We obtain structure results for non-compact Einstein manifolds with negative Einstein constant assuming an isometric Lie group action with compact, smooth orbit space. For the corresponding Riemannian submersion we derive sharp $L^2$-curvature estimates which rely on pointwise curvature estimates on the homogeneous fibres (coming from real geometric invariant theory), a generalized Helmholtz decomposition for smooth vector fields and a moment map description of the $L^2$-Ricci curvature tensor. This is joint work with R. Lafuente.