Professor, Department of Astronomy and Astrophysics
University of Chicago

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A Flat Universe

Key Concepts

Now let's have a look at the data again:

The position of the first peak indicates that the universe is very close to spatially flat.   In terms of a parameterization where the (dark) matter density and dark energy (or cosmological constant) dominates the energy density of the universe today,  a flat universe has &Omegam+&Omega&Lambda=1 and lies on the red line:

We will see why we introduce the dark energy in the next section.

How close to perfectly flat is the universe? The answer to that question is an currently an evasive "that depends".  In fact, reasonable people say different things and report constraints in the above plane that mean different things.  Here we display the literal 95% confidence constraints described by the Boomerang and Maxima groups in their respective detection papers.

The observations themselves are exquisitely precise and the ambiguity does not lie there.  The problem is that thing we shoved under the rug in the description of the test for curvature.  There is currently a small uncertainty in the length of the rulers in the angular diameter distance test: we do not yet know precisely how far sound can travel by recombination as compared with how far CMB photons travel since recombination.  The answer hinges mainly on the physical density of the dark matter as compared with the radiation and somewhat on the baryon density and the nature of the assumed dark energy.   That means any uncertainty in the Hubble constant translates into uncertainty on how flat the universe is.  Luckily the main effect from the physical density of dark matter will be resolved once the higher peaks are measured.