A Flat Universe
Key Concepts:
-
First peak position consistent with flat
universe
-
Precision currently limited by uncertainties in the
Hubble
constant through the physical density of the
dark matter
-
Main ambiguity will be removed by measuring
higher peaks.
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 Wm+WL=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.
