Scientific Framework

The ÆTHER/TSTU
Cosmological Theory

A scalar-tensor extension of General Relativity introducing a dynamic field φ that modifies gravity depending on local density — passing all solar-system tests while resolving several cosmological tensions.

Overview

The ÆTHER/TSTU framework (Tensor-Scalar Theory with Universal coupling) is an extension of General Relativity in which a scalar field φ — representing fluctuations of a cosmological mass density ΔM — couples non-minimally to matter. This coupling is mediated by a conformal factor \(\tilde{A}(\phi)\), creating an environment-dependent effective gravitational coupling \(G_{\rm eff}\).

The key physical insight is a chameleon screening mechanism: in high-density environments (stellar interiors, Solar System), the scalar field is heavily suppressed, recovering standard GR. In low-density environments (cosmic voids, galactic halos), the field becomes active, enhancing gravity and producing observable signatures.

Independent research. This framework was developed entirely outside academic institutions. All papers are deposited on Zenodo with open access. No peer review has been completed as of April 2026.

Mathematical Framework

Action & Lagrangian

The TSTU action in the Einstein frame is:

Eq. 1 — Einstein frame action
\[ S = \int d^4x \sqrt{-g} \left[ \frac{M_{\rm Pl}^2}{2} R - \frac{1}{2}(\partial\phi)^2 - V(\phi) + \mathcal{L}_m\!\left(\psi,\, \tilde{A}^2(\phi)\,g_{\mu\nu}\right) \right] \]

where \(R\) is the Ricci scalar, \(V(\phi)\) the scalar potential, and \(\tilde{A}(\phi) = e^{\beta\phi/M_{\rm Pl}}\) the conformal factor coupling the scalar field to matter, with \(\beta = 0.095\). In the Einstein frame, gravity is minimal (\(\frac{M_{\rm Pl}^2}{2}R\)) and the scalar-matter coupling appears through the conformal metric \(\tilde{A}^2(\phi)\,g_{\mu\nu}\).

The scalar potential takes a sextic form with a negative quartic term, which creates a secondary well enabling field saturation and the G_eff amplification mechanism:

Eq. 2 — Sextic potential (TSTU)
\[ V(\phi) = \frac{1}{2}m^2\phi^2 - \frac{\lambda_4}{4}\phi^4 + \frac{\lambda_6}{6}\phi^6 \]

The negative quartic term (\(-\lambda_4\phi^4/4\), with \(\lambda_4 > 0\)) is essential: it creates a secondary minimum that enables oscillonic (Ætheron) solutions and drives the field saturation underlying \(G_{\rm eff,max} = 1.35\,G_N\) (Paper XII). The stabilising sextic term prevents runaway behaviour.

Field Equations

Varying the action with respect to \(g_{\mu\nu}\) and \(\phi\) gives the modified Einstein equations and the Klein-Gordon equation:

Eq. 3 — Modified Einstein equations
\[ G_{\mu\nu} = \frac{1}{M_{\rm Pl}^2}\left[ T^{(\phi)}_{\mu\nu} + \tilde{A}^2(\phi)\,T^{(m)}_{\mu\nu} \right] \]
Eq. 4 — Klein-Gordon equation for φ
\[ \Box\phi = V_{,\phi}(\phi) - \beta\,\frac{\tilde{A}(\phi)}{M_{\rm Pl}}\,T^{(m)} \]

The effective gravitational coupling felt by matter is:

Eq. 5 — Effective gravitational coupling
\[ G_{\rm eff} = G_N \left(1 + 2\beta^2\right) \quad \text{(unscreened cosmological regime)} \]

Modified Friedmann Equations

In a flat FRW background with scale factor \(a(t)\), the Friedmann equations become:

Eq. 6 — Modified Friedmann equations
\[ H^2 = \frac{1}{3M_{\rm Pl}^2}\left[\rho_m + \rho_\phi\right], \quad \rho_\phi = \frac{\dot\phi^2}{2} + V(\phi) \] \[ \ddot{a}/a = -\frac{1}{6M_{\rm Pl}^2}\left[\rho_m + 3p_m + \rho_\phi + 3p_\phi\right] \]

The dark energy equation of state follows a CPL parameterisation: \(w(a) = w_0 + w_a(1-a)\), with MCMC best-fit values \(w_0 = -0.750\), \(w_a = -0.420\).

Screening Mechanism

The compatibility of ÆTHER/TSTU with precision solar-system tests is ensured by two complementary screening mechanisms.

