MTDF Research.

Overview

MTDF (Mesche's Tensor Dynamics Framework) investigates whether the gravitational phenomena usually attributed to dark matter and dark energy can be reproduced by an effective spacetime strain-tensor field sourced by ordinary baryonic matter. The framework is treated as a falsifiable research programme: every hypothesis is paired with reproducible numerical and observational tests, and every parameter is calibrated against independent measurements rather than fit to the validation data it is then judged against.

The current release (v1.1.7, July 2026) is archived on Zenodo with a stable DOI. Theory version V75, validation workbook V19.

Core framework

A covariant field-theoretic formulation in which the metric responds to a strain tensor Σ_μν = E·S̃_μν sourced by baryonic matter, where the strain S̃_μν is built from the covariant gradient of a displacement-like field ξ_ν and E is an elastic modulus. The framework is governed by four independently calibrated parameters and reduces to general relativity (and to a ΛCDM-like background) in the appropriate limits, producing testable deviations at galactic and large-scale-structure scales while remaining consistent with early-universe and Solar-System constraints.

Validation programme

The validation strategy is two-tiered. First, MTDF must reproduce ΛCDM's predictions in regimes where ΛCDM is heavily constrained, since failing here is a deal-breaker for any alternative cosmology. Second, MTDF must produce falsifiable, testable deviations elsewhere.

Cosmological-scale equivalence with ΛCDM (Planck CMB). Full Planck plik TTTEEE + low-ℓ + lensing MCMC on the corrected v2 implementation, compared against a matched ΛCDM control chain: Δχ² = −1.29 at bounded best fits. This is a maximum-likelihood comparison, not a Bayes factor or Bayesian evidence calculation. The coupling posterior k_f = 0.685 ± 0.500 is consistent with both 0 and 1: Planck alone cannot statistically distinguish MTDF from ΛCDM. This passes the gatekeeper test that any alternative cosmology must clear: precision CMB cosmology is reproduced.

The phenomenology customarily attributed to dark matter and dark energy emerges from the framework rather than being added as separate ingredients. No cold-dark-matter particle species is postulated, and no cosmological constant Λ appears in the equations of motion.

Late-universe and galactic-scale validation (15-pillar programme). Galaxy rotation curves (P1, P1B), cluster dynamics (P2), cosmological background and growth (P3 to P5, P9, P11 to P13), large-scale structure (P6, P8), high-redshift structure (P10, P10B) and astrophysical tests (P7). Headline result on the strict combined dataset: χ²/ν = 1.17 (DOF = 1741); 14/14 counted scalar consistency tests pass within 1σ, with the S₈ and fσ₈ growth rows carried separately as PREDICTION-CONTESTED (sharp sealed predictions in tension with ΛCDM-compressed weak-lensing inferences, under preregistered adjudication; shown as "(cont.)" in the dashboard). No free parameters are tuned per test.

Specific deviations and pre-registered predictions. MTDF predicts measurable signatures that standard ΛCDM does not. A supernova-void cross-correlation analysis (REVOLVER, Phase 3) returns Δχ² = 4.25 (p = 0.039, ~2σ), with all three void catalogues excluding zero at 95%. A pre-registered Jeans-equation forecast for JWST spectroscopy of the CDG-2 dark-galaxy candidate predicts σ_los ≈ 1.5 km/s under MTDF versus ≈ 7.4 km/s under an NFW halo, a clean ~5× separation that future JWST kinematic data will adjudicate. The corrected growth sector adds the registered GH-1 prediction: an fσ₈ excess over ΛCDM rising from about 2 percent at z = 1.5 to 4.1 percent at z = 0, testable by full-survey DESI and Euclid; and the preregistered FWD-S8 programme will test whether published low-S₈ values survive when an MTDF universe is analysed through ΛCDM compression pipelines.

Reproducibility. Every result above is regenerable from the public archive on a single workstation. The interactive Validation_Dashboard_V75.html exposes per-test residuals, χ², parameter sensitivity and goodness-of-fit summaries.