On classical de Sitter vacua in string theory

We review the prospect of obtaining tree‐level de Sitter (dS) vacua and slow‐roll inflation models in string compactifications. Restricting ourselves to the closed string sector and assuming the absence of NSNS‐sources, we classify the minimal classical ingredients that evade the simplest no‐go theorems against dS vacua and inflation. Spaces with negative integrated curvature together with certain combinations of low‐dimensional orientifold planes and low‐rank RR‐fluxes emerge as the most promising setups of this analysis. We focus on two well‐controlled classes that lead to an effective 4D, 𝒩 = 1 supergravity description: Type IIA theory on group or coset manifolds with SU(3)‐structure and O6‐planes, as well as type IIB compactifications on SU(2)‐structure manifolds with O5‐ and O7‐planes. While fully stabilized AdS vacua are generically possible, a number of problems encountered in the search for dS vacua are discussed.