Model-independent test of the FLRW metric, the flatness of the Universe,
  and non-local measurement of $H_0r_\mathrm{d}$
  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 (SN), we measure $H_0
r_\mathrm{d}$ without any model assumption. Our measurement of $H_0
r_\mathrm{d} = $($10033.20^{+333.10}_{-371.81}$ (SN) $\pm$ 128.19 (BAO)) km
s$^{-1}$ is consistent with Planck constrains for the flat {\Lambda}CDM model.
We also report that higher expansion history rates $h(z)$ (among the
possibilities) as well as lower-bound values of $H_0 r\mathrm{d}$ result in
better internal consistency among the independent data (H(z)rd and
$d_\mathrm{A}(z)/r_\mathrm{d}$ from BAO at $z=0.32$ and z=0.57 and
$d_\mathrm{L}$ 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. We then combine these observables to 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, by
introducing a new diagnostic for flat-FLRW, $\Theta(z)$, which only depends on
observables of BAO and SN data. Our results are consistent with a flat-FLRW
Universe within $2{\sigma}$.
