On the amount of peculiar velocity field information in supernovae from
  LSST and beyond
  Peculiar velocities introduce correlations between supernova magnitudes,
which implies that the supernova Hubble diagram residual carries information on
both the matter power spectrum at the present time and its growth rate. By a
combination of brute-force exact computations of likelihoods and Fisher matrix
analysis, we investigate how this information, which comes from supernova data
only, depends on different survey parameters such as covered area, depth, and
duration. We show that, for a survey like The Rubin Observatory Legacy Survey
of Space and Time (LSST) and a fixed redshift depth, the same observing time
provides the same cosmological information whether one observes a larger area,
or a smaller area during more years. We also show that although the peculiar
velocity information is peaked in the range $z \in [0, 0.2]$, there is yet
plenty of information in $z \in [0.2, 0.5]$, and for very high supernova number
densities there is even more information in the latter range. We conclude that,
after 5 years, LSST could measure $\sigma_8$ with an uncertainty of 0.17 with
the current strategy, and that this could be improved to 0.09 if the supernova
completeness is improved to 20%. Moreover, we forecast results considering the
extra parameter $\gamma$, and show that this creates a non-linear degeneracy
with $\sigma_8$ that makes the Fisher matrix analysis inadequate. Finally, we
discuss the possibility of achieving competitive results with the current
Zwicky Transient Facility.
