Real-time Cosmology with High Precision Spectroscopy and Astrometry

Breakthroughs in physics and astrophysics are often driven by technological advances, with the recent detection of gravitational waves being one such example. This white paper focuses upon how improved astrometric and spectroscopic measurements from a new generation of precise, accurate, and stable astronomical instrumentation can address two of the fundamental mysteries of our time -- dark energy and dark matter -- and probe the nature of spacetime. Instrumentation is now on the cusp of enabling new cosmological measurements based on redshifts (cosmic redshift drift) and extremely precise time-series measurements of accelerations, astrophysical source positions (astrometry), and angles (cosmic parallax). These allow tests of the fundamental framework of the universe (the Friedmann equations of general relativity and whether cosmic expansion is physically accelerating) and its contents (dark energy evolution and dark matter behavior), while also anchoring the cosmic distance scale ($H_0$).