$D=11$ $dS_5$ backgrounds with enhanced supersymmetry

We classify all warped $dS_5$ backgrounds in $D=11$ supergravity with enhanced supersymmetry. We show that backgrounds preserving $N=16$ supersymmetries consist of either a stack of M5 branes with transverse space $\mathbb{R}^5$, or a generalized M5-brane configuration with transverse space $\mathbb{R} \times N_4$, where $N_4$ is a hyper-Kahler manifold and the $M5$-brane harmonic function is determined by a hyper-Kahler potential on $N_4$. Moreover, we find that there are no backgrounds preserving exactly $N=24$ supersymmetries. Backgrounds preserving $N=32$ supersymmetries correspond to either $\mathbb{R}^{1,10}$ or $AdS_7\times S^4$.