Astronomers believe the answer may be
that the expansion is powered by vacuum energy,
energy that is hidden in the emptiness of space
that fills the universe.
Quantum physics requires "empty space" to be filled with
particles and anti-particles being continually created and annihilated. This could
involve a net vacuum energy, which, if present, would behave
like a repulsive force at large enough distances.
If this view is correct, then the source of the acceleration of the
universe is the vacuum that surrounds and permeates each one
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