  One of the primary mission objectives for the Roman Space Telescope is to
investigate the nature of dark energy with a variety of methods. Observations
of Type Ia supernovae (SNIa) will be one of the principal anchors of the Roman
cosmology program, through traditional luminosity distance measurements. This
SNIa cosmology program can provide another valuable cosmological probe, without
altering the mission strategy: time delay cosmography with gravitationally
lensed SN. In this work, we forecast lensed SN cosmology constraints with the
Roman Space Telescope, while providing useful tools for future work. Using
anticipated characteristics of the Roman SNIa survey, we have constructed mock
catalogs of expected resolved lensing systems, as well as strongly lensed Type
Ia and core-collapse (CC) SN light curves, including microlensing effects. We
predict Roman will find ~11 lensed SNIa and ~20 CCSN, dependent on the survey
strategy. Next, we estimate the time delay precision obtainable with Roman (Ia:
~2 days, CC: ~3 days), and use a Fisher matrix analysis to derive projected
constraints on $H_0$,$\Omega_m$, and the dark energy Equation of State (EOS),
$w$, for each SNIa survey strategy. A strategy optimized for high-redshift SNIa
discovery is preferred when considering the constraints possible from both SNIa
and lensed SN cosmology, also delivering ~1.5 times more lensed SN than other
proposed survey strategies.

Cosmology and Nongalactic Astrophysics