If mass/energy causes positive curvature in spacetime, and measurements of the curvature of the universe show that it is flat (or very close to flat), then is there something causing negative curvature to balance out the positive curvature from gravity? Or is this positive curvature negligible (or even infinitesimal?) when viewing the geometry of the universe? (Never studied GR or Non-Euclidean Geometry just know the basics)

  • $\begingroup$ I'm no astrophysicist, but presumably the answer has something to do with dark energy, since that is what is supposedly responsible for the fact that the universe's expansion is accelerating. If gravity were the only force acting, then the expansion should be slowing/ reversing (right?). $\endgroup$ – Time4Tea Aug 15 '18 at 1:15
  • $\begingroup$ Time4Tea dark energy was my first though also, but as the universe expands the density of dark energy remains constant while mass becomes more spread out. Consequently, (if magnitudes were equal) the magnitude of the curvature produced by gravity would be decreasing relative to the magnitude of the curvature produced by dark energy. So I don't see how they could cancel out if one changes and the other doesn't. $\endgroup$ – Knight98 Aug 15 '18 at 4:08

As you guessed in the comments, yes, it's caused by dark energy. The curvature of the Universe is very close to zero (i.e. flat) today; there's no stipulation that the curvature has to be constant, and indeed, if dark energy continues to dominate then it may well deviate from zero. The question of why we live exactly at the point where these things are balanced is known as the coincidence problem.

For more info, see the section on the density parameter here: https://en.m.wikipedia.org/wiki/Friedmann_equations

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  • $\begingroup$ So are you implying that (if dark energy's density is unchanging) the universe once had positive curvature, for a brief period was (or is) flat, and in the future will have negative curvature? Also since dark energy makes up around 70% of the universe while dark matter and ordinary matter only make up 30% should the universe have somewhat negative curvature today? $\endgroup$ – Knight98 Aug 16 '18 at 3:15

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