Testing the null energy condition with precise distance measurements
  We present an inequality between two types of distance measures to a single
source in general relativity. It states that for a given emitter and observer
the distance between them measured by the trigonometric parallax is never
shorter than the angular diameter distance provided that the null energy
condition holds and that there are no focal points in between. This result is
independent of the details of the spacetime geometry or the motions of the
observer and the source. The proof is based on the geodesic bilocal operator
formalism together with well known properties of infinitesimal light ray
bundles. Observation of the violation of the distance inequality would mean
that on large scales either the null energy condition does not hold or that
light does not travel along null geodesics.
