According to Newton's 3rd law if body a exerts a force them body b exerts a force that is equal but opposite. Therefore the universe exerts a force on everything that is inside the universe and the moon,planet, stars etc. exerts a force back on the universe.
According to http://www.kickassfacts.com/askus-after-the-big-bang-why-didnt-the-universe-re-collapse-under-its-own-self-gravity/
"It certainly slowed down under its own gravity, but not enough to recollapse.
There’s a very simple (and almost exact) analogy. Let’s represent the Big Bang by launching a rocket. For our purposes, it isn’t propelled at all after the moment of launch, but of course, initially it’s shot up at some very high speed. Your question is exactly analogous to asking why the rocket didn’t fall back down to the Earth.
The answer is that the rocket was launched with an initial speed greater than or equal to the Earth’s escape velocity. As the rocket moves up, gravity does slow it down, but gravity also gets weaker. Escape velocity is the speed where gravity weakens more quickly than it can slow the rocket to a halt. So even though the Earth’s gravity is certainly slowing it down as it goes up, it never slows it down so much that it stops and falls back down to the ground.
We can map this answer directly onto the expanding Universe. Why hasn’t it recollapsed under its own gravity? Because even though the gravity of all the matter and energy in the Universe does cause the expansion to slow down (or at least did, until recently), it was initially expanding so quickly that, like a rocket moving up at escape velocity, it never slowed down quite enough to stop and recollapse."