Testing the fidelity of Gaussian processes for cosmography

The dependence of implications from observations on cosmological models is an intractable problem not only in cosmology, but also in astrophysics. Gaussian processes (GPs), a powerful nonlinear interpolating tool without assuming a model or parametrization, have been widely used to directly reconstruct functions from observational data (e.g., expansion rate and distance measurements) for cosmography. However, the fidelity of this reconstructing method has never been checked. In this study, we test the fidelity of GPs for cosmography by mocking observational data sets comprising different number of events with various uncertainty levels. These factors are of great importance for the fidelity of reconstruction. That is, for the expansion rate measurements, GPs are valid for reconstructing the functions of the Hubble parameter versus redshift when the number of observed events is as many as 256 and the uncertainty of the data is similar to 3%. Moreover, the distance-redshift relation reconstructed from the observations of the upcoming Dark Energy Survey type Ia supernovae is credible.