Using spatial curvature with HII galaxies and cosmic chronometers to explore the tension in $H_0$. (arXiv:1901.06626v2 [astro-ph.CO] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Ruan_C/0/1/0/all/0/1">Cheng-Zong Ruan</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Melia_F/0/1/0/all/0/1">Fulvio Melia</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Chen_Y/0/1/0/all/0/1">Yu Chen</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Zhang_T/0/1/0/all/0/1">Tong-Jie Zhang</a>
We present a model-independent measurement of spatial curvature $Omega_{k}$
in the Friedmann-Lema^itre-Robertson-Walker (FLRW) universe, based on
observations of the Hubble parameter $H(z)$ using cosmic chronometers, and a
Gaussian Process (GP) reconstruction of the HII galaxy Hubble diagram. We show
that the imposition of spatial flatness (i.e., $Omega_k=0$) easily
distinguishes between the Hubble constant measured with {it Planck} and that
based on the local distance ladder. We find an optimized curvature parameter
$Omega_{k} = -0.120^{+0.168}_{-0.147}$ when using the former (i.e.,
$H_0=67.66pm0.42 , mathrm{km},mathrm{s}^{-1} ,mathrm{Mpc}^{-1}$), and
$Omega_{k} = -0.298^{+0.122}_{-0.088}$ for the latter ($H_0=73.24pm 1.74
,mathrm{km},mathrm{s}^{-1} ,mathrm{Mpc}^{-1}$). The quoted uncertainties
are extracted by Monte Carlo sampling, taking into consideration the
covariances between the function and its derivative reconstructed by GP. These
data therefore reveal that the condition of spatial flatness favours the {it
Planck} measurement, while ruling out the locally inferred Hubble constant as a
true measure of the large-scale cosmic expansion rate at a confidence level of
$sim 3sigma$.
We present a model-independent measurement of spatial curvature $Omega_{k}$
in the Friedmann-Lema^itre-Robertson-Walker (FLRW) universe, based on
observations of the Hubble parameter $H(z)$ using cosmic chronometers, and a
Gaussian Process (GP) reconstruction of the HII galaxy Hubble diagram. We show
that the imposition of spatial flatness (i.e., $Omega_k=0$) easily
distinguishes between the Hubble constant measured with {it Planck} and that
based on the local distance ladder. We find an optimized curvature parameter
$Omega_{k} = -0.120^{+0.168}_{-0.147}$ when using the former (i.e.,
$H_0=67.66pm0.42 , mathrm{km},mathrm{s}^{-1} ,mathrm{Mpc}^{-1}$), and
$Omega_{k} = -0.298^{+0.122}_{-0.088}$ for the latter ($H_0=73.24pm 1.74
,mathrm{km},mathrm{s}^{-1} ,mathrm{Mpc}^{-1}$). The quoted uncertainties
are extracted by Monte Carlo sampling, taking into consideration the
covariances between the function and its derivative reconstructed by GP. These
data therefore reveal that the condition of spatial flatness favours the {it
Planck} measurement, while ruling out the locally inferred Hubble constant as a
true measure of the large-scale cosmic expansion rate at a confidence level of
$sim 3sigma$.
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