States of low energy in homogeneous and inhomogeneous expanding spacetimes

We construct states on the algebra of the Klein–Gordon field that minimize the energy density in homogeneous and in inhomogeneous spacetimes, both with compact Cauchy hypersurfaces. The energy density is measured by geodesic observers and smeared over a spacelike slab of spacetime, entirely containing a Cauchy hypersurface and extended in time. We further show that these states are Hadamard states. The present construction generalizes the construction of states of low energy in Robertson–Walker spacetimes presented by Olbermann (2007 Class. Quantum Grav. 24 5011). (paper)