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8.3. Tensor degeneracy

All of the above applies to models in which scalar modes dominate. The possibility of a large tensor component yields additional degeneracies, as shown in figure 20. An n = 1 model with a large tensor component can be made to resemble a zero-tensor model with large blue tilt (n > 1) and high baryon content. Efstathiou et al. (2002) show that adding LSS data does not remove this degeneracy; this is reasonable, since LSS data only constrain the baryon content weakly. A better way of limiting the possible tensor contribution is to look at the amplitude of mass fluctuations today: this normalization of the scalar component is naturally lower if the CMB signal is dominated by tensors. These issues are discussed further below.

Figure 20

Figure 20. The tensor degeneracy. Adding a large tensor component to an n = 1 scalar model (solid line) greatly lowers the peak (dashed line), once COBE normalization is imposed. Tilting to n = 1.3 cures this (dot-dashed line), but the 2nd and subsequent harmonics are too high. Raising the baryon density by a factor 1.5 (dotted line) leaves us approximately back where we started.

Another way in which the remaining degeneracy may be lifted is through polarization of the CMB fluctuations. A nonzero polarization is inevitable because the electrons at last scattering experience an anisotropic radiation field. Thomson scattering from an anisotropic source will yield polarization, and the practical size of the fractional polarization P is of the order of the quadrupole radiation anisotropy at last scattering: P gtapprox 1%. This signal is expected to peak at ell appeq 500, and the effect was first seen by the DASI experiment (Kovac et al. 2002). Much more detailed polarization results were presented by the WMAP satellite, including a critical detection of large-scale polarization arising from secondary scattering at low z, thus measuring the optical depth to last scattering (Kogut et al. 2003). On large scales, the polarization signature of tensor perturbations differs from that of scalar perturbations (e.g. Seljak 1997; Hu & White 1997); the different contributions to the total unpolarized Cell can in principle be disentangled, allowing the inflationary test to be carried out.

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