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 $\Omega_k$.