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

1. B-mode polarization:  

   - The amplitude \( r \) is related to the power spectrum \( B \)-mode:  

     \[     C_\ell^{BB} = \frac{\pi}{4} A_t \left( \frac{\ell(\ell+1)}{2\pi} \right) \left( \frac{r}{0.1} \right),\]  

     where \( A_t \) is the amplitude of the primordial tensor.  

   - Target: Detect signals at the scales \( \ell \sim 80 \) (reionization) and \( \ell \sim 5 \) (inflation).  

2. Galactic Foreground Correction:  

   - Use multi-frequency to separate galactic dust (\( \nu > 100 \) GHz) and CMB signals.  

4.2.2 Galactic Distribution Anomalies  

Survey:  

- LSST (Vera C. Rubin Observatory):  

- 3D map of galaxies up to \( z \sim 3 \) with precision \( \Delta z \sim 0.02 \).