The CMB Temperature Is Simply the Geometric Mean: T_cmb =√T_minT_max of the Minimum and Maximum Temperature in the Hubble Sphere

In the Hubble sphere, we assume that the wavelength of pure energy spreads out in all directions. The maximum wavelength in the Hubble sphere is then the circumference of the Hubble sphere. We assume the minimum wavelength occurs in a Planck mass black hole, which is given by 4πRs,p = 8πlp. Here, we build further on the geometric mean CMB approach by Haug and Tatum and conclude that the CMB temperature is simply given as: Tcmb =√TminTmax, which is the geometric mean of the minimum and maximum physically possible temperatures in the Hubble sphere. This is again means the CMB temperature simply is the geometric mean of the Hawking temperature of the Hubble sphere (in black hole cosmology) and the Hawking temperature of the Planck mass black hole, se we have also Tcmb = THaw,HTHaw,p.