  Let $(M^n, g, f)$, $n\geq 5$, be a complete gradient expanding Ricci soliton
with nonnegative Ricci curvature $Rc\geq 0$. In this paper, we show that if the
asymptotic scalar curvature ratio of $(M^n, g, f)$ is finite (i.e., $
\limsup_{r\to \infty} R r^2< \infty $), then the Riemann curvature tensor must
have at least sub-quadratic decay, namely, $\limsup_{r\to \infty} |Rm| \ \!
r^{\alpha}< \infty$ for any $0<\alpha<2$.
