  Single-object imaging and spectroscopy on telescopes with apertures ranging
from ~4 m to 40 m have the potential to greatly enhance the cosmological
constraints that can be obtained from LSST. Two major cosmological probes will
benefit greatly from LSST follow-up: accurate spectrophotometry for nearby and
distant Type Ia supernovae will expand the cosmological distance lever arm by
unlocking the constraining power of high-z supernovae; and cosmology with time
delays of strongly-lensed supernovae and quasars will require additional
high-cadence imaging to supplement LSST, adaptive optics imaging or
spectroscopy for accurate lens and source positions, and IFU or slit
spectroscopy to measure detailed properties of lens systems. We highlight the
scientific impact of these two science drivers, and discuss how additional
resources will benefit them. For both science cases, LSST will deliver a large
sample of objects over both the wide and deep fields in the LSST survey, but
additional data to characterize both individual systems and overall systematics
will be key to ensuring robust cosmological inference to high redshifts.
Community access to large amounts of natural-seeing imaging on ~2-4 m
telescopes, adaptive optics imaging and spectroscopy on 8-40 m telescopes, and
high-throughput single-target spectroscopy on 4-40 m telescopes will be
necessary for LSST time domain cosmology to reach its full potential. In two
companion white papers we present the additional gains for LSST cosmology that
will come from deep and from wide-field multi-object spectroscopy.
