Cosmological models and constraints 24936 000μK^2 , and second, a broad plateau betweenl=400 andl=700 with
an amplitude of approximatelyl^2 Cl =10 000μK^2. The first peak is clearly
delineated and provides good evidence that the universe is spatially flat, i.e.
=1. The issue of a second acoustic peak is much less clear. In most flat
universe models with acoustic oscillations, the second peak is expected to appear
at an angular scale of aroundl=400. The angular resolution of the balloon
experiments is certainly good enough to see such a peak, but the power spectrum
data show no evidence for one. I argue that a flat line is an excellent fit to the
data pastl=300, and that any model which shows a peak in this region will be a
worse fit than a flat line. This does not necessarily mean that no peak is present;
the error bars are too large to rule out a peak, but the amplitude of such a peak is
fairly strongly constrained to be lower than expected given the first peak.
What does this mean for cosmological models? Within the model space
outlined in the previous section, there are three ways to suppress the second peak.
The first would be to have a power spectrum indexnsubstantially less than one.
This solution would force abandonment of the assumption of power-law initial
fluctuations, in order to match the observed amplitude of large-scale structure at
smaller scales. While this is certainly possible, it represents a drastic weakening in
the predictive power of the microwave background: essentially, a certain feature
is reproduced by arbitrarily changing the primordial power spectrum. While
no physical principle requires power-law primordial perturbations, we should
wait for microwave background measurements on a much wider range of scales
combined with overlapping large-scale structure measurements before resorting
to departures from power-law initial conditions. If the universe really did possess
an initial power spectrum with a variety of features in it, most of the promise
of precision cosmology is lost. Recent power spectra extracted from the IRAS
Point Source Survey Redshift Catalogue (Hamilton and Tegmark 2000), which
show a remarkable power law behaviour spanning three orders of magnitude in
wavenumber, seem to argue against this possibility.
The second possibility is a drastic amount of reionization. It is not clear the
extent to which this might be compatible with the height of the first peak and still
suppress the second peak sufficiently. This possibility seems unlikely as well, but
would show clear signatures in the microwave background polarization.
The most commonly discussed possibility is that the very low second
peak amplitude reflects an unexpectedly large fraction of baryons relative to
DM in the universe. The baryon signature discussed in section 7.4.4 gives a
suppression of the second peak in this case. However, primordial nucleosynthesis
also constrains the baryon–photon ratio. Recent high-precision measurements
of deuterium absorption in high-redshift neutral hydrogen clouds (Tytleret al
2000) give a baryon–photon number ratio ofη = 5. 1 ± 0. 5 × 1010 ,which
translates tobh^2 = 0. 019 ± 0 .002 assuming that the entropy (i.e. photon
number) per comoving volume remains constant between nucleosynthesis and
the present. Requiringbto satisfy this nucleosynthesis constraint leads to
microwave background power spectra which are not particularly good fits to the