Conclusion.

Starting from the field equation presented in a former paper [1] we have presented new results, based on numerical simulations, performed by F. Lansheat. This provides a possible explation of the spongy very large structure of the Universe and is an alternative to the classical pancakes theory, fot our structures are stable over a period of time comparable to the age of the Universe. Then we developped a theory of inverse gravitational lensing : the observed lensing effects could be mainly due to the effect of surrounding antipodal matter, acting like a distribution of negative mass, than to the action of the galaxy itself. This challenges the dark matter concept. Then, starting from the field equation S = c (T - A(T)) we have developped a cosmological model with "variable constants". Because of the hypothesis of homogeneity (T = A(T) = constant over space) the metric must be solution of the equation S = 0, although the total mass of this closed universe is non-zero  (T¹0). In order to avoid the triviality of the classical subsequent solution R » t, we have built a solution with "variable constants". We have derived the laws linking the different constants of physics :
G , c , h , m in order to keep the basic equations invariant, so that the variation of these constants is not measurable in the laboratory. The only effect of this process is the red shift, due to the secular variation of these constants.

...All the energies are conserved, but not the masses. We have found that all the characteristic lengths (Schwarzschild, Jeans, Compton, Planck) vary like the characteritic length R, whence all the characteristic times vary like the cosmic time t.

...As the energy of the photon hn is conserved over its flight, the decrease of its frequency is due to the growth of the Planck constant h » t

...In such conditions the field equations has a single solution, corresponding to a negative curvature and to an evolution law : R » t ^2/3.

...The model is no longer isentropic and s » Log t. The cosmologic horizon varies like R, so that the homogeneity of the Universe is ensured at any time, which challenges the inflation theory. We refind, for moderate distances, the Hubble's law. We find a new law : distance = f(z), very close to the classical one for moderate red shifts.

...An observational test is suggested, based on the values of the angular sizes of distant objects. Comparing the available data to the predictions of our model and to those of the (peculiar) Einstein-de Sitter model, we find a slight advantage for the first. Obviously, a single test cannot valid such a model.

 
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Achnowledgements :

This work is supported by the french CNRS and by the A. Dreyer Brevets et Développement company