Quantum discrete levels of the Universe from the early transPlanckian vacuum to the late dark energy
Abstract
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, classicalquantum gravity duality, and quantum spacetime. The quantum vacuum energy bends the spacetime 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 find the quantum discrete cosmological levels: size, time, vacuum energy, Hubble constant, and gravitational (GibbonsHawking) entropy and temperature from the very early transPlanckian 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 postPlanckian Universe t_{planck}≡t_{P}≤t ≤10^{61}t_{P}, the levels (in Planck units) are Hubble constant H_{n}=1 /√{(2 n +1 ) }, vacuum energy Λ_{n}=1 /(2 n +1 ), and entropy S_{n}=(2 n +1 ). As n increases, radius, mass, and S_{n} increase, H_{n} and Λ_{n} decrease, and consistently the Universe classicalizes. In the prePlanckian (transPlanckian) phase 10^{61}t_{P}≤t ≤t_{P}, the quantum levels are H_{Q n}=√{(2 n +1 ) }, Λ_{Q n}=(2 n +1 ), and S_{Q n}=1 /(2 n +1 ), Q denoting quantum. The n levels cover all scales from the far past highest excited transPlanckian level n =10^{122} with finite curvature, Λ_{Q}=10^{122}, and minimum entropy S_{Q}=10^{122}; n decreases till the Planck level (n =0 ) with H_{planck}=1 =Λ_{planck}=S_{planck} and enters the postPlanckian phase, e.g., n =1 ,2 ,…, n_{inflation}=10^{12},… , n_{cmb}=10^{114},… , n_{reoin}=10^{118},…, and n_{today}=10^{122}, with the most classical value H_{today}=10^{61}, Λ_{today}=10^{122}, and S_{today}=10^{122}. We implement the SnyderYang algebra in this context, yielding a consistent grouptheory realization of quantum discrete de Sitter spacetime, classicalquantum gravity duality symmetry, and a clarifying unifying picture.
 Publication:

Physical Review D
 Pub Date:
 December 2021
 DOI:
 10.1103/PhysRevD.104.123517
 arXiv:
 arXiv:2004.09257
 Bibcode:
 2021PhRvD.104l3517S
 Keywords:

 Physics  General Physics;
 83C;
 83F05;
 83C45;
 81T20
 EPrint:
 Published version in Phys Rev D, 54 pages, 1 figure, new material. arXiv admin note: text overlap with arXiv:1912.06655