From observation of type Ia supernovae, people perceive that the cosmic expansion is accelerating. The interpretation is under the invariant light speed since the Big Bang to the present. Has the light speed been constant for whole the process of cosmic expansion? Before examine light speed and cosmic expansion, we have to elucidate key features and definition of the time.

Starting from energy as vibration in multiple dimensions, I investigated requirements for a dimension to work as a time. Subsequently, I proposed a 4-dimensional spherical model of the universe, in which cosmic energy spreads with expansion in a 3D surface of a 4D sphere. Our observable energy like light and quantum particles is vibration of the intrinsic space energy in the 4D space. The radius of the 4D sphere is our observed Time that can be a common time for any locations of the 3D space. The model nicely fits the observed data of supernovae without introducing acceleration of space expansion or the dark energy.

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Invitation to the Energy Circulation Theory (ECT)