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cygx t1_jctjza4 wrote

Due to the metric expansion of space, the universe is not time translation invariant at cosmological scales, hence no energy conservation via Noether's first theorem. However, Noether's second theorem still applies due to general covariance, and you get an 'improper' / 'strict' (terminology differs) conservation law for any time-like vector field (in case of cosmological time, this yields the first Friedmann equation). However, these laws are non-covariant as they include gravitational contributions that cannot be localized via a stress-energy tensor. It's somewhat similar to what happens to energy conservation in rotating frames of reference, except that there's no longer such a thing as inertial frames that make energy conservation manifest. Consequently, a large portion of physicists find it less confusing to just state that energy conservation doesn't hold for the universe at large.

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