1- Introduction

Within the NTU framework, cosmology is not interpreted as the evolution of a pre-existing spacetime manifold, but as the progressive emergence of stable relativistic structures from an initially timeless, rigid, and stochastic relational substrate, whose underlying correlations are not initially constrained by relativistic causal propagation (before relativistic causal structure).

The framework investigates whether geometry, causality, and temporal ordering may arise through successive relational transitions occurring prior to determined spacetime reconstruction.

Unlike standard cosmological approaches, the primordial state is not described through metric expansion inside an already defined temporal framework. Instead, the NTU approach considers a pre-causal relational regime where neither global chronology nor stable geometry are fundamentally defined.

The NTU framework does not arise independently from the historical development of modern physics. Some of its underlying transformation principles may already be indirectly reflected in Louis de Broglie’s early attempts to reconcile coherent wave structures with relativistic constraints, difficulties that eventually contributed to the acceptance of probabilistic quantum interpretations.

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1.1 Pre-Causal Relational Substrate

The primordial state is modeled as a stochastic relational ensemble:

$\mathcal{R}_0 = \{ r_{ij}(\omega) \}$

where:

• $r_{ij}$​ represents fluctuating relational connections,
• $\omega$ denotes stochastic configurations,
• and no global metric structure is initially imposed.

In this regime:

• temporal ordering is undefined,
• causality is non-determined,
• geometric consistency remains local and unstable.

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1.2 Emergence of Relational Coherence

A first transition may correspond to the appearance of coherent relational correlations:

$\langle r_{ij} r_{kl} \rangle \neq 0$

This stage may generate primitive geometric consistency without fully stabilized spacetime structure.

The emergence of coherence may progressively reduce stochastic degrees of freedom and produce large-scale relational rigidity.

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1.3 Temporal Symmetry Breaking

The NTU framework investigates whether temporal orientation may emerge through spontaneous symmetry breaking mechanisms:

$\mathcal{T} : t \rightarrow -t$

The breaking of temporal symmetry could then generate:

• causal asymmetry,
• irreversible relational ordering,
• effective temporal directionality.

In this interpretation, time does not pre-exist the universe but emerges dynamically from relational stabilization.

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1.4 Relativistic Reconstruction

Stable relativistic spacetime may emerge only after sufficient relational rigidification:

$ds^2 = g_{\mu\nu} dx^\mu dx^\nu$

The metric tensor would therefore represent an effective large-scale description reconstructed from deeper relational processes.

General relativity would then appear as an emergent macroscopic limit rather than a fundamental ontological structure.

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1.5 Cosmological Consequences

Within this framework, several cosmological questions may acquire alternative interpretations:

• primordial homogeneity,
• emergence of causal horizons,
• origin of temporal asymmetry,
• gravitational organization,
• CMB and primordial neutrino correlations,
• large-scale structure stabilization.

The NTU framework further investigates whether some early cosmological phases conventionally interpreted as temporally separated could instead emerge from common relational transitions reconstructed secondarily through relativistic spacetime.

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1.6 Perspectives

The NTU cosmological approach remains exploratory and under development.

Current investigations focus on:

• stochastic relational dynamics,
• emergence of geometric stability,
• causal reconstruction mechanisms,
• and possible observable cosmological signatures associated with successive rigidification transitions.

2 – NTU cosmological genealogy tree

NTU Primordial State
│
├── Atemporal 3D substrate
│ ├── Planck-scale rigid nodes
│ ├── no time
│ ├── no causality
│ ├── no mass
│ ├── no spacetime
│ └── pre-links only
│
├── Proto-electrophotonic field emergence
│ │
│ ├── first global pre-link coherence
│ ├── no mass generation
│ ├── no baryonic matter
│ └── photon precursor state
│
│ Possible descendants:
│ ├── Electromagnetic field
│ ├── Fossil photons
│ └── Massless photon ontology
│
├── Inflation-like expansion
│ │
│ ├── rapid growth of NTU connectivity
│ ├── increase of accessible configurations
│ └── causal horizon formation
│
│ Possible interpretation:
│ ├── standard Inflation
│ └── inflaton as effective field
│
├── First causal rigidification
│ │
│ ├── emergence of ordered relations
│ ├── causal graph formation
│ └── pre-time causality
│
│ Correspondence:
│ └── Causal Set Theory
│
├── Photon–Neutrino entanglement era
│ │
│ ├── fossil photon structures
│ ├── neutrino-photon coupling
│ ├── emergence of neutrino sectors
│ └── flavor differentiation
│
│ Possible descendants:
│ ├── νe
│ ├── νμ
│ └── ντ
│
├── Quantum-geometric rigidification
│ │
│ ├── stable pre-link networks
│ ├── quantized surfaces
│ ├── quantized volumes
│ └── geometric emergence
│
│ Correspondence:
│ ├── Loop Quantum Gravity
│ └── Spin Foams
│
├── Emergence of spacetime
│ │
│ ├── stable temporal direction
│ ├── Lorentzian geometry
│ └── macroscopic causality
│
│ Correspondence:
│ └── CDT
│
├── Field differentiation era
│ │
│ ├── gravitational field
│ ├── electromagnetic field
│ ├── weak field
│ ├── strong field
│ └── Higgs-related structures
│
│ Possible interpretation:
│ ├── field condensations
│ ├── symmetry breakings
│ └── effective quantum fields
│
├── Projection era
│ │
│ ├── realization of events
│ ├── measurement
│ └── observable universe
│
│ Correspondence:
│ └── Holography
│
├── Extended structures
│ │
│ ├── strings
│ ├── branes
│ └── topological defects
│
│ Correspondence:
│ └── String / Brane theories
│
├── Continuum renormalized limit
│ │
│ ├── effective actions
│ ├── running couplings
│ ├── field stabilization
│ └── continuum approximation
│
│ Correspondence:
│ └── Asymptotic Safety
│
└── Thermodynamic universe
│
├── entropy
├── gravitation
├── large scale structures
└── cosmic evolution

    Correspondence:
    ├── Emergent Gravity
    ├── Entropic Gravity
    └── Fractal Thermodynamics

3- Cosmological chronology and successive phases of rigidification

Phase 0 — Primordial atemporal substrate and inflationary regime

At the most fundamental level, the Universe is described as a non-local stochastic substrate without predefined metric, duration or relativistic causality.

In this regime:

• simultaneity is not yet relative,
• correlations are unconstrained by light-speed propagation,
• physical entities do not yet possess stable inertial structure.

The substrate behaves as a globally correlated relational system whose fluctuations generate the preconditions for spacetime emergence.

Within the NTU framework, the inflationary phase is not interpreted as a rapid expansion of an already existing spacetime. Instead, inflation corresponds to a primordial regime of unconstrained global correlation before relativistic locking. The primordial substrate is instead characterized by unconstrained propagation of stochastic perturbations along what will later become the spatial axis reconstructed by relativistic spacetime.

The apparent superluminal homogenization of the observable Universe therefore does not require actual faster-than-light propagation through spacetime. Rather, it reflects the fact that relativistic causal constraints had not yet emerged.

In this interpretation:

• horizon uniformity arises naturally from pre-causal global connectivity,
• the inflationary regime corresponds to a phase of maximal relational fluidity,
• large-scale isotropy precedes the emergence of relativistic locality,
• spacetime expansion becomes a secondary emergent description reconstructed only after rigidification.