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How does the mass encased within the Hubble sphere/volume (both proper and comoving) change with time?

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It seems that we live in a universe which is accelerating, but with a decreasing Hubble constant (See How is the Universe's Expansion Accelerating if the Hubble Constant is Decreasing?)

In this universe the Hubble volume expands with time, and can overtake sources that are currently more distant than the Hubble length. That is the Hubble length increases faster than those objects are receding. And so the mass in the Hubble volume will increase.

(from Wikipedia, which cites Expanding Confusion:common misconceptions of cosmological horizons and the superluminal expansion of the universe)

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  • $\begingroup$ Are there any precise mass estimates on this (for example: in kg)? I've noticed that the mass + energy content of a Hubble volume (at this moment) is very close to that of a corresponding black hole and I'd like to know if this was always true or if this is true only for a given period of time. $\endgroup$ Dec 11, 2022 at 16:32
  • $\begingroup$ I think you're talking about a black hole cosmology. en.wikipedia.org/wiki/Black_hole_cosmology and see physics.stackexchange.com/questions/412998/… $\endgroup$
    – James K
    Dec 11, 2022 at 16:47

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