Relational Cosmological Superposition Theory: From the Informational Metric to Cosmology

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We propose a complete relational theory in which physical variables are not primitive but rather emergent from patterns of correlation. We postulate two ontological regimes: a S silent state, of zero relational entropy, timeless and ageometric, and a set of R relational states, where the growth of relational entropy SR enables a notion of time and an effective metric. The observer/observed separation is modeled as a choice of factorization of the Hilbert space, and it is precisely that choice which makes variables like space, time, and gravity exist.
Formally, we define SR as a sum of mutual information terms over families of bipartitions and reconstruct a metric gμν [I] from diffusion distances in the correlation graph. We show that informational null trajectories (those with minimal variation δSR = 0) define the causal boundary and provide an informational interpretation of c; coherent electromagnetic modes approximate this limit and act as windows from the R domain to S. The effective dynamics is implemented by means of an AQUAL-type action with an environmental acceleration scale a0(S); we demonstrate stability (absence of ghosts) in the 4D scalar–tensor extension and guarantee Lorentzian signature in the metric reconstruction.
At cosmic scale, we replace initial/final conditions with atemporal boundaries in S and derive Friedmann-type effective equations with a0(S)(z). Two paths lead R → S: extreme dispersion (homogenization of correlations) and extreme concentration (operatively dimensionless curvature). We present quantitative predictions and falsifiers: RAR band and evolution, strong lenses with the same μ and a0(S), photon coherence versus ∥∇S∥, BTFR shifts, speed/non-dispersion of gravitational waves, and a CMB/BAO/f σ8 fitting scheme to compare with ΛCDM. The theory thus becomes operational and falsifiable from the galactic scale to the cosmological scale.

The conceptual framework and original ideas are my own. Computational tools, including AI assistance, were used to support the mathematical formalization and structuring of the manuscript.