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instanton
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OK, I'm not an expert in cosmology but I'm quite curious about it. Current observations tells us that the universe is accelerating (in what sense I don't quite understand). On the other hand, the Friedman equation says that the scale factor a(t) has a positive second time derivative provided the equation of state of the whole universe obays some condition (e.g. \rho+3 p < 0 if the whole matter content in the universe is an ideal fluid). What bothers me is that the time t in Friedman equation is only the FRW coordinate time, not the proper time. So a(t) has a possitive second time derivative does not gurantee that the universe is accelerating irrespective of observers. In particular, in FRW coordinates, observers sitting at the origin of FRW coordinates should not be accelerating in t, because the actual radial coordinate should be a(t) times r, rather than just a(t). on the other hand, we can easily infer that other (comoving) observers sitting at other places of the universe should percieve us as being accelerating in their owh FRW coordinate (with the origin located at their own place). If the other observers are not comoving, they might found the evolotion of the universe very different from what we observe. So, what it really means by the statement that the universe is under acceletating expansion? Are we accelerating ourselves in the universe?