States of Low Energy in Homogeneous and Inhomogeneous, Expanding Spacetimes

Abstract

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).

Substantial modifications made in the text. This version was accepted for publication in Class. Quant. Grav

References in corpus (4)

• Quantum Field Theory on Curved Backgrounds -- A Primer
• Absolute quantum energy inequalities in curved spacetime
• States of Low Energy on Robertson-Walker Spacetimes
• Explicit harmonic and spectral analysis in Bianchi I-VII type cosmologies

Cited by in corpus (9)

• Hadamard states for a scalar field in anti-de Sitter spacetime with arbitrary boundary conditions
• Hadamard states for the Klein-Gordon equation on Lorentzian manifolds of bounded geometry
• "Vacuum-like" Hadamard states for quantum fields on curved spacetimes
• The spatial Functional Renormalization Group and Hadamard states on cosmological spacetimes
• Trace anomaly for chiral fermions via Hadamard subtraction
• Complex Structures for Klein-Gordon Theory on Globally Hyperbolic Spacetimes
• Bonus Properties of States of Low Energy
• Wigner distributions in Rindler spacetime and nonvacuum Minkowski states
• States of Low Energy on Bianchi I spacetimes