Kinematic constraints on spatial curvature from supernovae Ia and cosmic chronometers

Abstract

ABSTRACT An approach to estimate the spatial curvature Ωk from data independently of dynamical models is suggested, through kinematic parametrizations of the comoving distance [DC(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 parametrizations were done as function of redshift z. We used SNe Ia data set 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 DC(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 DC(z) and q(z) parametrizations are compatible with the spatially flat universe as predicted by many inflation models and data from cosmic microwave background. 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 Ωk.