Shortcomings of Shapiro delay-based tests of the equivalence principle on cosmological scales

Understand

The "Shapiro delay" experienced by an astronomical messenger traveling through a gravitational field has been used to place constraints on possible deviations from the equivalence principle.

• The standard Shapiro delay used to obtain these constraints is not itself an observable in general relativity, but is rather obtained by comparing with a fiducial Euclidean distance.
• There is not a mapping between the constraints obtained in this manner and alternative theories that exhibit equivalence principle violations.
• However, even assuming that the comparison with the fiducial Euclidean distance is carried out in a way that is useful for some class of alternative theories, we show that the standard calculation of these constraints cannot be applied on cosmological scales, as is often done.