Asymptotic Null Cosmology (ANC): A Convergence-Based Model of Universal End-State Dynamics

Kevin L. Brown, Independent Researcher
November 2025
DOI: 10.5281/zenodo.17608092

Informational Physics Ontology Paper

Abstract

This paper introduces Asymptotic Null Cosmology (ANC) — a mathematically defined, falsifiable cosmological model describing a Universe that expands indefinitely while approaching finite, convergent limits in expansion rate and entropy. The framework is built from explicit asymptotic constraints on the Hubble parameter H(t)H(t)H(t) and entropy S(t)S(t)S(t), yielding a cosmological end-state that avoids divergent acceleration (Big Rip) and unbounded entropy growth (classical heat death).

The paper further provides a conceptual interpretive layer through Triune Harmonic Dynamics (THD) by mapping large-scale cosmological behavior onto a tri-field system

F(t)=(I(t),E(t),M(t)),F(t) = (I(t), E(t), M(t)),F(t)=(I(t),E(t),M(t)),

representing informational, energetic, and structural degrees of freedom. The THD mapping does not assert physical correspondence; rather, it offers a structured informational lens through which the ANC limit can be represented as a harmonic fixed point.

The model includes complete falsifiability criteria across expansion, entropy, curvature, temperature, and dark-energy equation-of-state measurements, making ANC an empirically testable and structurally transparent cosmological hypothesis.

Core Contributions

1. Convergence-Based End-State Model

ANC defines the end-state of cosmological evolution through two explicit asymptotic constraints:

• H(t)→H∞>0H(t) \rightarrow H_\infty > 0H(t)→H∞>0

• S(t)→S∞<∞S(t) \rightarrow S_\infty < \inftyS(t)→S∞<∞

This produces a Universe that expands indefinitely while approaching stable thermodynamic and informational limits.

2. Informational Null Attractor

The asymptotic Friedmann condition

ρ+3P→0\rho + 3P \rightarrow 0ρ+3P→0

acts as a null attractor for large-scale dynamics, aligning with the ANC requirement that thermodynamic gradients vanish without reaching total equilibrium.

3. THD Tri-Field Interpretation Layer

The paper introduces a structured mapping between ANC and THD:

• I(t)I(t)I(t) tracks informational/entropy-like structure

• E(t)E(t)E(t) tracks energy density

• M(t)M(t)M(t) tracks curvature/structural prevalence

The harmonic projection

ϕ(t)=cII(t)+cEE(t)+cMM(t)\phi(t) = c_I I(t) + c_E E(t) + c_M M(t)ϕ(t)=cII(t)+cEE(t)+cMM(t)

approaches a finite limit under ANC, representing the tri-field equivalent of the asymptotic cosmological fixed point.

4. Full Falsifiability Structure

ANC specifies explicit, testable fail conditions:

• Divergent expansion (H(t)→∞H(t)\rightarrow\inftyH(t)→∞)

• Unbounded entropy growth

• Persistent nonzero curvature

• Phantom-energy equation of state (w<−1w < -1w<−1)

• Temperature collapse to absolute zero

Any one of these firmly falsifies the model.

Key Concepts

Asymptotic Expansion

A non-divergent exponential relaxation of the Hubble parameter toward a finite limit

H(t)=H∞+(H0−H∞)e−kt.H(t) = H_\infty + (H_0 - H_\infty)e^{-kt}.H(t)=H∞+(H0−H∞)e−kt.

Bounded Entropy

Entropy approaches a finite limit rather than diverging indefinitely.

Non-Zero Asymptotic Temperature

The Universe cools but stabilizes at a minimum non-zero temperature T∞T_\inftyT∞.

Informational Structure

ANC’s end-state maintains finite informational order despite vanishing thermodynamic gradients.

THD Harmonic Fixed Point

THD reframes the ANC limit as a stable tri-field equilibrium defined by the harmonic scalar ϕ∞\phi_\inftyϕ∞.

Relation to the THD Research Lineage

This paper connects with prior informational and harmonic frameworks, including:

• Scalar Field Framework for Quantum–Gravity Unification
  https://doi.org/10.5281/zenodo.15686918

• Energy–Information Equivalence (EIE)
  https://doi.org/10.5281/zenodo.16813373

• THD Equilibrium Index (TEI)
  https://doi.org/10.5281/zenodo.16990955

• Scalar Time Index (STI)
  https://doi.org/10.5281/zenodo.17423981

• Recursive Energy & the Mathematics of Awareness
  https://doi.org/10.5281/zenodo.17231648

• Scalar Message Encoding Protocol (SMEP)
  https://doi.org/10.5281/zenodo.17402807 

These works provide mathematical and informational frameworks used here for conceptual interpretation only.

Suggested Reviewer Evaluation Criteria

Reviewers may evaluate the ANC manuscript by:

Mathematical Rigor

• Consistency of convergence conditions

• Validity of asymptotic forms

• Internal coherence with Friedmann constraints

Falsifiability

• Clarity of empirical fail conditions

• Distinction between model predictions and interpretation

Interpretive Layer Clarity

• Appropriateness of the THD tri-field mapping

• Clear separation between cosmological equations and informational interpretation

Contribution to Theoretical Exploration

• Coherence of the ANC construction

• Utility of the convergence-based framing

• Conceptual clarity of the Informational Null Attractor

Keywords

Asymptotic Null Cosmology, bounded entropy, informational attractors, tri-field representation, Triune Harmonic Dynamics, harmonic fixed point, asymptotic expansion, informational structure, falsifiability, cosmological convergence, informational end-state dynamics.