A Model-Independent Measurement of the Spatial Curvature using Cosmic Chronometers and the HII Hubble Diagram

Abstract

We propose a model-independent way to determine the cosmic curvature using the Hubble parameter $H(z)$ measured with cosmic chronometers and the comoving distance $D(z)$ inferred from HII galaxies. We employ Gaussian processes to smooth the measure of distance and match it to $30$ values of $H(z)$. The curvature parameter $\Omega_k$ may be obtained individually for each such pair. The weighted average for the complete sample is $\Omega_k=-0.0013\pm0.0004$, suggesting a bias towards negative values. The accuracy of the curvature measurement improves with increased redshift, however, given possible systematic effects associated with local inhomogeneities. We therefore also analyze a high-redshift ($z>1.5$) sub-sample on its own, which is more likely to reflect the geometry of the Universe on large, smooth scales. We find for this set of data that $\Omega_k=-0.0111\pm0.0416$, consistent with zero to better than $1\sigma$. This result is in agreement with the spatially flat universe inferred from the cosmic microwave background observations. We expect this method to yield even tighter constraints on the curvature parameter with future, more accurate observations of HII galaxies at high $z$.