Dynamical dark energy in light of cosmic distance measurements I: a demonstration using simulated datasets

We develop methods to extract key dark energy information from cosmic distance measurements including the BAO scales and supernovae luminosity distances. Demonstrated using simulated datasets of the complete DESI, LSST and Roman surveys designed for BAO and SNe distance measurements, we show that using our method, the dynamical behaviour of the energy, pressure, equation of state (with its time derivative) of dark energy and the cosmic deceleration function can all be accurately recovered from high-quality data, which allows for robust diagnostic tests for dark energy models.