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The search for classically stable Type IIA de-Sitter vacua typically startswith an ansatz that gives Anti-de-Sitter supersymmetric vacua and then raisesthe cosmological constant by modifying the compactification. As one raises thecosmological constant, the couplings typically destabilize the classicallystable vacuum, so the probability that this approach will lead to a classicallystable de-Sitter vacuum is Gaussianly suppressed. This suggests thatclassically stable de-Sitter vacua in string theory (at least in the Type IIAregion), especially those with relatively high cosmological constants, are veryrare. 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 thenumber of moduli.

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