Stochastic Selection of Cosmological Constant in Chaotic Inflation: A String Theory Landscape Approach

| Observation | Related Parameters | Model Linkage |  

| Planck | \( r < 0.056 \), \( n_s \) | Validation of potential inflation ramps |  

| SDSS | \( \xi(r) \) large scale | Test the variation of \( \Lambda \) between bubbles |  

| DEC | Weak lensing map | Local dark energy anomaly detection |  

3. Future Experiments  

3.1 LiteBIRD (2027--2030)  

- Primary Aim: Measure primordial B-mode polarization with sensitivity \( \sigma(r) \sim 0.001 \).  

- Relevance to Model:  

  - If \( r \sim 0.003 \) is detected, it will support string theory based inflation.  

  - Special Signature: Oscillation pattern in \( B \)-mode from extra-dimensional resonance (prediction of braneworld theory).  

3.2 SKA (Square Kilometer Array, 2030+)