The euclidean vacuum: Justification from quantum cosmology

We evaluate the wave function of the universe for a de Sitter minisuperspace with inhomogeneous matter perturbations from a massive scalar field. From the Wheeler-DeWitt equation, we derive Schrodinger equations for the matter modes. We show that the matter part of the Hartle-Hawking wave function is the euclidean vacuum state of quantum field theory in curved spacetime.