Quantum discrete levels of the Universe from the early trans-Planckian vacuum to the late dark energy

We go forward in completing the Standard Model of the Universe back in time with Planckian and transPlanckian physics before inflation in agreement with observations, classical-quantum gravity duality, and quantum space-time. The quantum vacuum energy bends the space-time and produces a constant curvature de Sitter background. We link the de Sitter Universe and the cosmological constant to the (classical and quantum) harmonic oscillator. We fmd the quantum discrete cosmological levels: size, time, vacuum energy, Hubble constant, and gravitational (Gibbons-Hawking) entropy and temperature from the very early trans-Planckian vacuum to the classical vacuum energy today. For each level n = 0,1,2, ..., the two post- and pre-(trans)-Planckian phases are covered: In the post-Planckian Universe t(planck) t(p) <= t <= 10(61) t(p), the levels (in Planck units) are Hubble constant H-n = 1/root 2n + 1), vacuum energy Lambda(n) = 1/(2n + 1), and entropy S-n = (2n + 1). As n increases, radius, mass, and S-n increase, H-n and Lambda(n) decrease, and consistently the Universe classicalizes. In the pre-Planckian (trans-Planckian) phase 10(-61) t(p) <= t <= t(p), the quantum levels are Lambda(Qn) = root(2n + 1), Lambda(Qn) = (2n + 1), and S-Qn = 1/(2n + 1), Q denoting quantum. The n levels cover 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) with H-planck = 1 = Lambda(planck) = S-planck and enters the post-Planckian phase, e.g., n = 1,2, ..., n(inflation) = 10(12), ..., n(cmb) = 10(114), ..., n(reoion) = 10(118), and n(today) = 10(122), with the most classical value H-today = 10(-61), Lambda(today) = 10(-122) and 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.