Parameters of Cosmology: Measuring the Geometry of the Universe

The dominant angular scale for microwave background fluctuations is the angle subtended (linked directly) by the sonic horizon at the surface of last scatter. This distance serves as a ruler for measuring the geometry of the universe. In a flat universe, where light will move in a straight line, this scale is roughly one degree. In our temperature fluctuation spectrum, this corresponds to l = 180 on our graph.

If the universe is open, without enough gravitational matter to stop expansion, photons move on more rapidly diverging paths in a negatively curved space as shown on the right. This effect would cause our cosmic ruler to appear to have a smaller angular size. Thus if the universe were open, the location of the first peak in the fluctuation spectrum would appear at smaller angular scales, as indicated by the grey line.

If the universe were closed, with enough gravitational matter to reverse expansion, the angle would appear larger than one degree, represented by a first peak shifting to the left on our graph. A flat universe, where the force of gravitational matter is not forcing a collape or expansion, leaves our ruler image undistorted and remains at roughly 1 degree in size (red line).

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