An Exact CMB Photon Radiation Density of the Universe Derived from Rh = ct Cosmology

We will demonstrate that the photon energy density parameter Ωγ of the universe can be derived exactly inside RHt = ct cosmology. We find that it must be exactly: Ωγ = 1/ 5760π ≈5.526 × 10−5, which lies well within the 95% confidence interval for the photon radiation density reported by the Particle Data Group (PDG). Our exact result indicates that there is nouncertaintyintheradiationdensitywithinatleastsomesubclassesofRHt =ctcosmology and that such a model fits observations. Furthermore, in the standard model, the number density of CMB photons cannot be predicted from the Hubble parameter but only from the CMB temperature. For the first time, we derive a new equation for the number density of CMB photons that can predict the number density from only the Hubble parameter and the Planck length. This leads to a predicted number density of CMB photons equal to nγ = 410.71 ± 0.26 photons per cm^3, which is incredibly close to that reported by PDG when we use the H0 value recently described by Haug and Tatum, H0 = 66.8943 ± 0.0287 km/s/M pc. However, when using the H0 = 73.30 ± 1.04 km/s/Mpc value predicted by Riess et al., the photon number density prediction is far outside even the five-sigma confidence interval given by PDG. As we briefly discuss, this is related to why there is a Hubble tension in the Λ-CDM model.