Toward a direct measurement of the cosmic acceleration: the first preparation with FAST

Damped Lyman-$\alpha$ Absorber(DLA) of HI 21cm system is an ideal probe to directly measure cosmic acceleration in real-time cosmology via Sandage-Loeb(SL) test. During short observations toward two DLAs in the commissioning progress of FAST, we manage to exhibit an HI 21cm absorption feature from PKS1413+135 spectrum in one epoch with our highest resolution up to 100 Hz, preliminarily validating the frequency consistency under different resolutions and bandwidths. We make a Gaussian fitting to extract the spectral features, introduce two theoretical indicators to describe the fitted velocity uncertainty, and ultimately give a mean redshift and its constraint of $z_\mathrm{M}=0.24670045\pm0.00000036$ in accord with most literature. But our redshift error of the target is still three magnitudes higher than the level we can reach the drift signal. Though our first preparation has some flaws in time recording and diode settings, it still proves the correctness of our data process. Confined by limited observing time, we do not strech FAST's ability to obtain a better velocity constraint, so further researchs are needed and in schedule. With fine sensitivity and improving spectral resolution, such observations in FAST could have reasonable possibility to explore cosmic acceleration in late time universe practically.