Testing the null energy condition with precise distance measurements

TL;DR

This paper derives an inequality relating two cosmological distance measures under the null energy condition, providing a testable criterion for fundamental physics assumptions in general relativity.

Contribution

It introduces a new inequality between distance measures in general relativity that can be used to test the null energy condition with observational data.

Findings

The inequality holds if the null energy condition is satisfied.

Violation of the inequality suggests null energy condition failure or non-geodesic light paths.

The result is independent of specific spacetime geometries or observer/source motions.

Abstract

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.