256 The cosmic microwave background
Figure 7.4.Polarization power spectra from tensor perturbations: the full curve isClGand
the broken curve isCCl. The amplitude gives a 10% contribution to the COBE temperature
power spectrum measurement at lowl. Note that scalar perturbations give no contribution
toClC.
stating this conclusion is that primordial density perturbations producenoC-type
polarization as long as the perturbations evolve linearly. However, primordial
tensor or vector perturbations produce both G-type and C-type polarization of
the microwave background (provided that the tensor or vector perturbations
themselves have no intrinsic net polarization associated with them).
Measurements of cosmological C-polarization in the microwave background
are free of contributions from the dominant scalar density perturbations and thus
can reveal the contribution of tensor modes in detail. For roughly scale-invariant
tensor perturbations, most of the contribution comes at angular scales larger than
2 ◦(2<l<100). Figure 7.4 displays the C and G power spectra for scale-
invariant tensor perturbations contributing 10% of the COBE signal on large
scales. A microwave background map with forseeable sensitivity could measure
gravitational wave perturbations with amplitudes smaller than 10−^3 times the
amplitude of density perturbations (Kamionkowski and Kosowsky 1998). The
C-polarization signal also appears to be the best hope for measuring the spectral
indexnTof the tensor perturbations.