LISA could detect:
Time-delayed gravitational echoes after primary GW signals from SMBHB mergers, due to partial reflection at layer interfaces,
Anomalous phase shifts or modulations in the inspiral waveform --- e.g., in EMRI systems --- if GWs pass through nontrivial topological domains,
Non-perturbative frequency drift in continuous wave sources, analogous to layer-resonant modulation.
These effects scale with:
The density contrast and curvature gradient across the layer (Kr2ai(r)\Delta K \sim \partial_r^2 a_i(r)),
The incident angle and polarization of the wavefront with respect to the layer normal,
The coherence scale of the underlying fractal pattern.
4. Testable Predictions
Predicted GW echoes from SMBHBs at z3--10z \sim 3\text{--}10 should appear with:
Time delays: techoLlayer/c102--104s\Delta t_{\text{echo}} \sim L_{\text{layer}} / c \sim 10^2\text{--}10^4 \, \mathrm{s},
Echo-to-primary amplitude ratio: Aecho/Aprimary0.01--0.1\mathcal{A}_{\text{echo}} / \mathcal{A}_{\text{primary}} \sim 0.01\text{--}0.1,
Spectral localization at resonant frequencies tied to layer thickness and geometric spacing.
5. LISA's Observational Strategy and Synergy
LISA can cross-check for these phenomena via:
Matched filtering using modified templates that include boundary-induced phase shifts,
Stochastic background analyses sensitive to non-Gaussian tail features,
Cross-correlation with electromagnetic counterparts to constrain propagation delays inconsistent with CDM.
Furthermore, joint detection with PTA (Pulsar Timing Arrays) or ground-based detectors may reveal frequency-dependent delays, supporting a geometric dispersion mechanism.
6. Implications and Falsifiability
If such echoes or modulations are observed:
They would indicate nontrivial microstructure of spacetime beyond effective smooth manifolds,
Suggest a layered or discrete geometry with physical, observable consequences,
Provide indirect evidence of fractal topologies and non-local interference, as predicted by the model.
If LISA fails to detect any such anomalies within predicted bounds across multiple events, the energy scale or transparency of the layers would be tightly constrained --- providing falsifiability.
VI. Discussion
