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  1. Is it just the momentum from the Big Bang? If yes, how can it account for the acceleration of the expansion?
  2. Why isn't the collective gravitational force slowing it down?
  3. What part does dark energy play in the expansion?
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As far as I understood it, no one really knows. It is observable that the universe is expanding with increasing speed, therefore there has to be a form of energy driving it. We can meassure (or at least try) the amount of energy and find $\Omega_\lambda = 69.11\%$ (see $\lambda$CDM-Model)

To your questions:

1: I wouldn't imagine it as Big Bang momentum, for it is also changing. After the Big Bang, there was (or at least had to be, to make our comological model work) a period of inflation, meaning rapid expansion, which then slowed down again. I can't think of an explanation which includes some kind of finite momentum.

2: On small scales (speaking of galaxies), where densities are high, expansion doesn't act. Gravity is working against it.

3: It is responsible for the expansion. How exactly is not understood. (Little personal comment form my side. If a physicist calls something 'dark', it mostly likely means it is not understood)

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    $\begingroup$ 2: Gravity is slowing down the expansion of the Universe as a whole, and was dominating until 3.5 Gyr ago. Only "recently" has dark energy been dominating. $\endgroup$ – pela Feb 10 '16 at 22:10
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    $\begingroup$ 3: The how dark energy is responsible for acceleration (which is what I gather you meant by 'expansion') is well-understood: it follows rather trivially and directly from the Einstein field equation. What's not understood is the reasons/origins for the sign and magnitude of the dark energy. $\endgroup$ – Stan Liou Feb 11 '16 at 0:30
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    $\begingroup$ I think this question has been asked before. I'll comment here what I commented before. If I placed a bet on this, I would wager that dark energy is the result of a pressure caused by the energy in empty space. The real question should be " Why don't we find a lot more energy?" $\endgroup$ – Jack R. Woods Feb 11 '16 at 3:15
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    $\begingroup$ Just wanted to add that original answers as well as all your posts contribute to answering my questions. I don't see a way to indicate that in the current tool, so I'll mark the original answer as the answer. Thanks $\endgroup$ – signsgeek Feb 11 '16 at 19:59
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    $\begingroup$ @signsgeek watch this www.youtube.com/watch?v=GgKGPyFL-TM . I'm sure you will find it fascinating (and the math really isn't that bad). As regards to your question in the comment: "I'm sure you are aware that energy already accounts for 70% of the mass of the known universe". If Susskind and others are correct then the answer is "Yes. As space expands, the amount of energy increases. In addition the expansion of space should approach an exponentially accelerating expansion." $\endgroup$ – Jack R. Woods Feb 12 '16 at 23:51

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