The standard model of modern cosmology is the model of Hot Big Bang. This model, which collects the consensus of a majority of researchers, rests on a certain number of arguments and " evidence ". A handle of irreducible researchers challenges the validity of this model but no competitor model brings, at the present time, a credible alternative to Hot Big Bang (stationary universe of Fred Hoyle, tired light, symmetric universe, variable mass of Halton Arp 1999, etc...).

In spite of its apparent solidity, the model of Hot Big Bang suffers from great weaknesses due at the same time to its development and its consequences. The partisans of Hot Big Bang naturally stress its forces, its detractors its weaknesses.

In 1962, the author, dissatisfied with the model of Hot Big-bang devoted himself to a critical analysis of the bases of this model and established a more satisfactory alternative interpretation, of the well-known facts, according to him. This search led him to a new conception of the "age" of the universe and to the discovery of a parameter that he entitled temporalist constant To, of a value of 4,5546 10.17 seconds, that is to say approximately 14,43 billion years. This constant led him to a temporalist effect or "purpose of escape" with 1 Mpc = 67,71 Km/sec and to a value of Ho = 1 / 4,5546 10.17 sec. These values were established theoretically by the author in 1962. The last data given by WMAP ( February 2003) made it possible to fix the value of the constant Ho of Hubble at 71 Km/sec/Mpc ( with a margin of error of 5 % ) what well confirms the temporalist value of Ho is 67,71 Km/sec/Mpc. ( http://map.gsfc.nasa.gov/m_mm/mr_limits.html ).

If the value of this "age" of the universe is near now to the value of the temporalist constant To, its significance, for the cosmologists, is completely different.

The circumstances of the life made that the author had to give up his search during nearly 40 years. He took them again in 2001. He proposes today the temporalist model which is an alternative to the model of Hot Big Bang.

In a first part, a summary, as short as possible, of the model of Hot Big Bang, is presented, with the presupposed concepts, the forces and the weaknesses of the model.

In the second part, which is the most significant, the temporalist model is exposed, with its concepts, its bases, its multiple consequences, quantum and macroscopic: electric charge, constant of fine structure, redshift, gravitation and great structures of the universe, etc... and its tests. The author endeavoured to banish any arbitrary and unverifiable speculation, in accordance with the precepts of Popper (1934). The author considers, wrongly or rightly, that a model or a theory, based on unverifiable premises and which out of it, gives birth to largely speculative assumptions, cannot claim with the row of scientific valid model, because his theory is stripped of the rigour which is necessary for this qualification.