IIT 4.0 analysis of the gravitational wave stochastic background
In 2023, NANOGrav announced that pulsars across the galaxy are wobbling in sync — evidence of a background "hum" of gravitational waves filling all of space. But what's making the hum? The leading candidates are:
- Supermassive black hole mergers — billions of galaxy-center black holes spiraling together
- Cosmic strings — hypothetical cracks in spacetime from the early universe
- Primordial gravitational waves — ripples from inflation itself
- Phase transitions — the universe "boiling" as it cooled after the Big Bang
We applied Integrated Information Theory to ask: do these sources leave different causal fingerprints in the frequency spectrum?
Yes. Dramatically so.
| Source | Causal Determinism (EI) | Emergence Index | Effective Rank |
|---|---|---|---|
| SMBH mergers | 1.32 bits | 0.02 | 10/14 |
| Cosmic strings | 0.09 bits | 0.82 | 5/14 |
| Primordial | 0.07 bits | 0.72 | 6/14 |
| Phase transition | 0.20 bits | 0.94 | 4/14 |
SMBH mergers produce a "rich" signal — 10 out of 14 frequency bins carry independent information. Each frequency is doing its own thing. The causal structure is highly deterministic (if you know one frequency, you can predict what's happening nearby) but NOT emergent (the whole equals the sum of its parts).
Exotic sources (cosmic strings, phase transitions) produce a "simple" signal — only 4-6 independent frequencies. But their emergence index is 40-50x higher than SMBH mergers. This means: the whole spectrum is dramatically more structured than its individual frequencies suggest. Zooming out reveals hidden order.
Imagine listening to sound:
- SMBH mergers sound like an orchestra warming up — many independent instruments, each doing their own thing. Rich but disorganized.
- Cosmic strings sound like a single chord — fewer independent notes, but they harmonize in ways that create structure greater than any single note.
This emergence-vs-determinism ratio is a new metric that existing gravitational wave analysis doesn't use. It could help NANOGrav determine what's causing the hum.
Current methods for distinguishing GW sources focus on the spectral slope (how the amplitude changes with frequency). Our approach adds a second axis: causal structure. Two sources with similar spectral slopes could have very different emergence signatures. This is complementary information that doesn't exist in the current analysis toolkit.
All four models produce zero integrated information. This means the GW background — regardless of source — has no irreducible causal structure. Each frequency bin is ultimately independent of the others. The differences show up in emergence (how structure appears under coarse-graining) and determinism (how predictable the causal relationships are), not in Phi itself.
Models: NANOGrav 15-year parameters (A=2.4×10⁻¹⁵, f_ref=1/yr)
- SMBH: h_c(f) ∝ f^(-2/3)
- Cosmic strings: h_c(f) ∝ f^(-7/6)
- Primordial: h_c(f) ∝ f^(-1)
- Phase transition: peaked spectrum at f_peak = 5 nHz
Analysis: 14 frequency bins (f = 1.98-27.7 nHz), exact IIT engine (16,384 partitions per model)
Null test: 100 SMBH noise realizations, z=0.00, p=1.00
Reproduction:
cargo run --release -p gw-consciousness -- --null-samples 100Engine: ruvector-consciousness v2.1.0 Timestamp: 2026-03-31 UTC