As shown earlier: 

* (AIM- ab initio mundu (lat.) – from the beginning of the world).

Thus, the AIM theory is an open FK model with an increasing number of particles and with “running” ones, i.e. J-dependent; periods, masses and potential amplitudes.

In systems with periodic potentials, inhomogeneous dynamic solutions inevitably arise that are not destroyed. Consequently, in a system with potential (1) it is impossible to obtain a homogeneous solution as the final result. 

In this regard, it is necessary to introduce additional terms into Lagrangian (1), ensuring the destruction of nonlinear excitations. We believe that the initial terms of the “destruction mechanism” should be the first and second harmonics V(J) with the main and doubled periods alternating on (off) depending on the parity of J. 

We expect that in a system with the first and second harmonics alternately turning on (off) the previous one-dimensional solitons stop, but over time two-dimensional non-decaying dynamic excitations are formed.

After some time J_K ~ J₀ in (1), the following harmonics V_K(J) are turned on (off). At points J = J_K on the temporary dislocation chain of the AIM system, phase transitions occur with a change in the spatial dimension of dynamic excited states.

To summarize, for the AIM model we write: (1), 

where is the “destruction mechanism”, with each moment of time divided into K-instants, with the corresponding harmonics of the external potential. 

From general considerations it follows that V_K(J) ~ V₀(J), V₀(J₀) = 0. The phase transition points J_K are determined by inequalities (1).

From a cosmological point of view, the number of moments of the time is equal to the optimally round number, i.e. .

Let’s compare the generally accepted concepts with the concepts of the AIM model:

1. “Matter” – energy excitations on the time chain;

2. “Dark energy” - one-dimensional phase of matter (stationary); 

3. “Dark matter” - two-dimensional phase of matter (stationary);

4. “Visible matter” - three-dimensional phase of matter (dynamic);

5. The next phase is four-dimensional, etc.

Let us estimate the phase composition of matter at different stages of the development of the Universe.

Let X be the dynamic weight part of the Universe, then for a state of K phases we write:

  X+KX+K²X+K³X+…+K^K-1X=1; those. X= (K-1)/(K^K-1).

When K=3, X+3X+9X=1; X₃≈8%. Based on estimates of modern cosmology, for time intervals T_k we have:

T₃=30 billion years; T₂=90 billion years; T₁=180 billion years; T₄=7.5 billion years; T₅=1.5 billion years...; T = ∑T_k ≈ 310 billion years.

The AIM+ model assumes the return of the emitted atoms of the DFK –chain to the point of their departure, with the formation of two interacting subsystems in the AIM model.