A distance measurement of galaxies from JWST using star formation rate-stellar mass relation

We use the star formation rate-stellar mass relation ($SFR-M_{\ast }$) of galaxies to measure their luminosity distances as well as estimate cosmological parameters. We compile a sample of 341 high-redshift galaxies at $5<z<14$ and an additional 51 galaxies at $1.8<z<3.5$ from the JWST observations, which can be used to investigate the correlation between the star formation rate and stellar mass, and determine their cosmological distance. The relation $SFR\propto (M_{\ast }\mathrm{/}{M}_{\odot }{)}^{\gamma }$ can be applied to check the nonlinear correlation between the star formation rate and stellar mass $M_{\ast }$ of galaxies and give their distance. Additionally, it also can be used to test if the $SFR-M_{\ast }$ relation depends on redshift, and the data suggest that the $SFR$ is positively correlated with stellar mass, the $SFR-M_{\ast }$ relation of the high-redshift galaxies has a redshift dependence. Finally, we combine the galaxy sample with Type Ia supernova (SNIa) data from the Pantheon compilation to test the property of dark energy, specifically addressing whether its density deviates from the constant, and give the statistical analysis results.