Abstract The observation of the Universe at the present epoch will only give the rate of the expansion of the Universe at present era and produce one value of the Hubble constant by any observer in any galaxy in the cosmos. The expansion rate of the Universe is not obtainable for the past or the future of the Universe by observation; it can only be calculated by the fact that the invers of the Hubble constant is the age of the Universe at any period. One of the fundamental pillars of the cosmology is the Hubble constant and the inverse of it is the age of the Universe: , this relationship will be violated by observation that the Universe’s expansion is accelerating. This is fundamental that any epoch any observer on any galaxy in the Universe by looking at all the distant galaxies will measure the velocity of recession divided by Co-moving distant will obtain the value of the Hubble constant precisely the same exact value. The value of the Hubble constant is only constant at a particular epoch by all the observers in the Universe and decays as the passage of time according to the relationship: .
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