Chameleon Screening

In high-density environments, the effective mass of φ becomes large, suppressing its range. The effective coupling is:

Eq. 7 — Effective coupling under chameleon screening
\[ \beta_{\rm eff}(\rho) = \beta \cdot \frac{R_s}{r} \cdot f(\rho/\rho_c) \quad \text{with} \quad R_s = \frac{0.1}{\beta} \]
Location β_eff value Screening regime
Earth surface4.2 × 10⁻⁸Strongly screened
Solar corona~ 10⁻⁷Strongly screened
Galactic halo (10 kpc)~ 0.01Partially active
Cosmic voidβ = 0.095Fully active

Vainshtein Screening

At non-linear scales, kinetic braiding suppresses the scalar force. The Vainshtein radius is:

Eq. 8 — Vainshtein radius
\[ r_V = \left(\frac{r_s}{2\Lambda^3}\right)^{1/3}, \quad \Lambda^3 = M_{\rm Pl} H_0^2 \]

Inside \(r_V\), the scalar force is suppressed by \((r/r_V)^{3/2}\), recovering GR. This mechanism ensures solar-system tests pass with \(\delta G/G \lesssim 3.5 \times 10^{-4}\) at Earth — well below the Cassini bound of \(10^{-5}\) (Paper XI).

MCMC Constraints from Pantheon+

The free parameters of the model were initially constrained using a Markov Chain Monte Carlo analysis of the Pantheon+ Type Ia supernova dataset (1701 SNe Ia, 0.001 ≤ z ≤ 2.26):

Best-fit parameters — Paper I & II (Dec. 2025)
\[ H_0 = 76.2 \pm 0.8 \ \text{km/s/Mpc}, \quad \beta = 0.095 \pm 0.003, \quad \mu-1 = 0.018 \pm 0.002 \] \[ w_0 = -0.750,\quad w_a = -0.420,\quad \chi^2/{\rm dof} = 1.03 \]
📄 Paper XV update (May 2026, §3.5). The Paper II value \(H_0 = 76.2\) is identified as a statistical circularity artifact of the joint TSTU–cosmological likelihood under the fixed-β prior. A non-circular ΛCDM-pure refit of the same Pantheon+SH0ES dataset (1657 SNe + 77 Cepheid calibrators), with the full STAT+SYS covariance matrix and no TSTU constraint of any kind, yields:
Non-circular ΛCDM-pure refit — Paper XV §3.5 (May 2026)
\[ H_0 = 73.42 \pm 1.01 \ \text{km/s/Mpc}, \quad \Omega_m = 0.333 \pm 0.018 \] \[ M_B = -19.248 \pm 0.029,\quad \chi^2/{\rm dof} = 0.897 \]
This is in 0.29σ agreement with the standard SH0ES value (73.0 ± 1.0). The refined TSTU prediction is now \(H_0(z=0.5) \simeq 71.5\) km/s/Mpc (Paper XV §3.6), in 1.90σ marginal tension with the ΛCDM-pure fit and to be discriminated by TDCOSMO 2027–2030 gravitational-time-delay measurements.

Testable Predictions

Five predictions were pre-registered on Zenodo (Paper IX, 2025) before the Euclid DR1 data release expected in October 2026. This constitutes a hard falsifiability criterion.

\(\mu_{\rm voids} \approx 1.018\)
Void lensing enhancement

Unscreened φ field in cosmic voids produces enhanced weak lensing. Measurable by Euclid VIS + NISP.

Euclid DR1 · Oct 2026
\(f\sigma_8(0.5) = 0.468\)
Growth rate suppression

Modified growth of structures at z = 0.5 due to kinetic braiding. Euclid spectroscopic survey.

Euclid DR1 · Oct 2026
\(E_G\) deficit 1.1–3.4%
Gravitational slip

Deficit in the \(E_G\) cross-correlation estimator probing the gravitational slip parameter \(\eta \neq 1\).

Euclid DR1 · Oct 2026
\(\Delta t_{\rm coll} = 52\) Myr
JWST early collapse

Earlier gravitational collapse at z ~ 9.5 explains JWST massive galaxy excess. ΔlogM★ = +0.25 dex.

Consistent · JWST data
\(H_0(z=0.5) \simeq 71.5\)
Hubble constant (mid-redshift)

Paper XV §3.6 prediction (linear-growth reframing). The Paper II value (76.2) is superseded as a circularity artifact (Paper XV §3.5).

TDCOSMO test 2027–2030

Model Limitations & Open Problems

Transparency note. The following limitations are explicitly acknowledged in the papers. Independent verification is actively sought.

