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, tP, and the Hubble constant, H0, are important cosmologic constants. The goal is to accurately derive and demonstrate the inter-relationships of the CMB peak spectral radiance frequency, tP, and H0 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 H0 are derived from a previously published method used to derive tP. 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: νCMB, 160.041737 (06) × 109 Hz, ~160 × 109 Hz; 2.72519 K, 2.72548 ± 0.00057 K, H0 2.29726666 (11) × 10−18 s−1, ~2.3 × 10−18 s−1; and tP 5.3911418 (3) × 10−44 s, 5.39106 (32) × 10−44 s. Conclusion: The cosmic fundamental constants tP, H0, 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.
Highlights
Nomenclature and Abbreviations There are many fundamental constants and calculations utilizing these constants. For clarity they will be listed here. They include: neutron, n0, ν refers to the frequency equivalent of a constant, electron, e, Bohr radius, a0, Rydberg constant, R, speed of light, c, Planck’s constant, h, Planck’s time, tP, Planck time squared, tP2, Hubble constant, H0, Higgs boson, H0, cosmic microwave background peak spectral radiance, CMB, β, a ratio of a velocity divided by c, α, the fine structure constant, βH0d the β related to the Hubble constant, a qf is an integer fraction exponent, and δ is the difference between a fundamental constant’s exponent and its quantum fraction. 5.2
We have shown that it is possible to the first approximation derive the properties of hydrogen from the frequency of the neutron only in conjunction with the prime numbers 2, 3, 5, 7, 11 [30]
This method allows for derivation of physical constants independent of any specific associated typical experimental data
Summary
The cosmic microwave background radiation, CMB, is fundamental to observational cosmology, and is believed to be a remnant of the thermal radiation from the Big Bang [1]-[13]. It is considered a landmark test of the Big Bang model of the Universe. There has recently developed questioning if this is the only possible interpretation [14]. Utilizing quantum methods perhaps a Big Bang singularity can be avoided. This perspective is not well established, and not the standard approach
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