The universe is partitioned into quasi-independent topological layers or "bubbles," each governed by slightly different local curvature, expansion rate, and phase,
These layers emerge from quantum tunneling genesis, generating non-smooth transitions between adjacent domains,
Each layer has its own metric g(i)g^{(i)}_{\mu\nu}, and transitions are encoded through matching conditions at the boundaries using Israel junction formalism or effective scattering matrices,
The photon path follows a piecewise geodesic across multiple domains, accumulating phase shifts, lensing-like distortions, and amplitude modulations.
3. Ray-Tracing Setup
We model CMB photon trajectories originating from the surface of last scattering by:
Embedding N concentric layered domains with varying curvature kik_i, scale factor evolution ai(t)a_i(t), and local gravitational potential fluctuations i\Phi_i,
Solving null geodesics numerically for each region using:
 d2xd2+dxddxd=0\frac{d^2 x^\mu}{d\lambda^2} + \Gamma^{\mu}_{\alpha\beta} \frac{dx^\alpha}{d\lambda} \frac{dx^\beta}{d\lambda} = 0
 where \lambda is the affine parameter,-
At each boundary, applying continuity and refractive-like rules to compute transmission/reflection of wavefront distortions (phase slips, deflections),
Recording total angular deflection, phase rotation, and redshift history along the full path to compute the effective CMB temperature anisotropy:
 TT(n^)+[ddt+int]d\frac{\Delta T}{T} (\hat{n}) \sim \Phi + \int_{\gamma} \left[ \frac{d\Phi}{dt} + \Theta_{\text{int}} \right] d\lambda
 where int\Theta_{\text{int}} encodes interference across layers.
4. Simulation Results
