Null test of the cosmic curvature using H(z) and supernovae data

We introduce a model-independent approach to the null test of the cosmic curvature, which is geometrically related to the Hubble parameter H(z) and luminosity distance d(L)(z). Combining the independent observations of H(z) and d(L)(z), we use the model-independent smoothing technique, Gaussian processes, to reconstruct them and determine the cosmic curvature Omega((0))(K) in the null test relation. The null test is totally geometrical and does not assume any cosmological model. We show that the cosmic curvature Omega((0))(K) = 0 is consistent with current observational data sets, falling within the 1 sigma limit. To demonstrate the effect on the precision of the null test, we produce a series of simulated data of the models with different Omega((0))(K) . Future observations in better quality can provide a greater improvement to constrain or refute the flat universe with Omega((0))(K) = 0.