Rational hyperbolicity of simply connected hyperbolic polar manifolds

Let $M$ be a simply connected polar manifold, meaning a Riemannian manifold with an isometric polar group action, and suppose that $M$ is hyperbolic in the sense that its section has negative curvature. A simply connected hyperbolic polar manifold is rationally hyperbolic. This asserts that the rational homotopy type of $M$ has unbounded complexity, rather than being rationally elliptic. The claim is presented as a natural consequence of the preceding results, but the supplied text does not establish its resolution.