Toward a direct measurement of the apparent cosmic acceleration: roadmap and forecast on FAST.

HI absorption systems are great targets for direct measurement of the Sandage-Loeb (SL) effect throughout a wide range of redshift for ground-based radio telescopes. We demonstrate the significance of improving the accuracy of SL effect measurement in cosmological model selection. With its wide field of view and high sensitivity, we forecast that for 1 year of the upcoming commensal survey (CRAFTS) the FAST telescope is capable of discover about 800 HI absorption systems thereby improving the SL measurement accuracy. Aiming to measurement the cosmic acceleration at the precision level of $0.1\ \mathrm{cm\ s^{-1}\ yr^{-1}}$, we propose combined observation mode with blind-searching and targeted observation. For 10 years of consecutive targeted spectroscopic observation with the level of $0.1\ \rm Hz$ resolution, we could detect the first-order derivative of the cosmological redshift with the expected precision.