The Hawking Hubble Temperature as the Minimum Temperature, the Planck Temperature as the Maximum Temperature, and the CMB Temperature as Their Geometric Mean Temperature

Using a rigorous mathematical approach, we demonstrate how the Cosmic Microwave Background (CMB) temperature could simply be a form of geometric mean temperature between the minimum time-dependent Hawking Hubble temperature and the maximum Planck temperature of the expanding universe over the course of cosmic time. This mathematical discovery suggests a re-consideration of Rh=ctcosmological models, including black hole cosmological models, even if it possibly could also be consistent with the Λ-CDM model. Most importantly, this paper contributes to the growing literature in the past year asserting a tightly constrained mathematical relationship between the CMB temperature, the Hubble constant, and other global parameters of the Hubble sphere. Our approach suggests a solid theoretical framework for predicting and understanding the CMB temperature rather than solely observing it.1.

Predicting High Precision Hubble Constant Determinations Based on a New Theoretical Relationship between CMB Temperature and H0

Based on considerable progress made in understanding the Cosmic Microwave Background (CMB) temperature from a deep theoretical perspective, this paper demonstrates a useful and simple relationship between the CMB temperature and the Hubble constant. This allows us to predict the Hubble constant with much higher precision than before by using the CMB temperature. This is of great importance, since it will lead to much higher precision in various global parameters of the cosmos, such as the Hubble radius and the age of the universe. We have improved uncertainty in the Hubble constant all the way down to 66.8712 ± 0.0019 km/s/Mpc based on data from one of the most recent CMB studies. Previous studies based on other methods have rarely reported an uncertainty much less than approximately ±1 km/s/Mpc for the Hubble constant. Our deeper understanding of the CMB and its relation to H0seems to be opening a new era of high-precision cosmology, which may well be the key to solving the Hubble tension, as alluded to herein. Naturally, our results should also be scrutinized by other researchers over time, but we believe that, even at this stage, this deeper understanding of the CMB deserves attention from the research community.

Planck’s Oscillators at Low Temperatures and Haken’s Perturbation Approach to the Quantum Oscillators Reconsidered

In the first step the extremal values of the vibrational specific heat and entropy represented by the Planck oscillators at the low temperatures could be calculated. The positions of the extrema are defined by the dimensionless ratios between the quanta of the vibrational energy and products of the actual temperature multiplied by the Boltzmann constant. It became evident that position of a local maximum obtained for the Planck’s average energy of a vibration mode and position of a local maximum of entropy are the same. In the next step the Haken’s time-dependent perturbation approach to the pair of quantum non-degenerate Schr?dinger eigenstates of energy is re-examined. An averaging process done on the time variable leads to a very simple formula for the coefficients entering the perturbation terms.