  We study solutions to the Yang-Mills-Higgs equations on the maximal Cauchy
development of the data given on a ball of radius $R$ in $\mathbb{R}^3$. The
energy of the data could be infinite and the solution grows at most inverse
polynomially in $R-t$ as $t\rightarrow R$. As applications, we derive pointwise
decay estimates for Yang-Mills-Higgs fields in the future of a hyperboloid or
in the Minkowski space $\mathbb{R}^{1+3}$ for data bounded in the weighted
energy space with weights $|x|^{1+\epsilon}$. Moreover, for the abelian case of
Maxwell-Klein-Gordon system, we extend the small data result of Lindblad and
Sterbenz to general large data (under same assumptions but without any
smallness). The proof is gauge independent and it is based on the framework of
Eardley and Moncrief together with the geometric Kirchhoff-Sobolev parametrix
constructed by Klainerman and Rodnianski. The new ingredient is a class of
weighted energy estimates through backward light cones adapted to the initial
data.
