If the seeds for galaxy formation are indeed provided by
topological defects, we can expect the resulting power spectrum
of CMB fluctuations to differ from that predicted by inflation.
The full calculation of the power spectrum predicted by defects
is much harder than that for inflation, and consequently the
progress in this field has been relatively slow. Qualitatively,
however, the main difference from the inflationary scenario is
that
all
perturbations have to be generated causally, that is, they must
be within the horizon volume at a given epoch. Thus anisotropies
on scales above about
, as already measured by e.g the COBE satellite, have to be
generated
after
recombination, and correspond to late-time effects. (The horizon
size grows after inflation, roughly like
.) This entails, for example in the case of strings, the
calculation of the properties of the string network through
recombination to late times, which is computationally
intensive.
Recently new techniques to compute the power spectra have
become available. Figure
3
shows a comparison of predictions for global strings, monopoles
and textures made by Pen, Seljak & Turok [78] with experimental results from present CMB experiments.
The defect model predictions were each normalised to COBE at
. In practice, one is allowed to slide each of the curves up and
down so as to best match a range of criteria, rather than (as
here) matching a single large-scale
value. However, even with this freedom it is easily seen that
the models do not fit the data very well. There appears to be
evidence for a much larger acoustic peak in the data than
predicted by defect theories.
The same models can be used to predict the matter power spectrum; this is shown in Figure 4 .
Again, the models have been normalised to COBE, but a change in the normalisation does not appear to be sufficient to produce a good agreement between the predictions and experimental results. Therefore, at present, the models considered by Pen, Seljak & Turok appear to be ruled out by current experimental data, and the case for a topological defect origin of CMB fluctuations is less strong.
However, recent work[35] which uses an analytic expression for the evolution of local
strings from the radiation to matter dominated era as well as
including a non-zero cosmological constant, shows that it is
possible to produce results that contain a broad peak in the
angular power spectrum of the CMB (Figure
5). However, this peak occurs at
which is in disagreement with the CAT and OVRO detections
(Table
2) at these scales. The numerical method for calculating the
matter and CMB power spectra used in this work differs from that
of Pen, Seljak and Turok. It is unclear at present how to compare
the two sets of predictions.
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The Cosmic Microwave Background
Aled W. Jones and Anthony N. Lasenby http://www.livingreviews.org/lrr-1998-11 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |