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The Baryon Oscillation Spectroscopic Survey (BOSS) announced that BOSS has measured the scale of the universe to an accuracy of one percent. http://newscenter.lbl.gov/2014/01/08/boss-one-percent/

In their statement they also concluded: “One of the reasons we care is that a flat universe has implications for whether the universe is infinite,” says Schlegel. “That means – while we can’t say with certainty that it will never come to an end – it’s likely the universe extends forever in space and will go on forever in time. Our results are consistent with an infinite universe.”

The only problem is, empty space isn't empty; it contains a small amount of vacuum energy or zero point energy. https://en.wikipedia.org/wiki/Vacuum_energy

I am no whiz in math but I can add, if the universe is infinite and space contains even a small amount of energy, that means there is an infinite amount of energy and therefore mass in the universe. Where are the gravitational effects of this infinite mass?

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The Shell Theorem states that an isotropic spherical shell of massive matter exerts no gravitational force on a body inside it, because the pull from mass on opposite sides cancel each other out.

As soon as you get to sufficiently large distances from any point in space, the mass distribution gets fine grained enough to be effectively isotropic, and the entire Universe outside this bubble will be made up of such spherical shells.

The only remaining gravitational force is that due to anisotropies and inhomogeneities in the surroundings, and these will always be local.

If the Universe had a center of mass, the picture would be radically different -- any observer away from the center would experience a net pull towards it.


EDIT: Of course, the speed-of-light argument in Lewis Miller's answer is also partially correct (although it is unfortunately oversimplified to the level of being wrong). It is correct that our past light cone (a large chunk of which has always receded from us faster than light) limits which regions of Space can influence us causally. But I think the Universe becomes effectively isotropic well within our light cone.

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Even if the universe is infinite in extent, there is only a finite portion of it that can have a gravitational effect upon us. That is because beyond a certain finite distance space is expanding faster than the speed of light. Just as light from that region will never reach us, likewise gravity is also not reaching us from those remote regions.

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  • $\begingroup$ how can energy or matter travel faster than light? I wasn't thinking of the gravitational effects on Earth, but instead on the Cosmos. Wouldn't infinite mass tug at the super clusters and filaments of the Cosmic Web? blogs.scientificamerican.com/sa-visual/… $\endgroup$ Feb 7, 2017 at 16:39
  • $\begingroup$ Never mind about faster than speed of light, I found what you mean en.wikipedia.org/wiki/Hubble%27s_law But still don't understand why infinite mass doesn't affect the Cosmic Web $\endgroup$ Feb 7, 2017 at 16:49
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    $\begingroup$ This experiment needs confirmation, also the Cosmic Web is within the observable universe, so the above answer applies to everything within our "bubble". $\endgroup$
    – user140606
    Feb 7, 2017 at 17:31
  • $\begingroup$ It is a common misconception, but still wrong, that light from regions of the Universe receding at superluminal speed can never reach us. All regions of Space at cosmological redshifts larger than around 1.5 have always receded from us faster than light, and we routinely observe those on almost industrial scales these days. $\endgroup$
    – Thriveth
    Feb 9, 2017 at 10:32
  • $\begingroup$ For those who may be confused by @Thriveth above comment and the edited answer, the distinctions being made are between the Hubble volume (or sphere) and the observable universe (larger). $\endgroup$ Feb 9, 2017 at 16:36

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