Cosmic Time Physics -- On the relation between cosmological redshift and fine structure constant variation

Almost a century ago, Hubble discovered the cosmological redshift of extragalactic objects. The Friedmann-Lema\^itre-Robertson-Walker (FLRW) metric was presented as a solution of Einstein's field equations for a homogeneous and isotropic universe. The metric includes a time-dependent factor a(t), intended to explain the cosmological redshift. By contrast, for the Eintein's static universe (a=1), no reasonable redshift explanation was found. In this work, the Cosmic Time Physics (CTP) theoretical framework is developed. CTP moves the explanation of cosmological redshift from general relativity to electromagnetism domain. We show that the vacuum electric permittivity $\epsilon_0$ and the vacuum magnetic permeability $\mu_0$ can vary inversely one each other over cosmic time, maintaining the speed of light $c$ constant, while conducting the change on the vacuum impedance $Z_0$ and on the fine structure constant $\alpha$. This variation downscales the atomic energy levels with cosmic backtime, redshifting the wavelength and frequency exactly in the same manner they are observed, while maintaining the atomic quantification relations. Note that the increase on $\alpha$ with cosmic time has gone unnoticed experimentally so far since the search is performed on rest-frame (de-redshiftted signals), in spite of the manifestation of such variation is precisely the redshift. The application of CTP to general relativity drive to an angular-redshift relation $d_A(z)$ as a function of the age of the universe $t_0$ and its curvature $R_0$. As a first approximation, we show that CTP $d_A(z)$ is able to reproduce the LCDM $d_A(z)$ curve with $R_0=1800$ Mpc and $t_0=15.57$ Gly. Finally, the Friedmann equations without scale factor ($a=1$) are used to derive the requirements for the stability of CTP universe.