Status of kinematic cosmology with SN Ia: JLA, Pantheon and future
  constraints with LSST
  In this work we derive state-of-the-art model-independent constraints on
cosmology from SN Ia by measuring purely kinematical $\left( q,j \right)$ model
parameters (where $q$ and $j$ are related to the first and second derivative of
the Hubble parameter). For the JLA compilation of SN Ia an agreement within
2$\sigma$ of $\Lambda$CDM expectations is found, where best-fitting kinematical
parameters are $q=-0.66 \pm 0.11$ and $j=0.41 ^{+0.32}_{-0.33}$. With $q=-0.73
\pm 0.13$ and $j=0.76 ^{+0.41}_{-0.43}$ the Pantheon sample shows even better
agreement with the $\Lambda$CDM expectation of $j=1$ than JLA, hinting at less
systematics and/or a higher number of SN Ia alleviating tensions. For the
future we predict the precision achievable with SN Ia from the LSST deep survey
as $\Delta q \sim 0.05$ and $\Delta j \sim 0.1$, which is systematics-limited
and could lead to detect both deviations from $\Lambda$CDM (in $j$) or current
expansion rates measured (in $q$). In comparison, for standard cosmological
parameters we get $\Delta \Omega_\mathrm{m}=0.01$ and $\Delta w=0.07$ for LSST.
Given the high number of SN Ia expected for LSST, kinematical parameters in up
to 500 sky regions, each with their own individual Hubble diagram, can be
constrained. For each region an individual precision at the 10s of percent
level is within reach at current systematics-levels, comparable to present-day
full-sky surveys. This will determine anisotropy in cosmic expansion, or the
dark energy dipole, at the 10s of percent level at 10s of degree scales.
