  The light from a 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 wavefront. At gigahertz frequencies, the
arrival time difference can be determined to better than a nanosecond with
interferometry. If the space-time 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 distances to individual sources with sub-percent
precision and, hence, cosmological parameters such as the Hubble constant to
this precision. The precision increases quadratically with baseline length.
FRBs are the only known bright extragalactic radio source that are sufficiently
point-like. Galactic scattering limits the timing precision at <3 GHz, whereas
at higher frequencies the precision is set by removing dispersion. Furthermore,
for baselines greater than 100 AU, Shapiro time delays limit the precision, but
their effect can be cleaned with two additional detectors. Accelerations that
result in ~1 cm uncertainty in detector positions (from variations in the Sun's
irradiance, dust collisions and gaseous drag) could be corrected for with
weekly GNSS-like trilaterations. Gravitational accelerations from asteroids
occur over longer timescales, and so a setup with a precise accelerometer and
calibrating the detector positions off of distant FRBs may also be sufficient.
The proposed interferometer would also resolve the radio emission region of
Galactic pulsars, constrain the mass distribution in the outer Solar System,
and reach interesting sensitivities to ~0.01-100 micro-Hz gravitational waves.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology;Space Physics