We know that our universe is expanding i.e. volume of the universe is getting larger with time with total energy being conserved. My question is whether the energy density is getting smaller with time. If this is true then what is the effect of this phenomenon on all the celestial bodies?
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3$\begingroup$ Total energy is not conserved. The conservation of energy does not apply on cosmological scales. $\endgroup$– Steve LintonCommented Jul 23, 2019 at 15:47
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$\begingroup$ If I may: We don't know the volume of the universe is getting larger. The volume of the universe is much, much more likely than not, infinite. And I mean literally infinite (I have to say that due to the bewildering existence of 'multiple types of infinities' in theoretical astrophysics. $\endgroup$– White PrimeCommented Jul 24, 2019 at 13:04
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$\begingroup$ @WhitePrime That may well be true, but if you take any sufficiently large region and "anchor" its boundaries to the average trajectory of matter near them, it will be found to be expanding. $\endgroup$– Steve LintonCommented Jul 24, 2019 at 14:13
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2 Answers
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I am no expert and I am sure there will be a more rigorous answer later, but here my 2 cents:
It appears to me that the term "energy" and energy conservation becomes a bit more complicated in general relativity and cosmology, taking into account more abstract forms as the energy of the gravitational field or space curvature. As you seem to be more interested in the implications I just want to focus on the common forms of energy, i.e., radiation, matter and dark energy.
For a given expanding volume of space only the energy from matter (dark and normal) is dilutes as expected. You could say that with respect to expansion its energy is conserved. This means its energy density decreases with $\sim a(t)^{-3}$, where a is the scale factor (or just the diameter) of the universe.
Radiation additionally looses energy via cosmological red-shift, so its energy density decreases even faster with $\sim a(t)^{-4}$.
Finally you have the dark energy density. What makes it special is, that its density does not depend on $a(t)$. One can think of it as the energy associated with space itself. So if the universe expands new space and dark energy "appears" and its density stays constant.
So over time the average (matter and radiation) energy density decrease and approaches the energy of empty space itself (or vacuum energy).
Note, however, that this is only true for the average densities. In regions of space, that are held together by gravity, as our local group, the matter density will not decrease. On the contrary, these region are still contraction due to gravity.
So to answer your question on the effect on all the celestial bodies: Those which are gravitationally bound, won't notice much but others will drift apart never to see each other again.
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1$\begingroup$ Three points on conservation of energy: (1) It's an observed fact, not a primitive logical consequence of reality. It may or may not be true in all times and places and situations. (2) As far as we know, energy conservation is a consequence of time symmetry by Noether's theorem. In an expanding spacetime, time symmetry probably does not hold, so energy conservation probably doesn't either. (3) Besides all of the energies mentiond, there is the global energy of space-time itself. Calculating that is non-trivial, but some have argued persuasively that changes in it balance gains in dark energy. $\endgroup$ Commented Jul 24, 2019 at 17:27
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The experts say that as fast as the universe expands the increased space fills instantly with countless trillions of virtual particles which arrive from nowhere. Not only does this contravene the 1st Law of Thermodynamics (mass/energy can neither be created nor destroyed),but there is a discrepancy of 40 orders of magnitude (yes,40 orders of magnitude!) between the vacuum energy density required by Quantum Mechanics and cosmological observations. It has no effect on celestial bodies, though it should have, which is where the conflict with cosmological observations comes in. Supposedly, the 1st Law of Thermodynamics doesn't apply on a cosmological scale.
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2$\begingroup$ The first sentence doesn't make any sense, and could use some backing up. $\endgroup$– HDE 226868 ♦Commented Jul 23, 2019 at 18:33
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$\begingroup$ Why does the 40 orders of magnitude confllct between the alleged vacuum energy density and the results of cosmological observations not matter, and why is nobody willing to explain it? If there were a 40-orders-of-magnitude discrepancy between your official wages and your take-home pay, would you then hold the view that it doesn't matter? $\endgroup$ Commented Jul 25, 2019 at 9:09