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 .