Cosmological models and constraints 239oscillates arounda. If the oscillation amplitude is much larger thana=
3 ρb/ 4 ργ, then the oscillations are effectively about the mean temperature.
The positive and negative oscillations are of the same amplitude, so when the
apparent temperature is squared to form the power spectrum, all of the peaks
have the same height. However, if the baryons contribute a significant mass so
thatais a significant fraction of the oscillation amplitude, then the zero point
of the oscillations are displaced, and when the apparent temperature is squared
to form the power spectrum, the peaks arising from the positive oscillations are
higher than the peaks from the negative oscillations. Ifais larger than the
amplitude of the oscillations, then the power spectrum peaks corresponding to
the negative oscillations disappear entirely. The physical interpretation of this
effect is that the baryon mass deepens the potential well in which the baryons are
oscillating, increasing the compression of the plasma compared to the case with
less baryon mass. In short, as the baryon density increases, the power spectrum
peaks corresponding to compressions in potential wells get higher, while the
alternating peaks corresponding to rarefactions get lower. This alternating peak
height signature is a distinctive signature of baryon mass, and allows the precise
determination of the cosmological baryon density with the measurement of the
first several acoustic peak heights.
7.5 Cosmological models and constraints
The cosmological interpretation of a measured microwave background power
spectrum requires, to some extent, the introduction of a particular space of
models. A very simple, broad and well-motivated set of models are motivated
by inflation: a universe described by a homogeneous and isotropic background
with phase-coherent, power-law initial perturbations which evolve freely. This
model space excludes, for example, perturbations caused by topological defects
or other ‘stiff’ sources, arbitrary initial power spectra, or any departures from
the standard background cosmology. This set of models has the twin virtues
of being relatively simple to calculate and best conforming to current power
spectrum measurements. (In fact, most competing cosmological models, like
those employing cosmic defects to make structure, are essentially ruled out by
current microwave background and large-scale structure measurements.) This
section will describe the parameters defining the model space and discuss the
extent to which the parameters can be constrained through the microwave
background.
7.5.1 A space of models
The parameters defining the model space can be broken into three types:
cosmological parameters describing the background spacetime; parameters
describing the initial conditions; and other parameters describing miscellaneous
additional physical effects. Background cosmological parameters are as follows.