On the galactic scale the universe is inhomogeneous and redshift z is occasionally less than zero .
A scalar potential model ( SPM ) that links the galaxy scale z to the cosmological scale z of the Hubble Law is postulated .
Several differences among galaxy types suggest that spiral galaxies are Sources and that early type , lenticular , and irregular galaxies are Sinks of a scalar potential field .
The morphology-radius and the intragalactic medium cluster observations support the movement of matter from Source galaxies to Sink galaxies .
A cell structure of galaxy groups and clusters is proposed to resolve a paradox concerning the scalar potential like the Olber ’ s paradox concerning light .
For the sample galaxies , the ratio of the luminosity of Source galaxies to the luminosity of Sink galaxies approaches 2.7 \pm 0.1 .
An equation is derived from sample data , which is anisotropic and inhomogeneous , relating z of and the distance D to galaxies .
The calculated z has a correlation coefficient of 0.88 with the measured z for a sample of 32 spiral galaxies with D calculated using Cepheid variable stars .
The equation is consistent with z < 0 observations of close galaxies .
At low cosmological distances , the equation reduces to z \approx \exp ( KD ) -1 \approx KD , where K is a constant , positive value .
The equation predicts z from galaxies over 18 Gpc distant approaches a constant value on the order of 500 .
The SPM of z provides a physical basis for the z of particle photons .
Further , the SPM qualitatively suggests the discrete variations in z , which was reported by W. G. Tifft , 1997 , Astrophy .
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485 , 465 and confirmed by others , are consistent with the SPM .