  We show that derivation of Friedmann's equations from the Einstein-Hilbert
action, paying attention to the requirements of isotropy and homogeneity during
the variation, leads to a different interpretation of pressure than what is
typically adopted. Our derivation follows if we assume that the unapproximated
metric and Einstein tensor have convergent perturbation series representations
on a sufficiently large Robertson-Walker coordinate patch. We find the source
necessarily averages all pressures, everywhere, including the interiors of
compact objects. We demonstrate that our considerations apply (on appropriately
restricted spacetime domains) to the Kerr solution, the Schwarzschild
constant-density sphere, and the static de-Sitter sphere. From conservation of
stress-energy, it follows that material contributing to the averaged pressure
must shift locally in energy. We show that these cosmological energy shifts are
entirely negligible for non-relativistic material. In relativistic material,
however, the effect can be significant. We comment on the implications of this
study for the dark energy problem.
