Two testable predictions for space-based gravitational wave detectors: a phase correction and a redshift-dependent activation onset.
During binary black hole inspiral, the STF scalar field produces a correction to the gravitational wave phase. The quadrupole-level STF phase shift scales as:
This correction grows as f6 — a distinctive signature unlike standard GR post-Newtonian deviations. It is suppressed in the current LIGO/Virgo band by the small ratio (H0/ms)² ∼ 10−22, making it undetectable with current instruments. LISA’s lower frequency range and higher signal-to-noise ratios may bring it within reach.
In the paper’s four-level hierarchy, this is a Level 4 (Precision Refinement) test. Detection would constrain STF parameters; non-detection does not falsify the framework. This distinguishes it from the Level 3 predictions (r, Ω, a0) which are independently falsifiable.
This follows directly from the same cosmological threshold that generates the f6 phase correction — not a separate prediction but an epoch-dependent consequence of Prediction #10.
The cosmological threshold condition 𝒟crit(z) ∝ H(z) predicts that the orbital separation at which the STF activates scales with redshift:
The exponent −1/7 is fixed by the Kretschner definition and Peters inspiral scaling (Appendix D.11). This produces a parameter-free prediction: the f6 waveform deviation onset shifts to higher GW frequencies at higher redshift (~8.6% at z = 1). The activated fraction of GW events should decrease with redshift.
| Observation | Consequence |
|---|---|
| Onset frequency scales as H(z)−1/7 | Epoch-dependent threshold confirmed |
| No redshift dependence after time-dilation correction | Threshold model falsified (Lagrangian survives) |
| Wrong exponent observed | Curvature-rate definition or inspiral scaling requires revision |
| Instrument | Status | Frequency Band | Launch/Operation |
|---|---|---|---|
| LISA | Approved | 0.1 mHz – 0.1 Hz | ~2035 |
| Einstein Telescope | Proposed | 3 Hz – 10 kHz | ~2035 |
| LIGO A+ | Operational | 10 Hz – 5 kHz | Current |
Detection of a f6 phase deviation in high-SNR LISA events would constrain the STF coupling. Non-detection places upper bounds on parameters but does not falsify the core framework.