  In this paper, we study gradient Ricci expanding solitons $(X,g)$ satisfying
$$ Rc=cg+D^2f, $$ where $Rc$ is the Ricci curvature, $c<0$ is a constant, and
$D^2f$ is the Hessian of the potential function $f$ on $X$.
  We show that for a gradient expanding soliton $(X,g)$ with non-negative Ricci
curvature, the scalar curvature $R$ has at least one maximum point on $X$,
which is the only minimum point of the potential function $f$. Furthermore,
$R>0$ on $X$ unless $(X,g)$ is Ricci flat. We also show that there is
exponentially decay for scalar curvature for $\epsilon$-pinched complete
non-compact expanding solitons.
