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Since any and every galaxy can be selected as the central galaxy that experiences an equal pull up, down left right and up and down, the resulting conclusion is that there will be no change in relative position between the surrounding galaxies.
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This conclusion does not fit observations though.
We have evidence that suggests our universe is accelerating in its expansion. Enter dark matter and all that stuff I don't understand. Galaxies crash into each other - we are observing this now.
Does this change your opinion on GR? :-k
BTW... Welcome to the Board! =D>