Explanation of the Necessity of the Empirical Equations That Relate the Gravitational Constant and the Temperature of the CMB

Abstract

In previous papers, we proposed an empirical equation for the fine-structure constant. Using this equation, we proposed a refined version of our own former empirical equations about the electromagnetic force and gravity in terms of the temperature of the cosmic microwave background. The calculated values of the temperature of the cosmic microwave background ( T c ) and the gravitational constant ( G ) were 2.726312 K and 6.673778 × 10 -11 m 3 ⋅ kg -1 ⋅ s -2 , respectively. Then, for the values of the factors 9/2 and π in our equations, we used 4.488519503 and 3.132011447, respectively. However, we could not provide a theoretical explanation for the necessity of these empirical equations. In this paper, using the redefinition method for the UNIT, we show the necessity for our empirical equations.