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?