Model independent test of the FLRW metric, the flatness of the Universe, and non local measurement of $H_0$
Using measurements of $H(z) and $d_\mathrm{A}(z) from the Baryon Oscillation Spectroscopic Survey (BOSS) DR12 and luminosity distances from the Joint Lightcurve Analysis (JLA) compilation of supernovae, we test the Friedmann Lema\^itre Robertson Walker (FLRW) metric and the flatness of the Universe in a model independent way at two redshifts, namely 0.32 and 0.57. We then combine these observables to measure $H_0$ without any model assumption. Our measurement of $H_0 r_\mathrm{d} 10075.23 \pm 269.20$ km s$ 1} is consistent with Planck constrains for the flat \Lambda$CDM model. Assuming $r_\mathrm{d} 147.10$ Mpc, the fiducial value used in the BOSS analysis, we then derive $H_0 68.49 \pm 1.83$ km s$ 1} Mpc$ 1} which is compatible with the expected value of $H_0$ assuming the concordance model of cosmology, but possibly in slight tension with some local measurements. We also report that higher expansion history rates $h(z) (among the possibilities) as well as lower bound values of $H_0$ result in better internal consistency among the independent data $H(z) and $d_\mathrm{A}(z) from BAO at $z=0.32$ and $z=0.57$ and $d_\mathrm{L}(z) from JLA) we used in this work. This can be interpreted as an interesting and independent support of Planck cosmology without using any cosmic microwave background data.