  It is known that the Maxwell-Klein-Gordon equations in $\mathbb{R}^{3+1}$
admit global solutions with finite energy data. In this paper, we present a new
approach to study the asymptotic behavior of these global solutions. We show
the quantitative energy flux decay of the solutions with data merely bounded in
some weighted energy space. We also establish an integrated local energy decay
and a hierarchy of $r$-weighted energy decay. The results in particular hold in
the presence of large total charge. This is the first result to give a complete
and precise description of the global behavior of large nonlinear charged
scalar fields.
