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I understand that the accepted theory is that dark energy is scattered pretty much evenly between galaxies and pushes all galaxies outwards one from another another, with some exceptions of collisions such as the expected event in which Andromeda will collide in Milky Way in about 4.5 billion years.

Unorthodoxly, I wondered if the universe is expanding equally in a cosmos by dark energy that surrounds it from the outside and pulling everything towards it evenly while such pulling outwards might be finite if it's actually a giant mass sphere pulling everything towards it or infinite if it's infinitely expanding outwards along with galaxies.

Does either of the two unorthodox ideas supported, or dismissed, by evidence?

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No, it is not possible. Actually, Dark Energy can neither be repulsion from inside, nor attraction from outside. (Outside attraction is ruled out by Anna V's comment anyway).

There is an observational evidence for the above. That evidence is in the expansion rate of universe which exceeds speed of light at large enough distances. Any attraction, or repulsion would be eventually a force (gravity included, see next para) and could not make the "universe expand" (objects move wrt one another), at FTL inside space, if we were to go by relativity. Therefore, it can neither be internal repulsion, nor be external attraction, it has to be just expansion of space itself.

I mentioned gravity in context of attraction and repulsion because - if gravity (given sufficient distance to accelerate) was capable of accelerating something to FTL, then we know that escape speed from a black hole is $c$. That would also be ~speed at which a free falling object would enter the event horizon. Therefore if we were to shoot an object towards event horizon with fast speed, then it may have been possible for that object to attain FTL speeds prior to reaching EH, which is prohibited by relativity. I have not done any calculations about it but it seems at least with the help of slingshots with multiple black holes, it could have been possible for an object to attain FTL. Which goes against relativity as far as I know.

One more point to note is that the expansion of universe has been accelerating only for last ~5 billion years. Before that it was a slowing expansion. As we know for sure that it started out as accelerated expansion at big bang. So we already know that the expansion has switched from accelerating, to slowing down and then again to accelerating. Therefore the expansion is fluctuating between accelerating, and slowing down. Given the age of universe as 14 billion years and already two switches taken place, 5*3 = 15. In a billion years or so, it may again switch to slowing down expansion.

This fluctuation between accelerating, and slowing down of expansion suggests that both - inside attraction, and outside repulsion can be ruled out.

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No, does not make any sense.

I'll treat it a s a possible tentative hypothesis and explain why it makes little sense. See the wiki article on Dark Energy.

https://en.m.wikipedia.org/wiki/Dark_energy

The inner layer would act on the outer layer, but Dark Energy is repulsive, not attractive. So inside or not does not matter.

Also, if you mean a spatial 3D spherical universe, what that means is that evert high is on the surface, there's nothing inside. If you mean a 3D spherical space which is expanding in the fourth dimension, time, to fill spacetime, that Dark Energy if it is that, it means it was there at one time and then disappeared. When it was there it was attracting or repelling (if normal matter attracting, if abnormal dark energy repelling), and then it stopped doing that. But we know that dark energy has been active at least the last 5-7 billion years, we think there before also but too weak to have affected us much [yes, dark energy affects us more as the universe expands].

Your theory does not match any observations already made.

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