Model-independent determination of curvature parameter by using $H(z)$ and $D_A(z)$ data pair from BAO measurement

Abstract

We present a model-independent determination of the curvature parameter $\Omega_k$ by using the Hubble parameter $H(z)$ and angular diameter distance $D_A(z)$ from the recent baryon acoustic oscillation (BAO) measurements. Each $H(z)$ and $D_A(z)$ pair from a BAO measurement can constrain a curvature parameter. The accuracy of the curvature measurement improves with increased redshift of $H(z)$ and $D_A(z)$ data. By using the $H(z)$ and $D_A(z)$ pair derived from BAO Lyman $\alpha$ forest measurement at $z=2.36$, the $\Omega_k$ is confined to be -0.05$\pm$0.06, which is consistent with the curvature $-0.037^{+0.044}_{-0.042}$ constrained by the nine-year WMAP data only. Considering future BAO meausurements, at least one order of magnitude improvement of this curvature measurement could be expected.