Model-independent Reconstruction of the Cosmological Scale Factor as a Function of Lookback Time

We present a model-independent method of reconstructing scale factor against lookback time from the Observational Hubble parameter Data (OHD). The reconstruction method is independent of dynamical models and is only based on the Friedmann-Robertson-Walker metric. We also calculate the propagation of error in the reconstruction process. The reconstruction data errors mainly come from trapezoidal rule approximation and the uncertainty from OHD. Furthermore, the model discrimination ability of original OHD and reconstructed a-t data is discussed under a dimensionless standard method. The a-t data can present the differences between cosmology models more clearly than H-z data by comparing their coefficients of variations. Finally, we add 50 simulated H(z) data to estimate the influence of future observation. More Hubble measurements in the future will help constrain cosmological parameters more accurately.