System evolution and cosmology

There is a close analogy between the system evolution kinetics and the variation of the Hubble constant with time according to a relativistic hot big bang cosmology. Two papers have been written on the subject (Crevecoeur, 1997 & 1999).

Let us just recall here that , according to an hot big bang cosmology (see, for instance, Peebles, 1993), the universe is closed and governed by internal forces. It contains its whole energy from the beginning.

If we consider the universe as an evolving system, the interlocking force during its evolution will be gravitation. The adaptation process will lie in the fact that the universe's expansion is partly counteracted by the gravitational forces. According to this interpretation, the resulting evolution kinetics will be given by the observed expansion. The evolution parameter will then be the "scale factor R(t)". Indeed, Robertson and Walker introduced this factor in their metrics in order to have one single parameter for describing the universe's expansion in function of time.

We thus will write Equation E-2 as:


by definition of the "Hubble constant H".

In the classical polynomial models, we find that H=b/t, with, for instance, b=1/2 during the radiation-dominated and b= 2/3 during the matter-dominated era ("Einstein-de Sitter model").

In the exponential models ("de Sitter model", Hoyle and Bondi's model of steady universe, "inflationary models") we have: H=a  constant in time.

Therefore, using a system approach is equivalent to saying that the Hubble constant is not either (1) constant in space but not in time (polynomial models) or (2) constant in both time and space (exponential models), but rather a combination of (1) and (2). It suggests a way to combine the polynomial and exponential models when describing the universe's expansion, while remaining in agreement with Einstein's field equations.

In the adopted point of view, the equations of state are deduced, not imposed from the physics (which would give the classical results). In the second article quoted above, it is shown that this gives a simple procedure to evolve the cosmological parameters smoothly up to now.

It is also shown that "a " must have a non-zero value (even if it is very low compared to H) during the radiation- and matter-dominated eras if the actual pressure/density ratio at the end of the radiation-dominated era is not strictly zero.

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Page last revised: September 7th, 2015

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