Hidden pattern of self-invariant cosmic expansion: Empirical evidence from Hubble diagram of supernovae

Abstract

We present empirical evidence extracted directly from the Pantheon Catalog of SNeIa demonstrating that the speed of light varies as the universe expands. Moreover, the speed of light must vary in a specific quantifiable manner. To show this, we reformulate the kinematics of late-time acceleration using Dolgov's power-law cosmology $a=(t/t_0)^\mu$ [Phys. Rev. D 55, 5881 (1997)] and Barrow's varying speed of light $c=c_0a^{-\zeta}$ [Phys. Rev. D 59, 043515 (1999)]. In this cosmology, light traveling through an expanding universe undergoes an additional refraction caused by the varying c along its path, resulting in a modified Lemaitre redshift formula $1+z=a^{-(1+\zeta)}$. The new model achieves a high-quality fit to the Pantheon Catalog of SNeIa and exhibits a strong degeneracy along the locus $(1+\zeta)\,\mu=1$. This empirical relation indicates a self-invariant cosmic evolution: at all instants during the late-time epoch, the speed of light is exactly proportional to the rate of cosmic expansion, viz. $c=\mu^{-1}c_0t_0\,da/dt$, a characteristic that is absent in the $\Lambda$CDM model. This synchronous behavior between $c$ and $da/dt$ carries profound cosmological implications that we will discuss, regarding (i) the nature of late-time acceleration; (ii) a resolution to the horizon problem; (iii) Kolb's coasting universe model [Astrophys. J. 344, 543 (1989)]; (iv) a generalized cosmological principle into the time domain; and (v) a novel conformally flat metric applicable to cosmology. This newfound kinematic $c\propto da/dt$ relation represents a stringent requirement that any viable dynamical model of cosmology must satisfy, a requirement that the $\Lambda$CDM model does not fulfill. Thus, our paper delivers the clearest and most decisive evidence to date that challenges the standard $\Lambda$CDM paradigm of cosmology and calls for variable-$c$ modifications to General Relativity.