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everythingist t1_jak455w wrote

Long answer is long but here's a way to think about it that is physically accurate and not oversimplified as far as I know (I took general relativity 15 years ago so things get fuzzy and I could be forgetting a relevant detail or two)

A dark energy dominated (ie accelerating expansion) universe will have negatively curved spacetime at very large scales. The gravitational effect of regular mass (baryonic and dark both) is to generate local positive curvature of spacetime, which causes the geodesics of nearby objects to bend toward the mass aka falling inward. If you have a large amount of mass sprinkled throughout the universe, the positive curvature generated by that mass will partially offset the negative curvature effect caused by dark energy, slowing expansion.

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etherified t1_jal6iga wrote

Total layman jumping in here, but in the past I've wondered why the expanding space factor doesn't need to be included in calculating local mass-mass interactions. Even though the expansion is something exceedingly small (like 60 km/3 million light years every second or so?), it seemed that it should be included for precision in calculating how masses will move with respect to each other.

The typical answer (summarized) is that "local mass interaction totally overcomes spatial expansion, so only the gravitional effect exists in local systems", but it still seems that there would still have to be some accounting that some of the gravitional "pull" is having to be "used up" to counteract the expansion.

Your explanation above appears to make this even more necessary, since if we think of the expansion as negative curvature (which is in fact really the case), then even local space is, however minutely, curved in a negative way due to expansion. Therefore, any positive curvature of space is being exerted on that already negatively curved background, and hence the positive curvature of space would necessarily have to be minus whatever that negative curvature was (however miniscule).

Unless I should have been interpreting the typical answer to mean "local mass-mass interactions are of course affected by the expansion of space, but the local mass interaction is simply so large with respect to local spatial expansion, that the local effect of spatial expansion, while not zero, can be ignored for calculations". Or something to that effect.

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Aseyhe t1_jalhw7a wrote

> The typical answer (summarized) is that "local mass interaction totally overcomes spatial expansion, so only the gravitional effect exists in local systems", but it still seems that there would still have to be some accounting that some of the gravitional "pull" is having to be "used up" to counteract the expansion.

This is indeed the typical answer but it's not correct. Expansion of space doesn't affect particle dynamics at all. It's just a mathematical convention.

See for example this entry of the askscience FAQ

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FatSilverFox t1_jal7nh6 wrote

Alright I have no idea about anything, but I read your post and my first thought was “good question, but wouldn’t local interactions be identically impacted by expansion, thus negating expansion as a variable?” In other words: would it not be a constant applied to both masses?

Unless the local bodies are 2 different galaxies, in which case now I want to know too.

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BentonD_Struckcheon t1_jakhyfp wrote

Yeah I haven't thought much about this since college but I do remember curved geometries being introduced and the idea that the issue with whether or not the universe would eventually collapse in on itself was a function of which way the universe was curved.

Probably not remembering it right, but your comment jogged my memory.

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Aseyhe t1_jaliccb wrote

That's a bit different because that idea refers to the curvature of space, not spacetime. Space is a 3D surface in 4D spacetime. There are lots of possible choices of spatial surface, but there is a unique choice that makes the universe homogeneous (statistically the same everywhere on the surface). The curvature of this particular choice of spatial surface can indeed inform us as to whether the universe will eventually collapse.

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