This study presents results on detecting neutral atomic hydrogen (H i) 21 cm absorption in the spectrum of PKS PKS1413+13 at redshift z = 0.24670041. The observation was conducted by FAST, with a spectral resolution of 10 Hz, using 10 minutes of observing time. The global spectral profile is examined by modeling the absorption line using a single Gaussian function with a resolution of 10 kHz within a 2 MHz bandwidth. The goal is to determine the rate of the latest cosmic acceleration by directly measuring the redshift evolution of the H i 21 cm absorption line with Hubble flow toward a common background quasar over a decade or longer time span. This will serve as a detectable signal generated by the accelerated expansion of the Universe at redshift z < 1, referred to as redshift drift $\dot{𝑧}$ or the SL effect. The measured H i gas column density in this DLA system is approximately equivalent to the initial observation value, considering uncertainties of the spin temperature of a spiral host galaxy. The high signal-to-noise ratio of 57, obtained at a 10 kHz resolution, strongly supports the feasibility of using the H i 21 cm absorption line in DLA systems to accurately measure the redshift drift rate at a precision level of around 10−10 per decade.

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