Ultra-light scalar dark matter with the Lyman-$\alpha$ forest

International audienceUltra-light dark matter particles with mass ma ∼ 10 −22 eV, named Fuzzy DarkMatter (FDM), constitute the dark matter candidate with the lowest masspossible. They yield a remarkable phenomenology and could also provide asolution to the small scale CDM "issues". One probe for such models is theLyman-α forest, which provides an indirect measurement for the small-scalematter power spectrum. We compare simulation-based predictions for the Lyman-αforest with the SDSS-DR9 and higher-resolution data, and find that the data isin tension with FDM masses in the range $10^{−22} \le m_a \le 2 − 3 \times 10^{−21}$ eV