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. Four papers have been written on the subject (Crevecoeur, 1997,1999, Feb 2017&Sept 2017).

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:


or:

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 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.

The third article quoted above is an update of the first article taking account of the meanwhile discovery of the acceleration of the expansion.

Similarly, the fourth article quoted above is an update of the second article taking account of the acceleration of the expansion. The major difference is that, instead of imposing the pressure to be nil at present time in order to comply with the equation of state for the matter-dominated era, the pressure - density ratio is left free to be negative. The pressure - density ratio then naturally becomes negative (although close to zero in a first period) at maximum decoupling (379,000 hours). The acceleration of the expansion then starts around 7.12 Gyrs after the big bang as the deceleration parameter "q" becomes negative at this time. It is shown that the contribution of dark energy is negligible during the radiation-dominated era but becomes of the order of the contribution of matter during the matter-dominated era.



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