Well-defined equations of motion without constraint of external sources
  We present a new approach to constrained classical fields that enables the
action formalism to dictate how external sources must enter the resulting
equations of motion. If symmetries asserted upon the varied fields can be
modeled as restrictions in Fourier space, we prove that these restrictions are
automatically applied to external sources in an unambiguous way. In contrast,
the typical procedure inserts symmetric ansatze into the Euler-Lagrange
differential equations, even for external sources not being solved. This
requires ad hoc constraint of external sources, which can introduce
leading-order errors to model systems despite superficial consistency between
model field and source terms. To demonstrate, we consider Robertson-Walker
cosmologies within General Relativity and prove that the influence of
point-like relativistic pressure sources on cosmological dynamics cannot be
excluded by theoretical arguments.
