Considering an idea of F. Arago in 1853 regarding light dispersion through the light ether in the interstellar space, this paper presents a new idea on an alternative interpretation of the cosmological red shift of the galaxies in the universe. The model is based on an analogy with the temporal material dispersion that occurs with light in the optical fiber core. Since intergalactic space is transparent, according to the model, this phenomenon is related to the gravitational potential existing in the whole space. Thus, it is possible to find a new interpretation to Hubble's constant. In space, light undergoes a dispersion process in its path, which is interpreted by a red shift equation of the type Δz = HL, since H = (d2n/dλ2 Δv Δλ), where H means the Hubble constant, n is the refractive index of the intergalactic space, Δλ is the spectral width of the extragalactic source, and Δv is the variation of the speed of light caused by the gravitational potential. We observe that this "constant" is governed by three new parameters. Light traveling the intergalactic space undergoes red shift due to this mechanism, while light amplitude decreases with time, and the wavelength always increases, thus producing the same type of behavior given by Hubble's Law. It can be demonstrated that the dark matter phenomenon is produced by the apparent speed of light of the stars on the periphery of the galaxies, without the existence of dark energy. Based on this new idea, the model of the universe is static, lacking expansion. Other phenomena may be interpreted based on this new model of the universe. We have what we call temporal gravitational dispersion of light in space produced by the variations of the speed of light, due to the presence of the gravitational potential in the whole space.