Correction Procedure for Empirical Equations for Calculating the Cosmic Microwave Background Temperature

Abstract

We build upon previously proposed empirical equations involving the cosmic microwave background (CMB) temperature and extend the approach to include an empirical formulation for the fine-structure constant. To ensure consistency across these relationships, revised values for the CMB temperature ( T c ) and the gravitational constant (G) were obtained as 2.726312 K and 6.673778 × 10 − 11 m 3 ·kg − 1 ·s − 2 , respectively. Recognizing slight deviations from the experimentally observed values, the study aims to refine these predictions. An optimized procedure yielded a recalibrated CMB temperature of 2.7256307 K, directly matching the observed value of 2.72548 ± 0.00057 K. A central claim of this work is the validity of Equation (10) independent of the MKSA unit system. The recalculated gravitational constant, 6.68917534 × 10 −11 m 3 ·kg −1 ·s −2 , however, remains marginally greater than the accepted value of 6.6743 × 10 −11 . The paper also introduces potential compensation strategies to account for this discrepancy.