of de Sitter-space excitation energies is not reproduced, the finite width of de Sitter-space detector response functions is exhibited in the "laboratory" description.