Structural Selection · Dynamic Fields · Observable Cosmology · 2026

Version 10 · Dynamic Structural Selection in Cosmology

MAAT Dynamic Structural Selection

A complementary layer for physics: standard dynamics determines what is possible, while structural selection ranks what remains coherent enough to be realised.

Dynamics makes possibilities. Structure selects persistence.

Diagram of the MAAT Structural Selection Principle with dynamical base, master formula, structural selection layer, outcome, ingredients, and applications. — The MAAT Structural Selection Principle as a full input map: dynamics, reference measure, primitive defects, normalisation, sector weights, and selection rule.

31H(z) chronometer points

15.3661fixed MAAT χ²

0.5299best reduced χ²

581/616stable scan branches

See the H(z) test Read Paper 32 GitHub Repository

Plain language

The core idea

Imagine the universe as an orchestra. Cosmology tells us the tempo: how fast the universe expands. MAAT asks a second question: are the instruments still playing together coherently?

In technical language, MAAT adds a structural selection layer on top of ordinary dynamics. It does not replace field theory, general relativity, or ΛCDM. It asks which dynamically admissible configurations have enough internal support to persist.

Why it matters

From idea to testability

The dynamic MAAT programme turns structural weights into response fields, couples them to effective cosmology, and then computes observables. That makes the framework falsifiable: it can now be compared with data.

defects
d_a

covariance
C_ab

response
λ

cosmology
H(z)

data
χ²

The five structural sectors

MAAT evaluates configurations through five complementary structural supports.

H · Consistency

Does the configuration satisfy the equations or internal rules of the system?

B · Balance

Are constraints, symmetries, and conservation-like relations respected?

S · Activity

Is there controlled dynamical richness rather than frozen or chaotic behaviour?

V · Connectivity

Are the degrees of freedom coherently coupled instead of fragmented?

R · Robustness

Does the configuration remain stable under perturbations and near constraints?

Master formula

The selection layer

MAAT starts from ordinary dynamics \(S_0\) and adds a structural cost \(F_{\mathrm{MAAT}}\). Lower structural cost means stronger support.

\[ Z_{\mathrm{MAAT}}[J] = \int d\mu_0[X]\, \exp\left[ \frac{i}{\hbar}S_0[X] - \beta F_{\mathrm{MAAT}}[X] + J\cdot O[X] \right] \]

Structural support

The MAAT cost

Each sector contributes a defect \(d_a[X]\), converted into a support factor \(\Gamma_a[X]\). The weights \(\lambda_a\) set how strongly each sector shapes the final ranking.

\[ F_{\mathrm{MAAT}}[X] = -\sum_{a\in\{H,B,S,V,R\}} \lambda_a \log(\epsilon+\Gamma_a[X]), \qquad \Gamma_a[X]=\frac{1}{1+d_a[X]}. \]

From structural selection to cosmology

The current application computes observable expansion and growth proxies from the stable MAAT scalar branch.

Expansion

H(z)

The model predicts an expansion curve that can be compared directly with chronometer data.

3H² = ρ_m + ρ_r + ρ_Λ + ρ_MAAT

Dark-energy-like sector

w(z) and Ω_MAAT

The MAAT contribution remains small and behaves as a subdominant effective sector.

w_MAAT = p_MAAT / ρ_MAAT

Structure

Growth proxy

The framework also prepares a route toward growth observables such as fσ8.

ΔH/H = (H_MAAT-H_LCDM)/H_LCDM

Four-panel summary of MAAT observable predictions: Hubble history, relative deviation, equation of state, and growth proxy.

Observable prediction layer: expansion history, relative deviation, equation of state, and growth proxy.

Chi-square heatmap over MAAT parameter scan.

Paper 32 parameter scan: stable branches are evaluated by chronometer chi-square.

First data contact: the H(z) test

Paper 32 compares the MAAT expansion branch with 31 Cosmic Chronometer measurements.

Result

Close to ΛCDM, but not favoured

The conservative reading is important: MAAT survives this first diagnostic contact with H(z) data, but it does not outperform ΛCDM.

14.8759ΛCDM χ²