As a simple example, imagine a photon traveling through an expanding universe in a region with no other matter or energy (dark or otherwise). The expansion of space stretches the wavelength of the photon (cosmological redshift, which is distinct from Doppler redshift), causing it to lose energy. The photon loses energy with nothing around it gaining. Energy is lost because spacetime itself is changing, so Noether's theorem doesn't apply.
I wonder if we could add a scale-invariant component, and make the lost energy just a property of measuring it in a non-inflating reference frame.
Or, I should say, I wonder what contradictions that would lead to.