Gaias milli-arcsec (mas) astrometric precision allows systematic identification of optically-selected sub-kpc dual active galactic nuclei (AGN), off-nucleus AGN, and small-scale lensed quasars by `varstrometry -- where variability-induced astrometric jitter, i.e., temporal displacements of photocenter in unresolved sources, can be reasonably well detected or constrained. This approach extends systematic searches for small-scale ($gtrsim$ mas) dual and off-nucleus AGN to poorly explored regime between $sim 10$ pc and $sim 1$ kpc, with Gaias full sky coverage and depth to $Gsim 21$. We outline the general principles of this method and calculate the expected astrometric signals from the full time series of photocenter measurements and light curves. We demonstrate the feasibility of varstrometry by using Gaia DR2 data on a sample of variable pre-main sequence stars with known close companions. We find that extended host galaxies have a significant impact on the accuracy of astrometric and photometric variability in Gaia DR2, a situation to be improved in future Gaia releases. Using spectroscopically confirmed SDSS quasars, we present several examples of candidate sub-kpc off-nucleus or dual AGN selected from Gaia DR2. We discuss the merits and limitations of this method and follow-up strategy for promising candidates. We highlight Gaias potential of systematically discovering and characterizing the sub-kpc off-nucleus and dual AGN population in the entire optical sky.
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