waynehu
Professor,
Department of Astronomy and Astrophysics
University of Chicago
ACOUSTIC PEAKS
When the temperature of the Universe was 
K at a redshift 
, electrons and protons combined to form neutral hydrogen, an event usually
known as recombination ([Peebles, 1968,Zel'dovich et al, 1969]; see [Seager et al, 2000] for recent refinements).
Before this epoch, free electrons acted as glue between the photons and the
baryons through Thomson and Coulomb scattering, so the cosmological plasma was
a tightly coupled photon-baryon fluid [Peebles & Yu, 1970]. The spectrum depicted
in Plate 1 can be explained almost completely
by analyzing the behavior of this pre-recombination fluid.
In §3.1, we start from the two basic
equations of fluid mechanics and derive the salient characteristics of the anisotropy
spectrum: the existence of peaks and troughs; the
spacing between adjacent peaks; and the location
of the first peak. These properties depend in decreasing order of importance
on the initial conditions, the
energy contents of the Universe before recombination
and those after recombination.
Ironically, the observational milestones have been reached in almost the opposite
order.
Throughout the 1990's constraints on the location of
the first peak steadily improved culminating with precise determinations
from the TOCO [Miller et al, 1999], Boomerang, [de Bernardis et al, 2000] and Maxima-1
[Hanany et al, 2000] experiments (see Plate
1 top). In the working cosmological model
it shows up right where it should be if the present energy density of the Universe
is equal to the critical density, i.e. if the Universe is flat. The skeptic
should note that the working cosmological model assumes a particular form for
the initial conditions and energy contents of the Universe before recombination
which we shall see have only recently been tested directly (with an as yet much
lower level of statistical confidence) with the higher peaks.
In §3.2 we introduce the initial conditions
that apparently are the source of all clumpiness in the Universe. In the context
of ab initio models, the term ``initial conditions'' refers to the physical
mechanism that generates the primordial small perturbations. In the working
cosmological model, this mechanism is inflation
and it sets the initial phase of the oscillations to be the same across all
Fourier modes. Remarkably, from this one fact alone comes the prediction that
there will be peaks and troughs in the amplitude of the oscillations as a function
of wavenumber. Additionally the inflationary prediction of an approximately
scale-invariant amplitude of the initial perturbations implies roughly scale-invariant
oscillations in the power spectrum. And inflation generically predicts a flat
Universe. These are all falsifiable predictions of the simplest inflationary
models and they have withstood the test against observations to date.
The energy contents of the Universe before recombination all leave their distinct
signatures on the oscillations as discussed in §3.3-§3.5.
In particular, the cold dark matter and baryon
signatures have now been seen in the data [Halverson et al, 2001,Netterfield et al, 2001,Lee et al, 2001]. The coupling between electrons
and photons is not perfect, especially as one approaches the epoch of recombination.
As discussed in §3.6, this imperfect
coupling leads to damping in the anisotropy spectrum:
very small scale inhomogeneities are smoothed out. The damping phenomenon has
now been observed by the CBI experiment [Padin et al, 2001]. Importantly, fluid
imperfections also generate linear polarization as
covered in §3.7. Because the imperfection
is minimal and appears only at small scales, the polarization generated is small
and has not been detected to date.
After recombination the photons basically travel freely to us today, so the
problem of translating the acoustic inhomogeneities in the photon distribution
at recombination to the anisotropy spectrum today is simply one of projection.
This projection depends almost completely on one number, the angular diameter
distance between us and the surface of last scattering. That number depends
on the energy contents of the Universe after recombination through the expansion
rate. The hand waving projection argument of §3.1
is formalized in §3.8, in the process
introducing the popular code used to compute anisotropies, CMBFAST.
Finally, we discuss the sensitivity of the acoustic peaks to cosmological
parameters in §3.9.
Next: Basics
Up: Cosmic Microwave Background Anisotropies
Previous: CMB Polarization Field
Wayne Hu
2001-10-15