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Say we have a closed universe that follows the cosmological principle. As a result, mass is distributed equally and, if as far as I know, gravity should have no net effect on the movements of galaxies (as in, there are no peculiar velocities).

However, in the Big Crunch, the Universe stops expanding and gravity causes the scale factor to decrease. How is this possible? Shouldn't gravity have no effect on a homogenous and isotropic universe?

On that note, if gravity actually caused a collapse, would gravity cause the comoving coordinates of the galaxies to change?

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    $\begingroup$ Because the universe obeys the Freidmann equations. You are thinking about galaxies moving within space, but that is not what happens in a uniform universe, it is the space that contracts. $\endgroup$
    – ProfRob
    Apr 17, 2017 at 10:46

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You are thinking about gravity and how it affects the universe as a whole in the wrong way.

The dynamics of the universe are governed by the Friedmann equations, which can be solved to say how the scale factor of a homogeneous, isotropic universe behaves with time.

If there is enough gravitating matter/energy density in the universe then the scale factor may eventually decrease to zero in a finite time. The simplest case is a closed universe with no cosmological constant and a mass density greater than the critical density (which is not the universe we currently inhabit: our universe appears to be (a) flat and (b) expanding at an accelerating rate).

The interpretation of this is that the space between the galaxies is contracting. It is the reversal of what we currently observe in the expanding universe.

In the same way that you do not interpret the universal expansion of a homogeneous, isotropic universe as some sort of repulsion between galaxies; neither would the contraction be interpreted as some sort of attractive force between galaxies. As you rightly point out, in a strictly Newtonian sense, there would be no net gravitational force on any one galaxy and so its co-moving coordinates would be unchanged during the contraction.

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  • $\begingroup$ If gravity would not change the comoving coordinates of the galaxies, does that imply that gravity can cause two objects to apparently attract faster than light? $\endgroup$
    – Sir Cumference
    Apr 17, 2017 at 18:30
  • $\begingroup$ @SirCumference I don't know what this comment means. $\endgroup$
    – ProfRob
    Apr 17, 2017 at 19:15
  • $\begingroup$ You know how the Hubble flow can cause objects to apparently recede from us faster than light? Can gravity cause objects to come closer to us faster than light? $\endgroup$
    – Sir Cumference
    Apr 17, 2017 at 20:10
  • $\begingroup$ @SirCumference Those are different things. The Hubble flow is simply an expansion of the metric, and it doesn't care about speed of light. Gravitational collapse still implies 2 or more bodies moving under external forces, and therefore cannot exceed the speed of light. So the answer is no. $\endgroup$
    – Florin Andrei
    Apr 17, 2017 at 22:55
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Can gravity cause a Big Crunch, if the cosmological principle holds?

No. That's a myth that grew out of the Friedmann equations. Alexander Friedmann was a ballistics instructor on the Austrian front. He modelled the expanding universe as something like a cannonball fired aloft. See John Peacocks’s cosmological physics for an example: “the dynamics of the entire universe are the same as those of a cannonball fired vertically against the Earth’s gravity. Just as the Earth’s gravity defines an escape velocity for projectiles, so a universe that expands sufficiently fast will continue to expand forever. Conversely, for a given rate of expansion there is a critical density that will bring the expansion asymptotically to a halt”.

enter image description here                                   Image from Norbert Rumiano’s article a cosmological model

It’s totally wrong I'm afraid. Gravity doesn’t stop the universe expanding. A gravitational field is akin to a pressure-gradient in space. It makes matter fall down, but it doesn’t make space fall down. You can tell it’s wrong because Big Bang cosmology is said to be balanced on a knife edge, such that the density of the universe is incredibly close to the critical density. That’s just a re-heat of Einstein’s greatest blunder, wherein a slight increase in density would trigger contraction, and a slight decrease would trigger expansion. It’s also wrong because the 1998 supernova observations didn’t match any of the cannonball trajectories. They didn’t measure the expansion slowing down, they measured it speeding up. Like the ascending light beam speeds up, because the speed of light is spatially variable. Unfortunately people like John Moffat and João Magueijo and other VSL guys said the speed of light in the universe is slowing down, not speeding up. Unfortunately the Friedmann equations feature not just a fixed c, but a curvature k. Even though a gravitational field is a place where the speed of light varies because space is neither homogeneous nor isotropic. Not a place where space is curved.

Say we have a closed universe that follows the cosmological principle.

We have no evidence that the universe is closed, or that the cosmological principle is scientific. I think it's rather like saying I live in a forest, so everybody must see trees.

As a result, mass is distributed equally and, if as far as I know, gravity should have no net effect on the movements of galaxies (as in, there are no peculiar velocities).

The issue isn't with galaxies, it's with space. Space is expanding like the raisin cake analogy, and gravity won't stop that.

However, in the Big Crunch, the Universe stops expanding and gravity causes the scale factor to decrease. How is this possible? Shouldn't gravity have no effect on a homogenous and isotropic universe?

I don't think it is possible. Note that Einstein described a gravitational field as a place where space was neither homogeneous nor isotropic. So a homogeneous isotropic universe is one where there is no gravity.

On that note, if gravity actually caused a collapse, would gravity cause the comoving coordinates of the galaxies to change?

I would say no. I'd also say gravity doesn't cause a collapse.

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    $\begingroup$ You have a tendency to visit questions asking about theory, just to rant about the lack of evidence. That's not an answer, nor is Stack Exchange the place for that. $\endgroup$
    – Sir Cumference
    Mar 30, 2019 at 22:44
  • $\begingroup$ @Sir Cumference : This is a step-by-step answer that's factual with some great references. Pointing out that's there's no evidence for something is not a rant. $\endgroup$
    – John Duffield
    Mar 31, 2019 at 15:08
  • $\begingroup$ Would any of the downvoters care to point out where any aspect of this answer is incorrect or misleading? Or to any references or quotes that are out of context? Einstein really did describe a gravitational field as a place where "the speed of light is spatially variable", and a place where space "is neither homogeneous nor isotropic". $\endgroup$
    – John Duffield
    Apr 1, 2019 at 18:45

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