If the universe is constantly expanding, how is the law of conservation of energy obeyed?

Submitted by Pristine_Pop_7818 t3_11w9asm in askscience

Hello,

The essence of my question is basically that there most be some driving force behind the expansion of the universe, and as the universe gets larger, my assumption would be that this driving “force” would need more energy in order to expand it at the same (or even accelerated) rate. Doesn’t this seemingly break the law of COE, since it appears to have an ever increasing amount of energy with which it expands?

Thanks :)

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BlueParrotfish t1_jcytos0 wrote

Hi /u/Pristine_Pop_7818!

The answer is simply, that energy is not conserved in our expanding universe.

Noether's theorem tells us that any quantity which has a continuous differentiable symmetry in the action has an associated conservation law. That is, for example, the translational symmetry of the universe is associated in a one-to-one correspondence with conservation of momentum.
This also tells us, that time-symmetry is associated with conservation of energy. As our universe is expanding, time-symmetry is broken. Thus, Noether's Theorem tells us, that energy is not conserved in our universe. In practice, this means that dark-energy density is constant. Hence, as space(time) expands, dark energy is created.

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mfb- t1_jcyv2ko wrote

> In practice, this means that dark-energy density is constant.

We don't know if it is, that's just the easiest model.

A more well-studied example is the cosmic microwave background which loses energy from the expansion.

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ozymandian___ t1_jd0eij6 wrote

I just want to point out that the fact that the universe is expanding does not mean that it breaks time symmetry in a way that is relevant for Noether’s theorem. Systems can change over time and conserve energy. Furthermore, Noether’s theorem describes local physics, and local physics is unchanged by general relativity. Also, if you consider the energy of spacetime itself, then energy is conserved in the universe. There is a caveat that in GR the energy of spacetime curvature can’t be localized in the way energy usually is. This makes some people uncomfortable, and they choose to say energy is not conserved for the universe (seemingly ignoring that spacetime carries energy as in gravitational waves). You can just as well say that energy is conserved and that the energy of spacetime is only well defined for the universe as a whole.

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Pristine_Pop_7818 OP t1_jcyvlgs wrote

Ah cool thanks for the response! So essentially any conservation law breaks down in the absence of some symmetry defined by Noether’s Theoroem. Interesting

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