A Program for Multi-Messenger Standard Siren Cosmology in the Era of
  LIGO A+, Rubin Observatory, and Beyond
  The most promising variation of the standard siren technique combines
gravitational-wave (GW) data for binary neutron star (BNS) mergers with
redshift measurements enabled by their electromagnetic (EM) counterparts, to
constrain cosmological parameters such as $H_0$, $\Omega_m$, and $w_0$. Here we
evaluate the near- and long-term prospects of multi-messenger cosmology in the
era of future GW observatories: Advanced LIGO Plus (A+, 2025), Voyager-like
detectors (2030s), and Cosmic Explorer-like detectors (CE, 2035 and beyond). We
show that the BNS horizon distance of $\approx 700$ Mpc for A+ is well-matched
to the sensitivity of the Vera C. Rubin Observatory (VRO) for kilonova
detections. We find that one year of joint A+ and VRO observations will
constrain the value of $H_0$ to percent-level precision, given a small
investment of VRO time dedicated to target-of-opportunity GW follow-up. In the
Voyager era, the BNS-kilonova observations begin to constrain $\Omega_m$ with
an investment of a few percent of VRO time. With the larger BNS horizon
distance in the Cosmic Explorer era, on-axis short gamma-ray bursts (SGRBs) and
their afterglows (though accompanying only some of the GW-detected mergers)
supplant kilonovae as the most promising counterparts for redshift
identification. We show that five years of joint observations with Cosmic
Explorer-like facilities and a next-generation gamma-ray satellite with
localization capabilities similar to that presently possible with Swift could
constrain both $\Omega_m$ and $w_0$ to $15-20\%$. We therefore advocate for a
robust target-of-opportunity (ToO) program with VRO, and a wide-field gamma-ray
satellite with improved sensitivity in the 2030s, to enable standard siren
cosmology with next-generation gravitational wave facilities.
