  In this paper, we derive curvature estimates for 4-dimensional complete
gradient expanding Ricci solitons with nonnegative Ricci curvature (outside a
compact set $K$). More precisely, we prove that the norm of the curvature
tensor $Rm$ and its covariant derivative $\nabla Rm$ can be bounded by the
scalar curvature $R$ by $|Rm|\le C_a R^a$ and $|\nabla Rm| \le C_a R^a$ (on
$M\backslash K$), for any $0\le a <1$ and some constant $C_a >0$. Moreover, if
the scalar curvature has at most polynomial decay at infinity, then $|Rm| \le C
R$ (on $M\backslash K$). As an application, it follows that that if a
4-dimensional complete gradient expanding Ricci soliton $(M^4, g, f)$ has
nonnegative Ricci curvature and finite asymptotic scalar curvature ratio then
it has finite asymptotic curvature ratio, and $C^{1,\alpha}$ asymptotic cones
at infinity ($0 < \alpha < 1$) according to Chen-Deruelle [20].
