Just as there are no constraints placed on the Higgs field that is used by science to produce our universe.
So what is the problem?
Is my Creator not allowed the same privilages as your creator?
Firstly the limitations of evidence and observation apply to the Higgs boson and all other scientific theories. So to say that there are no constraints is obviously wrong. The Higgs field will eventually be abandoned if no empirical evidence is found for it. The LHC has been built to examine exactly this sort of question.
If you want your God to be judged on the same standards of observation, testing and evidence then that is fine.......
Somehow I doubt that you would like the results........