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

The possible time variation of the fundamental constants of nature has been an active subject of research in modern physics. In this paper, we propose a new method to investigate such possible time variation of the speed of light c using the updated Hubble diagram of high-redshift standard candles including Type Ia Supernovae (SNe Ia) and high-redshift quasars (based on UV-X relation). Our findings show that the SNe Ia Pantheon sample, combined with currently available sample of cosmic chronometers, would produce robust constraints on the speed of light at the level of c/c ₀ = 1.03 ± 0.03. For the Hubble diagram of UV+X-ray quasars acting as a new type of standard candle, we obtain c/c ₀ = 1.19 ± 0.07. Therefore, our results confirm that there is no strong evidence for deviation from a constant speed of light up to z ~ 2. Moreover, we discuss how our technique might be improved at much higher redshifts (z ~ 5), focusing on future measurements of the acceleration parameter X(z) with gravitational waves (GWs) produced by binary neutron star mergers. In particular, in the framework of the second-generation space-based GW detector, DECi-hertz Interferometer Gravitational Wave Observatory, the speed of light is expected to be constrained with a precision of Δc/c = 10^-3.