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 (IMRP Int Math Res Pap 109:1687-3017, 2006) 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 (Commun Math Phys 83(2):171–191, 1982a, 1982b) together with the geometric Kirchhoff–Sobolev parametrix constructed by Klainerman and Rodnianski (J Hyperbolic Differ Equ 4(3):401–433, 2007). The new ingredient is a class of weighted energy estimates through backward light cones adapted to the initial data.
