Excited-state spectra of de Sitter-space scalar fields

To illustrate gravitational effects on the dynamics of a quantized field, the spectrum of excited states available to a linear scalar field in de Sitter space is examined in detail. Explicit Schroedinger-picture wave functionals are obtained for the excitation-number eigenstates of the familiar Fock-space description. The field energies of these states are calculated from expectation values of the appropriate Hamiltonian. The Euclidean vacuum state is seen to be the lowest-energy de Sitter-invariant state, although for any massive or nonconformally coupled field instantaneous Hamiltonian diagonalization, breaking de Sitter invariance, yields states of lower energy. All other de Sitter-invariant vacua are characterized by uniform excitation, relative to the Euclidean vacuum, in all field modes. Associated with any vacuum state is a Fock-space basis of excited states. These have field energies in integral increments above the vacuum; i.e., they represent the quantized excitations of the field's normal modes