Part IV: The Next Paradigm

Chapter 13 — Cosmic Tests of Informational Holonomy

Empirical strategies for detecting memory, rotation, and curvature at universal scales

At the cosmic scale, IPSC predicts that the universe itself bears the imprint of its informational memory. These imprints appear as large-scale geometric asymmetries — in the polarization of the cosmic microwave background (CMB), in the spatial correlations of galaxies, and in potential global rotation of spacetime. Collectively, these constitute the phenomenon of informational holonomy: residual curvature and torsion left by feedback loops that occurred during earlier epochs of universal self-organization.

Testing these predictions requires bridging cosmology with information geometry. Whereas general relativity describes curvature as a function of stress–energy, IPSC models curvature as a function of informational coherence. Consequently, informational curvature may produce subtle but measurable deviations in the statistical structure of cosmological data. The following three research programs outline feasible empirical pathways to detect such effects using existing and forthcoming astronomical data.

Proposal 1: Polarization Correlations in the Cosmic Microwave Background

Rationale: The CMB records the oldest light in the universe, encoding anisotropies that reflect the geometry of spacetime at recombination. IPSC predicts that informational vorticity — topological twisting of correlations in the informational manifold — induces a preferred orientation in the CMB’s polarization field. This would manifest as non-random alignments in the E–B cross-spectra beyond inflationary expectations.

Methodology: Analyze CMB polarization data from the Planck, ACT, and upcoming LiteBIRD missions. Compute the mutual information between E-mode and B-mode polarization maps as a function of scale:

I(E;B) = ∑_ℓ P(E_ℓ) log[P(E_ℓ)/P(E_ℓ|B_ℓ)]

Under ΛCDM, this mutual information should vanish statistically. IPSC predicts a small but non-zero correlation peaking at multipoles ℓ ≈ 20–40, aligned with the so-called “axis of evil” anomaly. The amplitude of this residual signal quantifies the strength of the universe’s informational torsion.

Expected Signature: Non-random alignment of E–B polarization modes, consistent across independent datasets and not attributable to systematic error or foregrounds.

Proposal 2: Fractal and Topological Correlations in Large-Scale Structure

Rationale: The distribution of galaxies encodes the universe’s long-term feedback between curvature and entropy. IPSC predicts that this structure should exhibit scale-invariant clustering indicative of fractal memory — the geometric “echo” of past informational loops. These patterns should deviate slightly from random Gaussian initial conditions, producing correlated anisotropy across scales of 10–500 Mpc.

Methodology: Use data from the Sloan Digital Sky Survey (SDSS), Euclid, and the Vera Rubin Observatory (LSST) to compute correlation dimension D₂ and mutual information spectra among galaxy distributions:

D₂ = lim_r→0 [log C(r) / log r], I(r) = ∑ p(x,r) log [p(x,r)/p(x)p(r)]

IPSC predicts a mild departure from D₂ = 3 (Euclidean expectation) toward D₂ ≈ 2.95 ± 0.02 at scales where feedback geometry dominates. This fractional deficit corresponds to residual informational curvature, analogous to curvature deviations in general relativity but defined over informational, not spatial, metrics.

Expected Signature: Persistent, statistically significant (≥3σ) fractal correlation across intermediate cosmological scales, independent of observational bias.

Proposal 3: Detection of Cosmic Rotation and Informational Torsion

Rationale: IPSC generalizes the Gödel-like possibility of global rotation: the universe may exhibit weak vorticity arising from informational holonomy accumulated during early epochs. Such rotation would impart measurable signatures in galaxy spin alignments, quasar polarization vectors, and gravitational wave backgrounds.

Methodology: Aggregate spin-direction data from radio and optical surveys (e.g., LOFAR, Pan-STARRS) and cross-correlate with quasar polarization catalogues. Fit a global vorticity parameter ω₀ under the modified Friedmann equations incorporating informational torsion:

H² + (k/R²) = (8πG/3)ρ + ω₀² + Λ/3

IPSC predicts ω₀ ~ 10⁻¹⁷ s⁻¹, corresponding to a small but non-zero cosmological rotation rate. Such vorticity would also polarize the stochastic gravitational wave background, detectable via anisotropies in LISA or pulsar timing arrays (IPTA).

Expected Signature: Coherent preferred-axis alignment in galactic spin and quasar polarization data, consistent with a universal vorticity on the order of 10⁻¹⁷ s⁻¹.

Integration and Cross-Validation

Each of these cosmological tests targets a distinct but complementary manifestation of informational holonomy:

Polarization coupling — evidence of informational torsion during recombination.
Fractal clustering — signature of long-term informational memory in structure formation.
Global rotation — macroscopic residue of universal feedback curvature.

Confirmation of any one would be remarkable; confirmation of all three would constitute strong empirical evidence that spacetime curvature arises not from matter–energy alone but from the geometry of information itself. Negative results, conversely, would falsify IPSC’s cosmological predictions, forcing a reversion to standard ΛCDM with no informational degrees of freedom.

The next chapter unifies these micro, meso, and cosmic tests into a coherent Falsification Program — outlining how IPSC can be systematically challenged, validated, or refuted by experiment. Chapter 14 — The Falsification Program: A Framework for Testing Informational Phase Space Cosmology concludes this empirical section.