Curvature

The peaks in the CMB power spectrum are highly sensitive to the curvature of the early universe, as curvature affects both the angular scale and the sound horizon—the distance sound waves traveled from the Big Bang to the surface of last scattering. In a flat universe, \(\Omega_{k}\) = 0, the angular scale of the sound horizon aligns with predictions, requiring dark energy to account for the universe’s flatness despite insufficient visible matter. In an open universe,\(\Omega_{k}\) < 0, with a saddle-shaped geometry, light waves diverge, making the angular size of CMB fluctuations appear smaller and shifting acoustic peaks to smaller angular scales. Conversely, in a closed universe, \(\Omega_{k}\) > 0, resembling a sphere, light rays converge, making fluctuations appear larger and shifting peaks to larger angular scales. We can have confidence in the flatness of the universe due to fact that the angle at which we observe the CMB sound horizion would vary given a different curvature, and the angle we see only makes sense in a flat universe.

\(\Omega_{k}\)0