Kinematic Constraints on Spatial Curvature from Supernovae Ia and Cosmic
  Chronometers
  An approach to estimate the spatial curvature $\Omega_k$ from data
independently of dynamical models is suggested, through kinematic
parameterizations of the comoving distance ($D_{C}(z)$) with third degree
polynomial, of the Hubble parameter ($H(z)$) with a second degree polynomial
and of the deceleration parameter ($q(z)$) with first order polynomial. All
these parameterizations were done as function of redshift $z$. We used SNe Ia
dataset from Pantheon compilation with 1048 distance moduli estimated in the
range $0.01<z<2.3$ with systematic and statistical errors and a compilation of
31 $H(z)$ data estimated from cosmic chronometers. The spatial curvature found
for $D_C(z)$ parametrization was $\Omega_{k}=-0.03^{+0.24+0.56}_{-0.30-0.53}$.
The parametrization for deceleration parameter $q(z)$ resulted in
$\Omega_{k}=-0.08^{+0.21+0.54}_{-0.27-0.45}$. The $H(z)$ parametrization has
shown incompatibilities between $H(z)$ and SNe Ia data constraints, so these
analyses were not combined. The $D_C(z)$ and $q(z)$ parametrizations are
compatible with the spatially flat Universe as predicted by many inflation
models and data from CMB. This type of analysis is very appealing as it avoids
any bias because it does not depend on assumptions about the matter content of
the Universe for estimating $\Omega_k$.
