Measuring the Speed of Light with Updated Hubble Diagram of High-redshift Standard Candles

The possible time variation of the fundamental constants nature has been an active subject research in modern physics. In this paper, we propose a new method to investigate such speed light $c$ using updated Hubble diagram high-redshift standard candles including Type Ia Supernovae (SNe Ia) and quasars (based on UV-X relation). Our findings show that SNe Pantheon sample, combined with currently available sample cosmic chronometers, would produce robust constraints at level $c/c_0=1.03\pm0.03$. For UV+X ray acting as type candles, obtain $c/c_0=1.19\pm0.07$. Therefore, our results confirm there is no strong evidence for deviation from constant up $z\sim 2$. Moreover, discuss how technique might be improved much higher redshifts ($z\sim5$), focusing future measurements acceleration parameter $X(z)$ gravitational waves (GWs) binary neutron star mergers. particular, framework second-generation space-based GW detector, DECi-hertz Interferometer Gravitational-wave Observatory (DECIGO), expected constrained precision $\Delta{c}/c=10^{-3}$.