The Next Generation of Cosmological Measurements with Type Ia Supernovae
  While Type Ia Supernovae (SNe Ia) are one of the most mature cosmological
probes, the next era promises to be extremely exciting in the number of
different ways SNe Ia are used to measure various cosmological parameters. Here
we review the experiments in the 2020s that will yield orders of magnitudes
more SNe Ia, and the new understandings and capabilities to constrain
systematic uncertainties at a level to match these statistics. We then discuss
five different cosmological probes with SNe Ia: the conventional Hubble diagram
for measuring dark energy properties, the distance ladder for measuring the
Hubble constant, peculiar velocities and weak lensing for measuring sigma8 and
strong-lens measurements of H0 and other cosmological parameters. For each of
these probes, we discuss the experiments that will provide the best
measurements and also the SN Ia-related systematics that affect each one.
