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We derive exact theoretical value of the constant cosmic background radiation(CBR) temperature $T_0$ using the interconnections between the Gamow, Alpherand Herman (GAH) hot Big Bang cosmology model of the expanding Universe and themodified Freundlich redshift. As a result of this confluence an astonishingrelationship between $T_0$ and the four fundamental physical constants$c$,$\hbar$,$k$,$G$ is found including also the Melvin's value of theFreundlich constant $A_s$.Then the resulting predicted the CBR temperature is$T_0=2.76626 K$. This prediction show excellent agreement with the dataobtained from ground-based and balloon-borne observations and also with a meanof the perfect black-body spectrum CMB temperature $2.725 K$ measured COBE in1992. Using a new cosmological model we determine the horizon scale, age andmass of the present observable Universe. The calculations based on discreteredshift equations for the electromagnetic, electroweak phases and Planck epochof the Universe predicts a graviton and string masses, which are originatedbeyond on Planck time. The predicted graviton mass $m_Gr$ is about five ordersof magnitude less than the present "the best possible upper bounds on the massof the graviton", which may be "discovered" in the proposed LISA observations.We present quantitative new results for the different quantum-cosmologicalparameters. Finally, it is showed that the mystery largeness and smallnessdimensionless combination of the Quantum Cosmological constant $\Lambda_0$ andPlanck length $l_Pl$ may be derived as their ratio from the Trans-Planckredshift relation. Thus is found the meaning a famous largeness cosmologicalnumber $c^3/\hbarG\Lambda_0=2.8*10^{125}$ that is inverse of $\Lambda_0l_Pl^2=3.6*10^{-126}$, and "which in 1930s was a regarded as a major problem byEddington and Dirac".

On Synthesis of the Big Bang Model with Freundlich's Redshift and its Cosmological Consequences