The Case for Measuring Polarisation

The anisotropic nature of Thomson scattering generates linear polarisation in the CMB (see e.g. Chandrasekhar 1960, Rees 1968, Kaiser 1983, Bond & Efstathiou 1984, Polnarev 1985) which is expected to be at the 10% level of the temperature anisotropy quadrupole. This is in agreement with early experimental upper bounds (Penzias & Wilson 1965). However, measuring CMB polarization is a considerable experimental challenge (see e.g., Keating et al. 1998 and references therein), and it has never been detected. Current experiments designed to measure the polarised signal of the CMB include: POLAR, Polatron and SPOrt.

In general, the temperature anisotropies and the polarisation can be specified by three Stokes parameters, I, Q and U . The fourth Stokes parameter V measures circular polarisation and cannot be generated by Thomson scattering. Theoretical work since the Phase A report has demonstrated a strong scientific case for measuring the polarisation anisotropies. Furthermore, recent work suggests that the polarised components of Galactic emission should be small compared to the primordial signal over much of the sky in the PLANCK Surveyor frequency range (Prunet et al. 1998 ). Figure 1.8a shows raw sensitivity limits as a function of scale for detecting the polarised component of the CMB signal by the PLANCK satellite (it assumes 3 LFI channels, 4 HFI channels and 3 HFI polarization channels; taken from W. Hu's web page). It shows that the PLANCK Surveyor will provide an optimal experimental setup for detecting polarisation given its wide frequency coverage and high sensitivity. For comparison, the sensitivity limits for measuring the amplitude of the CMB anisotropies are also displayed.

Figure 1.8a: Sensitivity limits for CMB polarisation detection with Planck.

The main scientific reasons to measure polarisation are as follows:

$\bullet$ Differentiating between tensor and scalar modes: Any polarisation pattern can be separated into `electric' (E) and `magnetic' (B) components. Scalar perturbations produce a pure E-mode polarisation pattern, vector perturbations (generated in topological defect models) generate mainly a B-mode polarisation pattern and tensor modes generate an admixture of E- and B-modes (see e.g. Kamionkowsky & Kosowski 1996, Zaldarriaga & Seljak 1997). Measuring the polarisation pattern can provide a much more sensitive (and direct) test of the existence of tensor and vector modes than those derivable from the temperature anisotropies alone. The cross-correlation of the polarisation pattern with the temperature also allows a differentiation between scalar and tensor components (Crittenden & Turok 1995).

$\bullet$ Consistency checks for cosmological parameter estimates: The polarisation and polarisation-temperature power spectra are sensitive to cosmological parameters in a similar way to that described for the temperature power spectrum in the previous subsection. For example, figure  1.8b shows how the polarisation power spectrum C_p in scale-invariant, spatially flat, CDM models depends on the parameters $\Omega _b$ and H₀. The polarisation power spectra can therefore be used in their own right to estimate cosmological parameters. This provides an important consistency check of the experiment. A demonstration that we can recover consistent values of the cosmological parameters from the temperature and polarisation measurements would provide powerful evidence to the astronomical community that the results are free of systematic errors.

  

Figure 1.8b: Dependence of the polarisation power spectrum on the baryon density $\Omega _b$ and Hubble constant $h = H_0/100\,{\rm km}{\rm s}^{-1}{\rm Mpc}^{-1}$. In a), we show curves for several values of $\Omega _b$ with the Hubble constant fixed at h=0.5. In b), we show curves for several values of H₀ with the baryon density fixed at $\Omega_b = 0.05$. A scale-invariant, spatially flat, CDM model has been assumed.

$\bullet$ Reionisation in the intergalactic medium: The absence of a Ly$\alpha$ absorption trough in the spectra of high redshift quasars shows that the intergalactic medium must have been reionised at a redshift z > 5. However, it is not yet known when this reionization occurred, or by what mechanism. Polarization measurements of the CMB can set strong limits on the redshift of reionization () so probing the epoch when the first structures in the Universe are believed to have formed.

$\bullet$ Weak gravitational lensing: Gravitational lensing of the CMB polarization pattern caused by structures along the line-of-sight should produce a measurable distortion at the PLANCK sensitivities (Stompor & Efstathiou 1999). A detection of of weak gravitational lensing would constrain the amplitude and spectrum of mass fluctuations in the present Universe.

[last update: 1 August 1999 by P. Fosalba]