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

Abstract

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.