scaling relation in [C ii]-detected galaxies and its likely application in cosmology.

We identify and investigate a possible correlation between the |$\rm {[C\,II]} \,158{-}{\mu }m$| luminosity and linewidth in the |$\rm {[C\,II]}$| -detected galaxies. Observationally, the strength of the |$\rm {[C\,II]}\, 158{-}{\mu }m$| emission line is usually stronger than that of the carbon monoxide (CO) emission line and this |$\rm {[C\,II]}$| line has been used as another tracer of the galactic characteristics. Moreover, many |$\rm {[C\,II]}$| -detected galaxies are identified in z  > 4. Motivated by previous studies of the CO luminosity–full width at half-maximum correlation relation (LFR) and the available new |$\rm {[C\,II]}$| measurements, we compile samples of the |$\rm {[C\,II]}$| -detected galaxies in the literature and perform the linear regression analysis. The |$\rm {[C\,II]}$| LFR is confirmed at a robust level. We also demonstrate the possible application of the |$\rm {[C\,II]}$| LFR by utilizing it on the distance measurement of the high- z galaxy. As a result, we extend the cosmic spatial scale beyond the redshift z of 7. With the outcome of the distance measurement, we constrain the cosmology parameters in the Chevallier–Polarski–Linder model, which considers the evolution of dark energy. Consequently, the uncertainties of the w ₀ and w_a are reduced significantly when the measured distance data of the |$\rm {[C\,II]}$| -detected galaxies are included in the cosmological parameter constraint, exemplifying the potential of using the |$\rm {[C\,II]}$| -detected galaxies as a tracer to constrain the cosmological parameters. [ABSTRACT FROM AUTHOR]