Abstract
Our goal is to interpret the energy equation from doubly special relativity of Magueijo–Smolin with an invariant Planck energy scale to obtain the speed of light with an explicit dependence on the background temperature of the expanding universe (Nassif and de Faria. Phys. Rev. D, 86, 027703 (2012). doi:10.1103/PhysRevD.86.027703 ). We also investigate how other universal constants, including the fine structure constant, have varied since the early universe and, thus, how they have evolved over the cosmological time related to the temperature of the expanding universe. For instance, we show that both the Planck constant and the electron charge were also too large in the early universe. However, we finally conclude that the fine structure constant has remained invariant with the age and temperature of the universe, which is in agreement with laboratory tests and some observational data.
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