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We determine the necessary and sufficient conditions for warped product$dS_n$ solutions, $5 \leq n \leq 10$, to preserve supersymmetry in $D=11$supergravity, without assuming factorization of the Killing spinors. We provethat for $7 \leq n \leq 10$, all such solutions are flat, with vanishing4-form. We also show that the only warped product $dS_6$ solutions are eitherthe maximally supersymmetric $AdS_7 \times S^4$ solution, or $\mathbb{R}^{1,6}\times N_4$ where $N_4$ is hyperKahler, with vanishing 4-form. Supersymmetricwarped product $dS_5$ solutions are then classified; it is shown that all suchsolutions are generalized M5-brane configurations, for which the transversespace is $\mathbb{R} \times N_4$, and $N_4$ is a hyperKahler manifold. If the4-form is covariantly constant, then $N_4$ admits a hyperKahler potential.

Supersymmetric $dS_n$ solutions for $n \geq 5$ in $D=11$ supergravity