One of the weirdest facts about quantum physics is that particles are constantly springing into and out of existence all around us. Even within "empty space," which seems like it should contain no energy at all, there are virtual particle pairs that manifest for a moment before annihilating each other.
This means that energy is contained even in the empty vacuum of space itself, a fact which yields all sort of strange behavior. This vacuum energy may explain the dark energy that cosmologists observe, but the problem is that the theoretical calculations and experimental observations are off by quite a lot. ?If the theoretical calculations were correct, there'd be a lot more vacuum energy (sometimes called vacuum pressure) and the universe's acceleration would be a lot faster ... so fast that, in fact, the universe probably wouldn't have been able to form galaxies, stars, and planets.
It's precisely this sort of behavior that physicist Brian Greene refers to as quantum jitters in his popular science books. In fact, there's a very high likelihood that this sort of "energy from nothing" aspect of quantum physics provides the physical basis for the formation of the universe. The Big Bang theory describes how the universe proceeded from the moment of its creation, but doesn't actually dictate how that creation occurred. Actually, once you have the laws of quantum physics in place, the idea of manifesting something from nothing becomes relatively commonplace, as described in Lawrence Krauss' A Universe From Nothing and Hawking & Mlodinow's The Grand Design. Of course, general relativity is also needed, for that universe to begin expanding ... at least until we figure out a theory of quantum gravity.
Virtual particles are important in astrophysics for at least one other reason: they provide the basis for the Hawking radiation, the radiation that should be emitted by black holes.
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