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Usually it is said that the density of dark energy/vacuum energy remains constant as spacetime expands, so the total amount of them is increasing.

However, are there any examples of more "conventional" forms of energy (thermal, electromagnetic, matter...) that are increasing as spacetime expands?

vengaq
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  • Energy not being conserved at the cosmic scale doesn't mean that the useful energy is increasing. Indeed, the red shift makes the light of those galaxies "less useful" to us. – FlatterMann Oct 02 '22 at 12:00
  • Possible duplicate by OP: https://physics.stackexchange.com/q/728738/2451 – Qmechanic Apr 15 '23 at 10:24

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Accelerating expansion of the universe means that in our reference frame the kinetic energy of the galaxies (those outside of our local gravitationally bound cluster) would increase with time as those galaxies recede from us. The “catch” is that as expansion continues more and more galaxies recede beyond our cosmic horizon, so the kinetic energy that these galaxies have gained becomes inaccessible to us.

Conceptually this is not much different than increase in kinetic energy of a mass falling from rest toward gravitating body, while in this case we have galaxies falling toward cosmic horizon.

A.V.S.
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  • What makes you say their kinetic energy increases ? Expansion is not motion. It does not confer kinetic energy, even if it is accelerating. – ticster Oct 05 '22 at 20:06
  • Expansion is not motion With this I agree, these are notions from different categories. Specifically, “expansion” is an invariant (more or less) characterization of the flow (geodesic congruence etc.), while “motion” applies to an element of the flow and is frame dependent. But accelerating expansion does confer kinetic energy as measured in a frame rigidly stretched from our position. And we can convert this kinetic energy to other forms (such as perform useful works) by stretching a long rope to a distant galaxy and connecting our end of it to a generator. – A.V.S. Oct 06 '22 at 06:21
  • Expansion does not confer kinetic energy. Immobile points remain immobile even undergoing accelerated expansion. – ticster Oct 06 '22 at 09:51
  • Expansion does not confer kinetic energy OK, if we are splitting hairs not accelerating expansion per se, but the gravitational effect of dark energy does.Immobile points remain immobile Not true. Consider de Sitter universe (or the universe of ΛCDM in the distant future). A particle moving near the origin (which we place at our position) has conserved (Killing) energy $E=\frac{mv^2}{2}-\frac{m \alpha r^2}{2}+\text{relativistic corrections}$, so if we have an immobile particle at some distance from the origin, in the future it would be moving and thus having non-zero kinetic energy. – A.V.S. Oct 06 '22 at 12:02
  • Why would the distant particle start moving because of expansion ? If a particle is immobile in the CMB reference frame then it will remain as such regardless of expansion. It might be given kinetic energy by some other process, but not by expansion. – ticster Oct 06 '22 at 12:09
  • If the particle is immobile in CMB frame and is distant from us then it has kinetic energy in our frame with space distances measured by rigid rulers. And in the future, as Hubble flow would carry it further away, its kinetic energy would increase. This kinetic energy is quite real and can be extracted by a rope (as I outlined above). – A.V.S. Oct 06 '22 at 12:26
  • The distance increases, but its velocity is still 0. It is still immobile, it is the metric that is dynamic, not the particle's motion. The particle does not gain motion or kinetic energy. Your rope example is an interesting (and often cited) thought experiment, but it doesn't mean what you think it means. Whatever energy you might extract from it does not come from any expansion related kinetic energy. – ticster Oct 06 '22 at 12:33
  • It is still immobile You seem to harbor a misconception that the CMB frame is the only frame there is. What is immobile in one frame can move in another, in particular if we stretch a rigid ruler from us to a distant galaxy, an observer sitting on that ruler near that galaxy would notice that the galaxy is moving and has kinetic energy. The splitting of energy into “rest”, “kinetic” and “gravitational” is generally ambiguous, however in the newtonian limit it is well established, and ΛCDM does have a well defined newtonian limit. – A.V.S. Oct 06 '22 at 13:22
  • While the distance would increase in our own reference frame, it would be due to metric expansion and not motion. The particle is still immobile despite its distance to us increasing. – ticster Oct 06 '22 at 16:35
  • I think what you're having trouble with is the idea that the distance to us can increase and the particle is still immobile. This is perfectly possible when the metric is dynamic. – ticster Oct 06 '22 at 16:36
  • @ticster, No, it seems that it is you who erroneously believe that there are some mystical degrees of freedom of “dynamical metric” disconnected from the motion of matter. The “matter at rest/expanding space” viewpoint of CMB frame is complementary to the viewpoint of “rigid rulers/moving matter” corresponding to different choices of the Cauchy data. Forget about GR for a moment and consider Minkowski spacetime. Imagine test particle that has 4-velocity of $(γ, \vec{v}γ)$ and passes through the origin $(0,\vec{0})$. It has kinetic energy $E\approx mv^2/2$ (when $v\ll 1$)… – A.V.S. Oct 06 '22 at 19:24
  • … (cont.) But at the same time we can describe Minkowski spacetime as dynamical Milne universe with expanding metric with $a(\tilde{t})=\tilde{t}$, that same particle would be immobile w.r.t. to “CMB frame”. The initial data for the rigid/Cartesian specification of Minkowski are at a plane $t=\text{const}$, while for expanding/Milne universe they are at hyperboloid $t^2-r^2=\text{const}$. De Sitter universe also has both the expanding frame and static frame for a given geodesic viewed as a center. For ΛCDM universe de Sitter space could be seen as a background … – A.V.S. Oct 06 '22 at 19:44
  • … (cont. 2) So from the viewpoint of a frame of rigid rulers our patch of the universe asymptotically tends to static de Sitter background (with central massive cluster of our local group at the center) as more and more galaxies move toward cosmic horizon. And galaxies move in an ordinary way: galactic motion has momentum and kinetic energy and for small velocities/redshifts those are given by their Newtonian expressions. – A.V.S. Oct 06 '22 at 20:06
  • An expanding metric is indeed independent of the motion of matter, and vice versa. We're gonna have to agree to disagree on this one :) – ticster Oct 06 '22 at 21:34