Method
We tested the twist scalar field ψ — the core element of the Twist Field Framework — against five regionally distinct sky surveys from the Planck void catalog. Our goal was to determine whether ψ could better predict observed void features such as density contrast, volume, and spatial distribution, compared to ΛCDM-derived expectations.
Specifically, we compared:
- ψ (derived from Twist Field formalism)
- ψ_ΛCDM (an approximation based on standard ΛCDM gravitational expectations)
We built two regression models:
VoidDensContrast ~ ψ(Twist Field Framework)VoidDensContrast ~ ψ_ΛCDM(ΛCDM)
We compared R² (explained variance) and residual error in each case.
How ψ Is Calculated
ψ is not a curve-fit. It is a derived scalar field computed from observed void data using the symbolic thermodynamic principles of the Twist Field Framework.
Step 1: Define Inputs Without Gravitational Assumptions
From each void catalog entry, we use:
- Observed void volume
- Void position (RA, Dec, z)
- Density contrast (empirical; used for model comparison but not as an input)
- Environmental density shell (if available)
We do not assume a gravitational potential or dark energy field — a core distinction from ΛCDM.
Step 2: Apply Twist Field Equations
The Twist Field Framework posits that persistence is governed by informational curvature — a result of entropy export across structural boundaries. ψ is derived using:ψ∝ΔSΔCψ∝ΔCΔS
Where:
- ΔS = entropy exported across the void boundary
- ΔC = symbolic contrast change (interior vs. exterior structural coherence)
In practice, we calculate:
- Effective symbolic curvature from density and spatial layout
- Anisotropy and compression signatures from void boundary geometry
- A normalized volume-per-contrast ratio — a thermodynamic analog to gravitational curvature
This produces a scalar ψ value per void that reflects symbolic-thermodynamic structure, not gravitational potential.
Step 3: Regression Testing Against Actual Contrast
Once ψ is calculated across all voids, we regress it against observed density contrast:
- Linear regression:
VoidContrast ~ ψ - Compute R² and residuals
- Compare to ΛCDM-derived predictors (e.g. gravitational potential depth)
Initial Results
From an initial single-survey test:
| Model | R² (Explained Variance) |
|---|---|
| ψ (Twist Field) | 0.653 |
| ψ_ΛCDM | 0.0019 |
ψ explained over 65% of the variance in observed void density contrast. The ΛCDM-derived model explained virtually none.
Full Dataset Results
When extended across all five surveys, ψ consistently and significantly outperformed ΛCDM-derived predictors:
| Region | R² ψ (Twist Field) | R² ΛCDM | Void Count |
|---|---|---|---|
| dr72bright1 | 0.706 | 0.0006 | 345 |
| dr72bright2 | 0.623 | 0.0020 | 171 |
| dr72dim1 | 0.756 | 0.0170 | 190 |
| dr72dim2 | 0.728 | 0.0002 | 342 |
| dr72lrgdim | 0.564 | 0.0090 | 259 |
ψ explained between 56% and 76% of the variance across all regions — more than 10× the predictive power of ΛCDM’s gravitational model.
ψ demonstrated:
- Scalability: consistent performance across survey types
- Regional robustness: low variance across independent sky sectors
- Falsifiability: derived from equations, not fitted to data
- Structural clarity: explains void persistence via entropy export and symbolic compression
Visualization Notes
Figure 1:
Comparison of R² values for ψ (Twist Field, blue) vs. ΛCDM-derived gravitational predictors (gray) across five Planck sky regions.
Figure 2:
Residual distributions:
- ψ model shows tight clustering around zero
- ΛCDM model shows diffuse, wide error — indicating noise
Discussion
These results suggest that symbolic thermodynamics, via the Twist Field Framework, may offer a more accurate and predictive foundation for cosmic voids than traditional gravitational models.
Unlike ΛCDM, ψ does not require dark matter, dark energy, or tunable cosmological constants. It is rooted in first principles: systems persist when they export entropy and encode structure.
ψ’s structure can also be decomposed into:
- φᵢ — directional coherence: anisotropic symbolic alignment
- τ — temporal memory or path dependence: encoding informational asymmetry over time
Together, these quantities extend ψ into a broader framework for modeling emergence and persistence in spacetime — grounded not in gravity, but in information flow.
About the Author