Analytical enclosure of G_eff,max (Paper XIII). The N-body result \(G_{\rm eff,max} = 1.35\,G_N\) is now analytically bounded from both sides: \(1.070 = G_{\rm eff}^{\rm BG} \leq G_{\rm eff,max} \leq G_{\rm eff}^{\rm lin} = 1.623\). Both bounds are parameter-free from β = 0.095. The exact value 1.350 requires a non-linear damping factor \(\mathcal{A} = 0.624\) — a falsifiable conjecture for 3D PDE simulation. This closes the open problem of Paper XII to the extent possible analytically.

Simulation scope. JWST N-body simulations are 2D, Newtonian, without baryonic feedback or cosmological expansion. They provide proof-of-concept, not production-level cosmological forecasts.

Consciousness module. Papers VII and the Brain simulation mode are explicitly exploratory. The Kuramoto coupling K_eff/K_c ≈ 2 result is a formal analogy, not a physical prediction about consciousness.

No peer review yet. As of April 2026, the ÆTHER/TSTU papers have not undergone formal peer review. Feedback and critical analysis are welcome via the contact page.

Biology — Cross-Scale Applications (Paper V)

Paper V extends the same Klein-Gordon field formalism to biological systems, proposing that pathological transitions — from healthy tissue to cancer, balanced cognition to neuroinflammation, metabolic homeostasis to syndrome — share universal dynamical signatures.

Distinct research programme. Paper V and its addenda constitute a separate biological application of the ΔM framework. They are not part of the cosmological core (Papers I–IV, VI–XIV). Their epistemological status is exploratory and phenomenological — empirical validation with clinical data is ongoing.

The Master Equation Across Scales

The same forced, damped Klein-Gordon equation that governs scalar field dynamics in cosmology is applied to biological fields:

Paper V — Master equation for biological transitions
\[ \frac{\partial^2 \Phi}{\partial t^2} + \Gamma\frac{\partial \Phi}{\partial t} - c^2\nabla^2\Phi + V'(\Phi) = J(x,t) \] \[ \Delta M = J - \Gamma\frac{\partial\Phi}{\partial t} \quad \text{(system fate parameter)} \]

The key parameter ΔM determines system fate: sustained ΔM > 0 drives pathological bifurcations when the effective mass \(m^2_{\text{eff}} = V''(\Phi) \to 0\), while ΔM < 0 enables homeostatic recovery.

Three Biological Scales

The framework is applied at three independent scales, each with its own model, parameters, and timescale:

Scale Model Application Timescale
Tissue Klein-Gordon PDE Tumour dynamics · J_c = 0.77 Hours–3 days
Neural E-I-S-N coupled ODEs Cortical neuroinflammation 10–30 days
Systemic 6-organ Kuramoto Metabolic syndrome · R < 0.3 Circadian (24h)

Validated Prediction S1 — Glucose Variability

The most empirically tested prediction of Paper V concerns metabolic syndrome. Prediction S1 states that glucose coefficient of variation (CV) ≥ 30% is an early warning signal preceding diabetes onset.

RR = 2.36 [2.09, 2.65]
NHANES 2017–2020

Real-world cross-sectional data, n = 3,138. Glucose CV ≥ 30% → prediabetes. AUC = 0.945.

Empirically confirmed
RR = 1.68 [1.55, 1.80]
CGM Gold-Standard Simulation

Calibrated to literature longitudinal estimates (HR ~ 1.5–2.0). Consistent with causal interpretation.

Calibrated · consistent
m²_eff → 0
Universal early warning

Effective mass approaching zero precedes bifurcation by 5–20 days. Proposed as universal biomarker for pathological transitions.

Clinical validation needed
Limitation. These results demonstrate association, not causation. The NHANES analysis is cross-sectional and uses a proxy CV measurement (HbA1c–fasting discrepancy, r ~ 0.3–0.5 with true CGM CV). Longitudinal validation (UK Biobank, Framingham) is the recommended next step.
📄
ÆTHER/TSTU Publications
Full archive available on Zenodo • ORCID 0009-0006-9944-4606

To ensure you always have access to the most up-to-date versions, addenda, and new releases, the complete list of papers, datasets, and simulation scripts is maintained directly on the Zenodo repository.

🔬 Access the full ÆTHER/TSTU collection on Zenodo zenodo.org → 📚 AETHER: De la Cosmologie à la Conscience (Preprint) book.html →
💡
Support the research
Independent research — zero institutional funding
This work is produced entirely outside any academic institution — no grant, no laboratory, no public or private funding. The papers, the book, the interactive simulator and all numerical analyses were carried out on personal time and personal funds. Any contribution, however modest, directly helps fund research time, computing resources and publication costs.
💳 Soutenir via PayPal 📱 Soutenir via Paylib

Les dons ne sont pas déductibles fiscalement. Ils vont directement au chercheur. Merci. 🙏

© 2025–2026 Vincent AUFRAY — ÆTHER/TSTU Framework