As space expands the gravitational potential Energy increases. So does the potential energy between Atoms and quarks and so on. I have read several times that these effects are so minuscule that they are negligible. However, it does not seem so to me when considering the large timeframes of the universe. The Hubble constant is about 2.2x10^-18 s^1. 13 billion years are 4x10^17 s . Ignoring the fact that the expansion is not constant over time (though slower in the past nonetheless accelerating) when talking about the origin and future of the universe these numbers are too much in the same ballpark as to being ignored. What am I missing? Thanks in advance

This is too basic of a thought to speculate about its implications on my behalf. But an increase in pot energy and hence increase in mass is somehow desirable concerning dark matter.

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    $\begingroup$ Welcome to physics.SE! As space expands the gravitational potential Energy increases Not true. Energy is not globally conserved in general relativity, and the concept of gravitational potential energy is not useful in this context. So does the potential energy between Atoms and quarks and so on. Not sure what you mean here. Are you talking about atoms expanding? That doesn't happen. Even larger objects like galaxies have negligible expansion due to cosmological expansion. See physics.stackexchange.com/questions/70047/… . $\endgroup$ – user4552 Dec 19 '18 at 23:45
  • $\begingroup$ You have some typos in your post. Please clarify what you mean by "The Hubble constant is about 2.2x10^-18 s^1. 13 billion years are 4x10^17 s". $\endgroup$ – Virgo Dec 20 '18 at 3:26
  • $\begingroup$ Nothing change within bound systems, either they are gravitationally or electrically bound nor within nuclei. At least until these things aren't breaking apart in far away future. Expansion does to these things nothing, like a mass suspended to a rope does not fall until the rope breaks. Hope this clarifies although in layman words. $\endgroup$ – Alchimista Dec 20 '18 at 12:50

From a Newtonian perspective, the gravitational potential energy becomes less negative as the Universe expands. However, the kinetic energy of the particles decreases in such a way to cancel this decrease of the negativity of the potential. So overall there is no change to the total mass of the Universe as it expands. Although, I should note that the Newtonian approximation breaks down once one considers length scales which are not much smaller than the Hubble radius which is approximately 14 billion light-years.

  • $\begingroup$ This looks true & I've up-voted it, but, since the up-vote was made after the edit (itself subsequent to your answer) adding a "cosmology" tag, I'm obligated to mention that, even though NASA uses Newton's theory to plot orbits, its uselessness for any potentially infinite cosmology is very concisely described by Guth (using only the simplest algebra & geometry) on p.295-298 in the 1997 ed. of his pop. sci. book titled "The Inflationary Universe", available in the U.S. thru inter-library loans. $\endgroup$ – Edouard Sep 3 '19 at 15:23
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    $\begingroup$ I added a sentence about the length scale on which the Newtonian approximation breaks down. $\endgroup$ – Virgo Sep 4 '19 at 9:30

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