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A closed model of the universe was constructed according to the assumption that very minor fraction of the dark energy transfers so slowly to matter and radiation. The cosmological parameter is no longer fixed but represents so slowly decreasing function with time. In this model the universe expands to maximum limit at tme = 26.81253 Gyr, then it will contract to a big crunch at tbc = 53.6251 Gyr. Observational tests to the closed cosmic model were illustrated. Distributions of the universe expansion and contraction speed established in this model which indicated that the expansion speed in the early universe is appreciably high, then it will decrease rapidly until it vanishes at tme. However, the contraction speed of the universe increases continuously until the time just before tbe. Distributions of the universe expansion and contraction acceleration were performed empirically which confirmed the previous result were performed empirically. In the closed cosmic model the universe history can be categorized into six main stages, these are the first radiation epoch, the first matter epoch, the first dark energy epoch, the last dark energy epoch, the last matter epoch and the last radiation epoch. Distributions of the density parameters of the radiation, matter, dark energy and the total density as well as the distributions of temperature of the radiation and non-relativistic matter were all investigated in this model at all epochs of the universe.
The cosmological constant problem is reanalyzed by imposing the limitation of the number of degrees of freedom (d.o.f.) due to entropy bounds directly in the calculation of the energy density of a field theory. It is shown that if a quantum field theory has to be consistent with gravity and holography, i.e. with an upper limit of storing information in a given area, the ultraviolet momentum cut-off is not the Planck mass, Mp, as naively expected, but where Nu is the number of d.o.f. of the universe. The energy density evaluation turns out completely consistent with Bousso’s bound on the cosmological constant value. The scale , that in the “fat graviton” theory corresponds to the graviton size, originates by a self-similar rearrangement of the elementary d.o.f. at different scales that can be seen as an infrared-ultraviolet connection.