Measuring Space-Time Geometry over the Ages

Understand

Theorists are often told to express things in the "observational plane".

• One can do this for space-time geometry, considering "visual" observations of matter in our universe by a single observer over time, with no assumptions about isometries, initial conditions, nor any particular relation between matter and geometry, such as Einstein's equations.
• Using observables as coordinates naturally leads to a parametrization of space-time geometry in terms of other observables, which in turn prescribes an observational program to measure the geometry.
• Under the assumption of vorticity-free matter flow we describe this observational program, which includes measurements of gravitational lensing, proper motion, and redshift drift.