Bearing these caveats in mind, it is certainly of interest to begin this process of quantitative comparison of CMB data with theoretical curves. Figure 21 shows

a set of recent data points, many of them discussed above, put on a common scale (which may effectively be treated as ), and compared with an analytical representation of the first Doppler peak in a CDM model. The work required to convert the data to this common framework is substantial, and is discussed in Hancock et al. (1997) [35], from where this figure was taken. The analytical version of the power spectrum is parameterised by its location in height and left/right position, and enables one to construct a likelihood surface for the parameters and , where is the height of the peak, and is related to a combination of and , as discussed above. The dotted and dashed extreme curves in Figure 21 indicate the best fit curves corresponding to varying the Saskatoon calibration by ±14%. The central fit yields a 68% confidence interval of

with a maximum likelihood point of after marginalisation over the value of . Incorporating nucleosynthesis information as well, as sketched above (specifically the Copi et al. [22] bounds of are assumed), a 68% confidence interval for of is obtained. This range ignores the Saskatoon calibration uncertainty. Generally, in the range of parameters of current interest, increasing lowers the height of the peak. Thus taking the Saskatoon calibration to be lower than nominal, for example by the 14% figure quoted as the one-sigma error, enables us to raise the allowed range for . By this means, an upper limit closer to 70 km s The best angular resolution offered by MAP is 12 arcmin, in its highest frequency channel at 90 GHz,
and the median resolution of its channels is more like 30 arcmin. This means that it may have
difficulty in pining down the full shape of the first and certainly secondary Doppler peaks in the
power spectrum. On the other hand, the angular resolution of the Planck Surveyor extends
down to 5 arcmin, with a median (across the six channels most useful for CMB work) of about
10 arcmin. This means that it will be able to determine the power spectrum to good accuracy, all
the way into the secondary peaks, and that consequently very good accuracy in determining
cosmological parameters will be possible. Figure 19, taken from the Planck Surveyor Phase A study
document, shows the accuracy to which , and can be recovered, given coverage of 1/3
of the sky with sensitivity 2 × 10^{–6} in per pixel. The horizontal scale represents
the resolution of the satellite. From this we can see that the good angular resolution of the
Planck Surveyor should mean a joint determination of and to 1% accuracy is
possible in principle. Figure 22 show the likelihood contours for two experiments with different
resolutions.

These figures do not, however, take into account any reduction in sensitivity as a result of the need to separate Galactic foregrounds from the CMB. Nevertheless, simulations using a maximum entropy separation algorithm (Hobson, Jones, Lasenby & Bouchet, in press) suggest that for the Planck Surveyor the reduction in the final sensitivity to the CMB is very small indeed, and that the accuracy of the cosmological parameters estimates indicated in Figure 19 may be attainable.

One additional problem is that of degeneracy. It is possible to formulate two models with similar power spectra, but different underlying physics. For example, standard CDM and a model with a non zero cosmological component and a gravity wave component can have almost identical power spectra (to within the accuracy of the MAP satellite). To break the degeneracy more accuracy is required (like the Planck Surveyor) or information about the polarisation of the CMB photons can be used. This extra information on polarisation is very good at discriminating between theories but requires very sensitive polarimeters.

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