Objects Appear Smaller as They Recede: How Proper Motions Can Directly Reveal the Cosmic Expansion, Provide Geometric Distances, and Measure the Hubble Constant

Objects and structures gravitationally decoupled from the Hubble expansion will appear to shrink in angular size as the universe expands. Observations of extragalactic proper motions can thus directly reveal the cosmic expansion. Relatively static structures such as galaxies or galaxy clusters can potentially be used to measure the Hubble constant, and test masses in large scale structures can measure the overdensity. Since recession velocities and angular separations can be precisely measured, apparent proper motions can also provide geometric distance measurements to static structures. The apparent fractional angular compression of static objects is 15 microarcseconds per year in the local universe; this motion is modulated by the overdensity in dynamic expansion-decoupled structures. We use the Titov et al. quasar proper motion catalog to examine the pairwise proper motion of a sparse network of test masses. Small-separation pairs (< 200 Mpc comoving) are too few to measure the expected effect, yielding an inconclusive 8.3 +/- 14.9 microarcsec/yr. Large-separation pairs (200-1500 Mpc) show no net convergence or divergence for z < 1, -2.7 +/- 3.7 microarcsec/yr, consistent with pure Hubble expansion and significantly inconsistent with static structures, as expected. For all pairs a "null test" gives -0.36 +/- 0.62 microarcsec/yr, consistent with Hubble expansion, and excludes a static locus at ~5-10 sigma significance for z ~ 0.5-2.0. The observed large-separation pairs provide a reference frame for small-separation pairs that will significantly deviate from the Hubble flow. The current limitation is the number of small-separation objects with precise astrometry, but Gaia will address this and will likely detect the cosmic recession.