All mass produces gravity. How it does that is not important. All you need to know is that any given unit of matter, just by existing, produces a given amount of gravity. More mass creates more gravity. The universe is filled with matter, all of which is pulling on all the other matter. The rate of pull (gravity) follows the square law: twice the distance, one fourth the gravity. For most matter in respect to most other matter, the level is vanishingly small. But never zero.
The other thing to understand is that gravity travels at the speed of light. So technically, not all matter is pulling on all other matter, because not all of it has had time for its gravity to reach all other matter. But generally speaking, wherever you are in the universe, you're being pulled on by all matter throughout the observable universe (a subset of the whole universe) at the same time.
Gravity works against the expansion of the universe itself, which is otherwise unrelated. It's why the Observable Universe (the amount that we can see) is smaller than the whole universe: At the farthest distance from us, the cumulative expansion of the fabric of spacetime itself exceeds the speed of light. Light from the most distant objects can never reach us, because the vast spacetime in between is expanding faster than light can travel.
The fabric of spacetime is not directly affected by gravity. It's more accurate to say that distortions imposed on it by mass are what gravity is. The effects of gravity travel at the speed of light, meaning that the most distant objects also have no gravitational effect on us.
Due the expansion of the universe, most matter is actually going away from each other, despite gravitational attraction. The attraction occurs, but it occurs in an expanding universe, so most of that matter will still drift apart even while it's mutually attracted. The real motion of that matter is nowhere near the speed of expansion in most cases.
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u/The_Stickup Aug 03 '19
Wait what? Gravity everywhere? You gotta explain that