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Gaia's milli-arcsec (mas) astrometric precision allows systematicidentification of optically-selected sub-kpc dual active galactic nuclei (AGN),off-nucleus AGN, and small-scale lensed quasars by `varstrometry' -- wherevariability-induced astrometric jitter, i.e., temporal displacements ofphotocenter in unresolved sources, can be reasonably well detected orconstrained. 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 Gaia's full sky coverage and depth to$G\sim 21$. We outline the general principles of this method and calculate theexpected astrometric signals from the full time series of photocentermeasurements and light curves. We demonstrate the feasibility of varstrometryby using Gaia DR2 data on a sample of variable pre-main sequence stars withknown close companions. We find that extended host galaxies have a significantimpact on the accuracy of astrometric and photometric variability in Gaia DR2,a situation to be improved in future Gaia releases. Using spectroscopicallyconfirmed SDSS quasars, we present several examples of candidate sub-kpcoff-nucleus or dual AGN selected from Gaia DR2. We discuss the merits andlimitations of this method and follow-up strategy for promising candidates. Wehighlight Gaia's potential of systematically discovering and characterizing thesub-kpc off-nucleus and dual AGN population in the entire optical sky.

Varstrometry for Off-nucleus and Dual sub-Kpc AGN (VODKA): Methodology and Initial Results with Gaia DR2