The Derivation of the Cosmic Microwave Background Radiation Peak Spectral Radiance, Planck Time, and the Hubble Constant from the Neutron and Hydrogen

Abstract

Purpose: The cosmic microwave background radiation, CMB, is fundamental to observational cosmology, and is believed to be a remnant from the Big Bang. The CMB, Planck time, t P , and the Hubble constant, H 0 , are important cosmologic constants. The goal is to accurately derive and demonstrate the inter-relationships of the CMB peak spectral radiance frequency, t P , and H 0 from neutron and hydrogen quantum data only. Methods: The harmonic neutron hypothesis, HNH, evaluates physical phenomena within a finite consecutive integer and exponential power law harmonic fraction series that are scaled by a fundamental frequency of the neutron as the exponent base. The CMB and the H 0 are derived from a previously published method used to derive t P . Their associated integer exponents are respectively +1/2, −3/4, and −128/35. Results: Precise mathematical relationships of these three constants are demonstrated. All of the derived values are within their known observational values. The derived and known values are: ν CMB , 160.041737 (06) × 10 9 Hz, ~160 × 10 9 Hz; 2.72519 K , 2.72548 ± 0.00057 K , H 0 2.29726666 (11) × 10 −18 s −1 , ~2.3 × 10 −18 s −1 ; and t P 5.3911418 (3) × 10 −44 s, 5.39106 (32) × 10 −44 s. Conclusion: The cosmic fundamental constants t P , H 0 , and CMB are mathematically inter-related constants all defined by gravity. They are also directly derivable from the quantum properties of the neutron and hydrogen within a harmonic power law.