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

TL;DR

This work tests whether late-time cosmic acceleration can be explained within a Dolgov-style power-law cosmology combined with Barrow's varying speed of light (VSL) by inferring the kinematic functions $a(t)$ and $c(a)$ from Pantheon SNeIa data. It introduces a modified Lemaitre redshift and luminosity-distance relation under $a(t)\propto t^{\mu}$ and $c(a)\propto a^{-\zeta}$, uncovering a prominent degeneracy along $(1+\zeta)\mu=1$ and evaluating four cases: EdS, Dolgov, Kolb, and SIG. The analysis finds that, while EdS and naïve Dolgov models underperform, the SIG configuration ($\mu=2/3$, $\zeta=1/2$) provides the best fit to Pantheon data, predicts $c\propto\dot{a}$, and yields an effectively infinite horizon without dark energy or inflation, suggesting a new kinematic framework for cosmology. The results imply a generalized Copernican principle in the time domain and motivate a conformally flat metric with potential implications for resolving the Hubble tension and constraining viable cosmological dynamics beyond $\Lambda$CDM.

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.

Figures (4)

• Figure 1: The supernova emitted $\lambda_{SN}$ and the observer detects $\lambda_{MW}$. Note that $\frac{\lambda_{MW}}{\lambda_{SN}}\neq\frac{\lambda_{2}}{\lambda_{1}}$ in general, rendering the Lemaître redshift formula, $1+z=a^{-1}$, invalid for VSL cosmology.
• Figure 2: 68% and 95% constraint contours, deduced from Pantheon Catalog and VSL power-law cosmology $\{a\!\propto\!t^{\,\mu},\,c\!\propto\!a^{-\zeta}\}$. A degeneracy tracking the locus $(1+\zeta)\,\mu\!=\!1$ is prominent. In Table I below, Kolb case and SIG case outperform the "benchmark" $\Lambda$CDM model in terms of $\chi^{2}$. Additional advantages of SIG over $\Lambda$CDM are provided in the main text.
• Figure 3: Upper panel: Re-plotting Figure \ref{['fig:mu-zeta']} in terms of $\{\mu,\mu\,\zeta\}$. The dotted yellow line in Figure \ref{['fig:mu-zeta']} becomes a straight line $\mu+\mu\,\zeta=1$. Lower panel: Distribution of the sum $\mu+\mu\,\zeta$ as constructed from the upper panel; the distribution exhibits a pronounced symmetric peak at $\mu+\mu\,\zeta=1$ and width $\sim0.2$.
• Figure 4: 68% and 95% constraint contours for models satisfying $(1+\zeta)\,\mu\!=\!1$. The distribution of $t_{0}$ is insensitive to $\mu$. The parameters for the SIG and Kolb cases are given in Table I.