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My confunion stems from the common knowledge that: in the Einstein Field equations, the terms are ordered so that terms for the matter and energy are on the right, and on the left you find the terms for curvature of spacetime, due to the aforementioned energy and matter.

At first look this question appears fairly obvious; it's on the left because it was discovered after the field equations were formulated and had to be slotted in later to balance everything out.

However if you consider what I mentioned in the first paragraph- the left side has the terms for curvature, I find it confusing that amongst all these terms for curvature there is the cosmological constant: which is, according to Wikipedia: 'the value of the energy density of the vacuum of space.' Which is an energy term.

This led me to think, The constant is a balancing term so that the equations work, this may sound ridiculous but are we sure it is actually an energy term, representative of dark energy. The fact that it is on the left with the curvature terms got me thinking if there was a possibility it's just an intrinsic value of spacetime that arises due to curvature?

The other obvious answer is that you just move it over to the right somewhere during the calculations. This doesn't make sense to me either, because, if the idea of: energy on the right and curvature on the left, requires terms to be shifted around in order to work then surely it's not supposed to work like that.

There is probably a very simple answer to this that I'm overlooking, or I'm over thinking it, the thought just bugged me, any insight would be helpful.

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    $\begingroup$ Which side of the equation any term occurs on is not a question of physics, or maths, it's a question of convention. $\endgroup$
    – user107153
    Jun 26, 2017 at 22:00
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    $\begingroup$ I think you're reading into it a bit too much. $\endgroup$
    – knzhou
    Jun 26, 2017 at 22:07
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    $\begingroup$ I do feel you are over thinking it,TBH, although I would agree that none of the writers of my textbooks has ever changed the convention or set a trick problem using it. $\endgroup$
    – user154420
    Jun 26, 2017 at 22:10
  • $\begingroup$ Thank you all, that was the response I was looking for, I was just worried there was some deeper meaning that I wasn't understanding. $\endgroup$ Jun 27, 2017 at 5:59
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    $\begingroup$ Also, some people like to think of dark energy as contributing directly to the stress-energy tensor, in which case it doesn't appear in the EFE at all, but the physics is still unchanged. At the end of the day, it's just a question of where you put your parentheses. $\endgroup$
    – tparker
    Jul 1, 2017 at 15:23

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The cosmological constant can be placed anywhere in the EFE. Einstein placed it on the left, I'd think, with the idea that it is simply a property of spacetime. It is much more recently (20, 30 years ago?) that it's been labeled as dark energy.

When you place it on the right side you can represent it as a type of energy with negative pressure and positive energy density. In cosmology it is best to treat it that way and it then add it's density to the matter and radiation density, and gets us to the critical density. Thus when we say that dark energy is about 68% of the universe, and matter (dark and visible) the rest (to a very good approximation today, with radiation less than 1%), and the sum gives (again to a very good approximation) the critical density, we can account for all the energy-matter, and we are led to a flat (spatial) universe.

The spatial curvature k is then 0. If it wasn't you could, and sometimes it is expressed in cosmology that way, account for the equivalent mass-energy due to that curvature, the same way, as a percent of the total. Turns out it's close to 0. So, no, curvature can not account for source of the dark energy.

Part of the reason that it was labeled as dark energy is that a similar kind of energy, with negative pressure, is assumed/estimated to have caused the inflation early in the universe history.

There is still research ongoing on what it really is. One model has been quintessence which is a quantum field, and there's others. The most suspected answer is that it is the energy of the vacuum, but the calculations don't quite match.

Either way, it's just a symbol and you can represent it, or model it, as dark energy, or maybe other things.

See https://en.m.wikipedia.org/wiki/Dark_energy

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I think it is because of the metric tensor along with cosmological constant (Λgμν). Metric tensor being property of spacetime, we don't want it to be on the right.

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