No Asymptotic Acceleration without Higher-Dimensional de Sitter Vacua

Understand

There has recently been considerable interest in the question whether and under which conditions accelerated cosmological expansion can arise in the asymptotic regions of field space of a $d$-dimensional EFT.

• We conjecture that such acceleration is impossible unless there exist metastable de Sitter vacua in more than $d$ dimensions.
• That is, we conjecture that `Asymptotic Acceleration Implies de Sitter' (AA$\Rightarrow$DS).
• Phrased negatively, we argue that the $d$-dimensional `No Asymptotic Acceleration' conjecture (a.k.a.~the `strong asymptotic dS conjecture') follows from the de Sitter conjecture in more than $d$ dimensions.