According to Quantum Mechanics is it possible that the famous "dark energy" and "zero-point energy" are the same thing that drives the accelerated expansion of the universe or maybe related to each other?
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Nobody knows. There are multiple explanations for dark energy that haven't been eliminated. One of the explanations that hasn't been eliminated is zero point energy:
http://arxiv.org/abs/1205.3365.
Another possible explanation is that the alleged expansion is actually a result of neglecting the effects of inhomogeneities on averaging:
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