Discrete universe theory: unified effective extension from a fractal causal network

Resumo

We present the Discrete Universe Theory, an Effective Field Theory whose high-energy completion is described by a discrete causal network with a spectral fractal dimension of approximately 2.72, inspired by Causal Dynamical Triangulations. In this approach, continuous spacetime emerges from a fundamental discrete structure made of interconnected causal elements, while matter, fields, and observed interactions arise as collective excitations of this network.

Spectral analysis of the network Laplacian reveals a self-similar hierarchy of eigenvalues governed by the golden ratio, giving rise to a discrete tower of Kaluza-Klein modes interpreted as the internal fractal structure of quarks. The theory introduces three fundamental complex scalar fields, labeled Phi-h, Phi-l, and Phi-m, each associated with different vacuum densities and responsible for generating observable properties of matter, mass, interactions, and cosmological structure. The Phi-m field acts as a unifying component among the gravitational, dark, and cosmological sectors, while an emergent macroscopic coherence field, Psi-c, describes organized collective states of the vacuum.

The effective action preserves the gauge symmetry of the Standard Model together with an additional Abelian symmetry for a massive dark photon, enabling stable coexistence between matter and antimatter. Electromagnetism is reinterpreted as a dynamical manifestation of fundamental pairs called h-plus and h-minus, from which electric and magnetic fields, the wave-particle duality of light, and the Law of Similars naturally emerge — proposed as a microscopic principle responsible for magnetic alignment and the behavior of macroscopic magnets without violating Gauss’s law.

The model further incorporates a fifth dark dimension associated with the Phi-m field, responsible for holographic movement, for interpreting quantum tunneling as transit through this energy dimension, and for the existence of non-local correlations strongly suppressed at macroscopic scales. Corpuscular light arises as a longitudinal solitonic solution of the effective electromagnetic field, while the local Planck constant becomes dynamically dependent on the vacuum density.

In the cosmological sector, the theory predicts a cyclic universe with alternating phases of contraction and expansion, governed by the dynamics of the fundamental fields. A Markov Chain Monte Carlo fit using data from Planck 2018, Baryon Acoustic Oscillations, and the Pantheon-plus supernova sample yields a Hubble constant of 73.2 plus or minus 1.3 kilometers per second per megaparsec and positive Bayesian evidence (logarithm of the Bayes factor equal to plus 3.2) relative to the standard Lambda-CDM model. All currently considered experimental bounds — including those from the Large Hadron Collider, fifth-force searches, dark photon constraints, Lorentz invariance tests, and precision quantum electrodynamics — remain satisfied within the analyzed parameter space.

The theory proposes a unified framework in which spacetime, matter, fields, gravity, magnetism, and cosmology emerge from a single discrete, causal, fractal structure, providing falsifiable observational predictions and recovering, in the appropriate limits, General Relativity and the Standard Model.