Three critical observational windows are emphasized here:
Strong lensing time-delay cosmography,
Redshift drift measurements,
Gravitational wave tensor-mode signals.
Each tests a different aspect of the proposed theory: geometric consistency, dynamical evolution, and primordial perturbations.
2. Strong Gravitational Lensing: Probing Inhomogeneous Curvature
In the standard cosmology, time delays between lensed images constrain the angular diameter distances and hence the Hubble parameter H0H_0. In this model:
Layer-dependent variations in curvature kik_i and Hubble flow HiH_i may lead to directional anisotropies in time delays,
The effective lensing potential may include contributions from interlayer interference terms and phase entanglement effects.
We expect observable deviations in Fermat potential reconstructions across sky patches, particularly if the light paths traverse multiple curvature domains. This could manifest as:
tmulti-layertCDM,\Delta t_{\text{multi-layer}} \neq \Delta t_{\Lambda\text{CDM}},
with corrections due to ijcos(ij)\alpha_{ij} \cos(\theta_i - \theta_j) terms in the extended Friedmann structure.
Data sources: H0LiCOW, STRIDES, and upcoming Rubin LSST time-delay programs.
3. Redshift Drift: Direct Measurement of Cosmic Acceleration
The redshift drift (Sandage--Loeb test) offers a model-independent probe of the expansion history by tracking the rate of change of redshift for distant sources over decades:
dzdt0=H0(1+z)H(z).\frac{dz}{dt_0} = H_0(1+z) - H(z).
