Variable Fine Structure Constant from Maximal-acceleration Phase Space Relativity

Recently, we presented a new physical model that links the maximum speed of light with the minimal Planck scale into a maximal-acceleration Relativity principle in the spacetime tangent bundle and in phase spaces (cotangent bundle). The maximal proper-acceleration bound is a = c/Λ in full agreement with the old predictions of Caianiello, the Finslerian geometry point of view of Brandt and more recent results in the literature. Inspired by the maximal-acceleration corrections to the Lamb shifts of one-electron atoms by Lambiase, Papini and Scarpetta, we derive the exact integral equation that governs the Renormalization-Group-like scaling dependence of the fractional change of the fine structure constant as a function of the cosmological redshift factor and a cutoff scale Lc, where the maximal acceleration relativistic effects are dominant. A particular physical model exists, when the cutoff scale is the Planck scale, with ΩΛ = 1 , where the Universe, as a whole, behaves effectively as a ’black hole’, whose Hubble horizon is expanding at the speed of light.