The generalized Alekseevsky conjecture for expanding homogeneous Ricci solitons

Let $M=G/H$ be a homogeneous Ricci soliton with $c<0$, where $G$ is a transitive Lie group and $H$ is the isotropy subgroup. A homogeneous Ricci soliton is a Riemannian homogeneous space whose metric satisfies the Ricci soliton equation with soliton constant $c$. Generalized Alekseevsky conjecture. The subgroup $H$ is a maximal compact subgroup of $G$ and, consequently, $M$ is diffeomorphic to $\mathbb R^n$. The theorem immediately preceding this statement proves the analogous assertion for solvmanifolds, while the conjecture concerns arbitrary expanding homogeneous Ricci solitons and remains unresolved in the stated generality.