2022MNRAS.517.2508W

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 w₀ 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.