2023ApJ...947L..23B

The light from an extragalactic source at a distance d will arrive at detectors separated by 100 au at times that differ by as much as 120(d/100 Mpc)^–1 nanoseconds because of the curvature of the wave front. At gigahertz frequencies, the arrival time difference of a point source can be determined to better than a nanosecond with interferometry. If the spacetime positions of the detectors are known to a few centimeters, comparable to the accuracy to which very long baseline interferometry baselines and global navigation satellite systems (GNSS) geolocations are constrained, nanosecond timing would allow competitive cosmological constraints. We show that a four-detector constellation at Solar radii of ≳10 au could measure geometric distances to individual sources with subpercent precision. The precision increases quadratically with baseline length. Fast radio bursts (FRBs) are the only known bright extragalactic radio source that are sufficiently point-like for this experiment, and the simplest approach would target the population of repeating FRBs. Galactic scattering limits the timing precision at ≲3 GHz, whereas at higher frequencies the precision is set by removing the differential dispersion between the detectors. Furthermore, for baselines greater than 100 au, Shapiro time delays limit the precision, but their effect can be cleaned at the cost of two additional detectors. Outer solar system accelerations that result in ∼1 cm uncertainty in detector positions could be corrected for with weekly GNSS-like trilaterations between members of the constellation. The proposed interferometer would not only provide a geometric constraint on the Hubble constant, but also could advance solar system, pulsar, and gravitational wave science.