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.Comment: v2: 31 pages + appendices; few additions, including references and 5 figures. A Mathematica Notebook is provided here as an ancillary file with all solutions of this paper arXiv:2101.06251, as well as those of arXiv:2005.1293