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The question I have is: Why is space (almost perfectly) flat in our neighbourhood? (I am disregarding the deviations due to the sun and the planets.)

Is it correct to say that space is (almost) flat because throughout the universe, masses are distributed (almost) homogeneously? (Greetings to Sciama.)

Or is it more correct to say that space is (almost) flat because that is what occurs without any mass at all? In this case, the answer might be: space is almost flat because there is so little mass in the universe. Is this closer to the truth?

Or is there a third answer?

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  • $\begingroup$ possible duplicate of Difference between horizon and flatness problems & how inflation solves flatness (w/out math) $\endgroup$
    – user10851
    Commented Mar 1, 2015 at 7:47
  • $\begingroup$ I am asking for the flatness in our neighbourhood - not necessarily on the flatness of the universe. I did not think about inflation at all. $\endgroup$
    – Hans973
    Commented Mar 1, 2015 at 7:57
  • $\begingroup$ What do you mean by "flat" here? Do you mean the cosmological meaning of the word (i.e., lack of curvature), or do you mean the geometric meaning (i.e., the solar system is a plane)? $\endgroup$
    – Kyle Kanos
    Commented Mar 1, 2015 at 16:29
  • $\begingroup$ I meant "flat" as opposite to "curved". $\endgroup$
    – Hans973
    Commented Mar 1, 2015 at 18:00

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"Or is it more correct to say that space is (almost) flat because that is what occurs without any mass at all? In this case, the answer might be: space is almost flat because there is so little mass in the universe."

This is correct if you limit yourself to the vicinity of the solar system, spacetime is relatively flat because there is relatively small mass in the solar system. It is definitely not true in general; spacetime near the event horizon of a black hole is very curved, as is the overall structure of the Universe.

Here's a related mathematical fact. Zoom in on area of spacetime, and it locally appears flat. And the further you zoom in, the flatter it looks. This is a consequence of the equations of GR. By the time you are zooming down to the scale of the solar system, you have zoomed so far (compared to the size of the Universe) it looks almost totally flat.

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  • $\begingroup$ Exactly. I.e., the question is not “why is space flat?” (it isn't) but “why does everything we do occur on a scale so small that space appears flat to us?” – to which the answer, I suppose, can't be given as anything more satisfying than the anthropic principle. $\endgroup$
    – leftaroundabout
    Commented Mar 1, 2015 at 11:55

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