The fundamental properties of the spacetime fabric of the local Universe cannot be determined without an observable, ultra-accurate standard of inertiality, which can be applied to any celestial object from high-z quasars to an exoplanet orbiting a nearby star. The only currently plausible method of setting such a standard is the establishment of an inertial reference frame based on grid stars anchored by extragalactic sources. An astronomical reference frame at 1 μas accuracy covering the entire sky will make it possible to observe and measure (rather than speculate) a wide range of physical and cosmological phenomena, essentially promoting new observational science. To name a few, it will allow for the first time the direct detection of the acceleration of the Solar System within the Milky Way and the Local Group toward the Virgo cluster. Meaningful experimental constraints will be put on the broadband power of the relic gravitational waves, to constrain the mass function of free-floating planets and comets, to resolve the puzzles of the origin of radiation from radio-loud quasars and the coronal activity in tight RS CVn binaries, and obtain more accurate tests of alternative gravitation theories. All of this will be accomplished by observing the motion and relative position of a large number of stars and distant "fixed" quasars.