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

- Target: Anomalies in the *two-point correlation function* \( \xi(r) \) on a scale \( >100 \) Mpc due to local variations \( \Lambda \).  

- Euclid (ESA):  

- Galaxy spectroscopy to measure redshift-space distortions (RSD).  

Data analysis:  

1. Statistical Filtration:  

   - Calculate the deviation \( \xi(r) \) from the standard \( \Lambda \)CDM prediction using the estimator: \[\xi(r) = \frac{DD(r) - 2DR(r) + RR(r)}{RR(r)},     \]  

where \( DD, DR, RR \) are pairs of data-data, data-random, and random-random.  

2. Machine Learning:  

   - Convolutional Neural Networks (CNN) algorithm to identify anomalous patterns in galaxy maps.  

Instrument Specification Table  

| Instrument | Key Parameters | Abilities |