HOLISMOKES -- I. Highly Optimised Lensing Investigations of Supernovae,
  Microlensing Objects, and Kinematics of Ellipticals and Spirals
  We present the HOLISMOKES programme on strong gravitational lensing of
supernovae as a probe of supernova (SN) physics and cosmology. We investigate
the effects of microlensing on early-phase SN Ia spectra using four different
SN explosion models, and find that within 10 rest-frame days after SN
explosion, distortions of SN Ia spectra due to microlensing are typically
negligible ($<$1% distortion within the 1$\sigma$ spread, and $\lesssim$10%
distortion within the 2$\sigma$ spread). This shows great prospects of using
lensed SNe Ia to obtain intrinsic early-phase SN spectra for deciphering SN Ia
progenitors. As a demonstration of the usefulness of lensed SNe Ia for
cosmology, we simulate a sample of mock lensed SN Ia systems that are expected
to have accurate and precise time-delay measurements in the era of the Rubin
Observatory Legacy Survey of Space and Time (LSST). Adopting realistic yet
conservative uncertainties on their time-delay distances and lens angular
diameter distances (of 6.6% and 5%, respectively), we find that a sample of 20
lensed SNe Ia would allow a constraint on the Hubble constant ($H_0$) with 1.3%
uncertainty in the flat $\Lambda$CDM cosmology. We find a similar constraint on
$H_0$ in an open $\Lambda$CDM cosmology, while the constraint degrades to $3\%$
in a flat $w$CDM cosmology. We anticipate lensed SNe to be an independent and
powerful probe of SN physics and cosmology in the upcoming LSST era.
