A Global View on The Search for de-Sitter Vacua in (type IIA) String Theory

TL;DR

This paper analyzes the rarity of classically stable de-Sitter vacua in Type IIA string theory, showing that their probability decreases exponentially with the number of moduli, especially for higher cosmological constants.

Contribution

It provides a statistical and conceptual framework demonstrating the Gaussian suppression of stable de-Sitter vacua in Type IIA string theory.

Findings

Stable de-Sitter vacua are exponentially rare in the string landscape.

The probability of stability decreases with the number of moduli.

Higher cosmological constants further suppress the likelihood of stability.

Abstract

The search for classically stable Type IIA de-Sitter vacua typically starts with an ansatz that gives Anti-de-Sitter supersymmetric vacua and then raises the cosmological constant by modifying the compactification. As one raises the cosmological constant, the couplings typically destabilize the classically stable vacuum, so the probability that this approach will lead to a classically stable de-Sitter vacuum is Gaussianly suppressed. This suggests that classically stable de-Sitter vacua in string theory (at least in the Type IIA region), especially those with relatively high cosmological constants, are very rare. The probability that a typical de-Sitter extremum is classically stable (i.e., tachyon-free) is argued to be Gaussianly suppressed as a function of the number of moduli.