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

2. Galaxy Data: Large Scale Matter Distribution (SDSS, DES)  

- Survei SDSS (Sloan Digital Sky Survey):  

- Measures galaxy correlation function \( \xi(r) \) to \( z \sim 0.7 \).  

- Key Findings:  

    - Deviations \( \xi(r) \) on the scale \( >100 \) Mpc may indicate local variations \( \Lambda \) (polycentric bubbles).  

    - Consistency with \( \Lambda \)CDM, but uncertainty is still large.  

- Survei DES (Dark Energy Survey):  

  - Matter distribution map up to \( z \sim 1.5 \) using weak lensing.  

  - Relationship to Mode*:  

    - If \( \Lambda \) varies locally, residuals will appear in the lensing map at ultra-large scales.  

Observation Data Table