By highlighting the major shortcomings of modern cosmology, in this paper, an attempt is made to verify the cosmic acceleration in a quantum mechanical approach. With reference to the valuable opinion of Edwin Hubble, redshift can be related to a new atomic phenomenon. If light is coming from the atomic matter of the galaxy, then the observed redshift can be interpreted as an index of the galactic atomic ‘light emission mechanism’. Clearly speaking, redshift may not be connected with ‘galaxy receding’. The authors propose the following: During cosmic evolution, an ‘aged’ hydrogen atom emits an energetic photon. As the age of the hydrogen atom increases, it emits photons with increased quanta of energy and thus past light quanta emitted from an old galaxy will have less energy and show a red shift with reference to our galaxy. During its journey light quanta will not lose energy and there will be no change in the light’s wavelength. If so current cosmological changes may be reflected in any existing atom. The possible assumptions are : 1) At any given cosmic time, Hubble length can be considered as the gravitational or electromagnetic interaction range. 2) Being a primordial evolving black hole and Hubble’s constant being the angular velocity, universe is always rotating with light speed. 3) In atomic and nuclear physics, atomic gravitational constant is squared Avogadro number times the Newton’s gravitational constant and is discrete as , where n =1,2,3.. 4) Key conceptual link that connects the gravitational force and non-gravitational forces is - the classical force limit, . Ratio of classical force limit and the imaginary electroweak force magnitude is . 5) Avogadro number is discrete and thus the imaginary electroweak force is discrete and can be expressed as and it seems to be more fundamental than the electromagnetic and strong nuclear forces. 6) Discrete imaginary electroweak force may be the responsible force for revolving electron’s discrete total energy in hydrogen atom. 7) Characteristic nuclear radius and Reduced Planck’s constant increases with cosmic time. 8) It can be suggested that, fermion and its corresponding boson mass ratio is not unity but a value close to This idea can be applied to quarks, leptons, proton and the charged Higgs fermion. One can see “super symmetry” in low energies as well as high energies.