  We derive exact theoretical value of the constant cosmic background radiation
(CBR) temperature $T_0$ using the interconnections between the Gamow, Alpher
and Herman (GAH) hot Big Bang cosmology model of the expanding Universe and the
modified Freundlich redshift. As a result of this confluence an astonishing
relationship between $T_0$ and the four fundamental physical constants
$c$,$\hbar$,$k$,$G$ is found including also the Melvin's value of the
Freundlich constant $A_s$.Then the resulting predicted the CBR temperature is
$T_0=2.76626 K$. This prediction show excellent agreement with the data
obtained from ground-based and balloon-borne observations and also with a mean
of the perfect black-body spectrum CMB temperature $2.725 K$ measured COBE in
1992. Using a new cosmological model we determine the horizon scale, age and
mass of the present observable Universe. The calculations based on discrete
redshift equations for the electromagnetic, electroweak phases and Planck epoch
of the Universe predicts a graviton and string masses, which are originated
beyond on Planck time. The predicted graviton mass $m_Gr$ is about five orders
of magnitude less than the present "the best possible upper bounds on the mass
of the graviton", which may be "discovered" in the proposed LISA observations.
We present quantitative new results for the different quantum-cosmological
parameters. Finally, it is showed that the mystery largeness and smallness
dimensionless combination of the Quantum Cosmological constant $\Lambda_0$ and
Planck length $l_Pl$ may be derived as their ratio from the Trans-Planck
redshift relation. Thus is found the meaning a famous largeness cosmological
number $c^3/\hbarG\Lambda_0=2.8*10^{125}$ that is inverse of $\Lambda_0
l_Pl^2=3.6*10^{-126}$, and "which in 1930s was a regarded as a major problem by
Eddington and Dirac".
