perform the COsmic Dynamics EXperiment (CODEX). The experiment is designed to detect the SL-test signals by observing the Lyman–$\alpha$ absorption lines within the redshift range of $2\lesssim z\lesssim 5$. The forecast of using the redshift drift from the E-ELT to constrain dark energy models has been extensively discussed; see, e.g., Refs. [@Liske:2008ph; @Geng:2014hoa; @Geng:2014ypa; @Guo:2015gpa; @He:2016rvp; @Liu:2018kjv; @Lazkoz:2017fvx; @Zhang:2013mja; @Martinelli; @Corasaniti:2007bg; @Balbi:2007fx; @Zhang:2007zga; @Zhang:2010im; @Geng:2018pxk; @Geng:2015ara; @Yuan:2013wpa]. It has been shown that the redshift drift in the redshift range of $2< z< 5$ is rather useful to break the parameter degeneracies generated by other observations and thus can play an important role in the cosmological estimation in the future.

The Square Kilometre Array (SKA) has recently started construction for the stage of Phase one. Actually, SKA can also perform the research of real-time cosmology. Instead of detecting the Lyman-$\alpha$ absorption lines of quasar, SKA will measure the spectral drift in the neutral hydrogen (HI) emission signals of galaxies to implement the measurement of redshift drift in the redshift range of $0 < z < 1$. Obviously, the redshift drift data of SKA provide an important supplement to those of E-ELT.

In this work, we will study the real-time cosmology with 