  The standard model of the universe is further completed back in time before
inflation in agreement with observations, classical-quantum gravity duality and
quantum space-time. Quantum vacuum energy bends the space-time and produces a
constant curvature de Sitter background. We link de Sitter universe and the
cosmological constant to the (classical and quantum) harmonic oscillator.
Quantum discrete cosmological levels are found: size, time, vacuum energy,
Hubble constant and gravitational (Gibbons-Hawking) entropy from the very early
trans-planckian vacuum to the classical today vacuum energy. For each level $n
= 0, 1, 2,...$, the two: post and pre (trans)-planckian phases are covered: In
the post-planckian universe, the levels (in planck units) are: Hubble constant
$H_{n} = {1}/\sqrt{(2n + 1)}$, vacuum energy $\Lambda_{n} = 1/(2n + 1)$,
entropy $S_n = (2n + 1)$. As $n$ increases, radius, mass and $S_n$ increase,
$H_n$ and $\Lambda_n$ decrease and {\it consistently} the universe {\it
classicalizes}. In the pre-planckian (trans-planckian) phase, the quantum
levels are: $H_{Qn} = \sqrt{(2n + 1)},\; \Lambda_{Qn} = (2n + 1)/1,\; S_{Qn} =
1/(2n + 1)$, $Q$ denoting quantum. The $n$-levels cover {\it all} scales from
the far past highest excited trans-planckian level $n = 10^{122}$ with finite
curvature, $\Lambda_Q = 10^{122}$ and minimum entropy $S_Q = 10^{-122}$, $n$
decreases till the planck level $(n = 0)$ and enters the post-planckian phase
e.g: $n = 1, 2,...,n_{inflation} = 10^{12},... ,n_{cmb} =
10^{114},...,n_{reoin} = 10^{118},...,n_{today} = 10^{122}$ with the most
classical value $H_{today} = 10^{-61}$, $\Lambda_{today} = 10^{-122}$,
$S_{today} = 10^{122}$. We implement the Snyder-Yang algebra in this context
yielding a consistent group-theory realization of quantum discrete de Sitter
space-time, classical-quantum gravity duality symmetry and a clarifying
unifying picture.(Abridged)
