Model-independent reconstruction of the cosmological scale factor as a function of lookback time

TL;DR

This paper introduces a model-independent method to reconstruct the universe's scale factor over time using observational Hubble data, enhancing model discrimination and forecasting the impact of future measurements.

Contribution

It develops a new reconstruction technique based solely on the FRW metric, independent of specific cosmological models, and assesses error propagation and future data influence.

Findings

Reconstruction method effectively derives scale factor from Hubble data.

a-t data better distinguishes cosmological models than H-z data.

Future observations with more Hubble data improve parameter constraints.

Abstract

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. 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 fifty simulated H(z) data to estimate the influence of future observation. More Hubble measurements in the future will help constrain cosmological parameters more accurately.