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So I am currently reading the book We have no idea by Jorge Cham and Daniel Whiteson.
In one of their chapters they talk about how gravity is a force that only attracts and doesn't repel, most of the time. Dark energy is what makes up 68% of the universe and the only way we know it exists is from its rapid expansion.

The expansion isn't slowing down, however, it is speeding up. Gravity is a force that is said to be a force that only attracts and doesn't repel, unlike electromagnetism, the weak force and the strong force. Gravity should be slowing down that expansion, and I am wondering if anyone can explain this or is this concept out of our reach.

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In addition to not knowing, there's other reasons to suspect gravity wouldn't reverse. There's no known force that reverses over distance (OK, the strong force, kinda/maybe but over very short distances). Also, the expansion of space explains things that we seem to observe or suspect occurred like galaxies moving away from us faster than the speed of light and the rapid expansion that's suspected to have happened very shortly after the big bang. Gravity can't do either of those things.

There's also the problem of how would gravity know that things are so far apart that they should start repelling, where nearby galaxies are still too close but more distant galaxies the repulsion kicks in? It doesn't make a whole lot of sense that gravity would account for both attraction and expansion of space.

That's not to say it's impossible. We don't know how gravity works or what it is, so, maybe. Never say never, until something is understood.

@eshaya's answer, "We don't know" is probably the more straight forward answer to this question, but I wanted to point out some problems with repulsive gravity theory as well.

In addition (and I don't understand precisely why), but the gravitational waves discovery has ruled out some theoretical gravity/dark energy proposals.

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We do not yet know the answer to this question. We observe the universal expansion, which should be slowing down from mutual gravitational attraction, is not slowing down as much as it should and might not be slowing down at all about now. One explanation for this is that the cosmological constant, an added term in Einstein's equations of General Relativity is non-zero. This term allows for gravity to effectively repel by causing expansion in low density regions. For the entire universe, the expansion resulted from an initial impulse (the Big Bang) and gravity has been working against this, trying to compress it. With the cosmological constant included, as more and more regions of the universe reach sufficiently low densities, gravity reverses and enhances expansion.

Alternatively, some think the expansion is due to some particle or another force that provides a negative pressure in the universe.

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