Tachyonic de Sitter Solutions of 10d Type II Supergravities

Cosmological models of the early or late universe exhibit (quasi) de Sitter space-times with different stability properties. Considering models derived from string theory, the swampland program does not provide for now a definite characterisation of this stability. In this work we focus on de Sitter solutions of 10d type II supergravities, candidates for classical de Sitter string backgrounds: surprisingly, all known examples are unstable with eta(V) < -1. We aim at proving the existence of such a systematic tachyon, and getting formally a bound on the value of eta(V). To that end, we develop three methods, giving us various sufficient conditions for having a tachyon upon assumptions, in analogy with de Sitter no-go theorems. Our analysis eventually indicates the existence of variety of different tachyons, and related bounds on eta(V). We use this knowledge to find 10 new de Sitter solutions of type IIB supergravity, that have tachyons of a different kind, higher eta(V) values and new 6d geometries. One solution even appears to be stable, with however non-compact extra dimensions.