[shomp]

Noether's theorem tells us when symmetry guarantees conservation, but it says nothing about conservation in the absence of that symmetry - it's not a biconditional statement. Talking about endless expansion is like observing 1 second of a pendulum's swing and concluding there's no time symmetry because it's only moving in one direction. The symmetry exists at the full cycle scale, not the snapshot scale.

[antognini]

It's true that it leaves open the possibility of a conserved quantity that is not associated with a symmetry. But the kinds of conservation laws we are thinking about, like conservation of energy, do originate from a symmetry. So if the symmetry is broken it is very reasonable to assume that the conservation law would be broken as well.