I hope in my first post I find in this forum some of those who are interesting in theoretical cosmology to help me not to believe the ideas which I am going to introduce to be much more or less important than they really are.

Perhaps, the simplest shape of space-time one can think of is the 4-ball in which the radius represents the cosmological time and the hypersurface (3-sphere) represents our 3-space ( x, y, z ).

This attractive shape is not far from the imagination of physicists but it is excluded for two reasons:

1-It seems to contradict the results of the global application of Einstein’s field equation because according to this model the global geometry of the universe depends only on the age of the universe and has nothing to do with the average density of the universe as (supposed to be) implied by the field equation.

2-It contradicts the acceleration of the expansion of the universe which is (supposed to be) supported by the observational data about red-shifts because a model of a spherical space with radial time implies a steady expansion of the universe.

Instead of hurriedly excluding this shape of space-time our proposed cosmological model tries to overcome these difficulties.

We can overcome the first difficulty easily by adopting a good definition for the cosmological constant which eliminates the dependence of the global geometry of the universe on its average density and relates it directly to the age of the universe. The cosmological constant which satisfies these requirements is the quantity that composed of two parts: the geometrical part which is the curvature of the universe determined by the age of the universe and the material part which is the average density of the universe .This proposed definition of the cosmological constant will not only enable us to use the simple model of radial time and spherical space but will also solve all the problems of modern cosmology which are generated from the dependence of the global geometry of the universe on its density like the Cosmological Constant Problem without hypothetical concepts (dark energy, inflation, multi-verse, extra dimensions … etc.).

This will not affect the successful local application of the field equation because of the small value of the average density compared to the density of the source of the gravitation field (the zero-point vacuum energy density is canceled out because it is a part of both the cosmological constant and the stress-energy tensor)

Now, let us turn to the second difficulty with our proposed model of the accelerating expansion of the universe or more precisely the cosmological red-shift which is assumed to be a result of the acceleration of the expansion. Surprisingly, our simple spherical model which denies this acceleration offers another interpretation of this cosmological red-shift. It can be proved mathematically by analyzing the world-line of light as it travels through this shape of space-time between the source and the observer that it is a logarithmic spiral which leads to a red-shift given by:

Redshift is equal to e^(angle between the world-line of the source and the observer) _ 1

This agrees with the observational data and reproduces Hubble’s Law in small values of this angle.