Empirical study of the Pantheon SNeIa Catalog within power-law cosmology and varying speed of light

Abstract: In this paper, we investigate the kinematics of late-time acceleration within Dolgov's power-law cosmology $a=\left(t/t_{0}\right)^μ$ [Phys. Rev. D 55, 5881 (1997)] and Barrow's varying speed of light $c=c_{0}\,a^{-ζ}$ [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 $1+z=a^{-(1+ζ)}$. The model achieves a high-quality fit to the Pantheon Catalog of Type Ia supernovae and exhibits a notable degeneracy along the locus $(1+ζ)\,μ=1$. This empirical relation indicates that $c=μ^{-1}c_{0}\,t_{0}\,\frac{da}{dt}$, a characteristic that is not present in the $Λ$CDM model. We will discuss the implications of these findings in the context of (i) late-time acceleration; (ii) the horizon problem; (iii) Kolb's coasting universe model [Astrophys. J. 344, 543 (1989)]; (iv) a generalization of the cosmological principle to the time domain; and (v) the emergence of a novel conformally flat metric applicable to cosmology.