If confirmed, early massive galaxy abundance strengthens the case for non-standard initial conditions,
Suggests cosmological dynamics are influenced by topological interference and scale-dependent curvature,
Challenges the inflationary mechanism as the sole seeder of structure --- offering a complementary or alternative origin rooted in quantum-layered genesis and holographic boundary flows.
D. LISA: Echoes from Geodesic Scattering at Layer Boundaries
1. Background: Gravitational Wave Observables Beyond Binary Mergers
The upcoming Laser Interferometer Space Antenna (LISA) will probe low-frequency gravitational waves (GWs) in the range of 104101Hz10^{-4} - 10^{-1} \,\mathrm{Hz} --- opening a window into:
Supermassive black hole binaries (SMBHBs) at high redshift,
Extreme mass-ratio inspirals (EMRIs) probing strong-field gravity,
Cosmological gravitational backgrounds from early universe phenomena.
LISA also provides sensitivity to waveform distortions from nontrivial spacetime geometry, including echoes, delays, and modulations caused by the underlying topology or structure of spacetime.
2. Fractal-Layered Spacetime and Geodesic Echoes
In the proposed framework, the universe contains hierarchically nested curvature layers separated by quasi-transparent topological boundaries. These boundaries:
Modulate the local refractive index for geodesics,
Cause partial scattering or phase shifting of gravitational waves traversing them,
Act analogously to semi-permeable membranes in multilayered media.
For a GW propagating radially, the geodesic deviation equation is perturbed by additional terms:
D2d2+R uu+j(j)uu=0\frac{D^2 \xi^\mu}{d\tau^2} + R^\mu_{\ \nu\alpha\beta} u^\nu \xi^\alpha u^\beta + \sum_j \delta(\Sigma_j) \Delta Gamma^\mu_{\alpha\beta} u^\alpha u^\beta = 0
Where (j)\delta(\Sigma_j) represents a layer boundary at hypersurface j\Sigma_j, and \Delta \Gamma^\mu_{\alpha\beta} encodes the discontinuity in the Christoffel symbols due to geometric layer mismatch.
3. Observable Consequences: Gravitational Echoes and Phase Delays
