Primary anisotropies in Temperature

Archeops Map at 143 GHz. Both primordial fluctuations and galactic signal are visible [from Archeops collaboration]

CMB anisotropies in Polarization

Until decoupling, photons mainly interact with free electrons via Thomson scattering. This interaction selects the polarization direction which is orthogonal to the scattering plane. To produce a polarized scattered radiation the incoming radiation on electrons must be quadrupolar. Density fluctuations that already produce temperature anisotropy also lead to such quadrupolar fluid velocity field and therefore to a polarized component of the CMB. This component is correlated to the temperature anisotropy and shows even parity patterns on the sky. The relevant quantity to analyze it statistically and to account for its parity was named E, by analogy with the parity of an electric field.

While confirming the inflationary paradigm and the physics of CMB anisotropy generation,  the CMB polarization provides complementary information to temperature anisotropy measurements and permits the breaking of degeneracy between cosmological parameters (e.g. scalar spectral index and reionization optical depth). It gives exclusive information on the details of reionization history. It is also distorted by the weak lensing of large scale structures and this can be used to constrain neutrino absolute mass.

A second source of quadrupoles is the primordial gravitational wave background potentially generated in the very early universe during Inflation. It is considered as the Holy Grail of the quest for CMB polarization, since it would provide information on the primordial universe when it was younger than  ~10^-32 sec and when physical processes happened at energies of ~10¹⁵GeV, still far beyond the reach of particle accelerators. The imprint of these gravitational waves is characterized by odd-parity patterns in the polarization field, and the relevant quantity to study these patterns statistically was named B, once again by analogy, but this time with a magnetic field. The key is that density perturbations do not produce B type polarization, and so, its detection would actually sign the presence of a significant amount of primordial gravitational waves at recombination. However, as exciting as this possibility may be, one should keep in mind that the amplitude of the signal may very well remain undetectable.

We have investigated the secondary polarization induced by the CMB primary quadrupole. We have focused on the effect on large scale structures. More precisely, we have used hydrodynamical simulations of large scales structures to predict the polarized signal at the scales of galaxy clusters and filaments. We find that the dominant polarized signal is due to the scattering on electrons in the warm ionized gas in filaments which is a signal at large  scales. The hot ionized gas in clusters also induces polarized anisotropies which contribution dominates at smaller scales.

From the observational point of view, our group is involved in several experiments that aim at characterizing the CMB polarization angular power spectra. We are PI of the Planck-HFI instrument. We have a deep involvement both on the instrumental parts and data analysis. We are also involved in the data analysis of BICEP and EBEX. BICEP started its first year of observation from South Pole this year 2006. EBEX is a balloon borne experiment that will have its first scientific flight in 2008.

Secondary anisotropies from transverse motion of structures

Transverse motions of the structures mimic the effect of a non-static gravitational potential in the case of intrinsically static potentials. The blue and red shifting of CMB photons entering a gravitational potential ahead of the structure path, and in its wake respectively, leaves a bipolar imprint in CMB.  The effect of a cluster population is too small to be used to measure cluster transverse velocities.

Secondary anisotropies from scattering effects

Inhomogeneous reionization:
The scattering of CMB photons off moving electrons generates secondary anisotropies through Doppler effect. The distribution of their amplitudes and sizes is modulated by spatial variations of the density field or of the ionization field. In the non-linear regime the density modulations are due to collapsed structures. The modulation by variations of ionization fraction causes the the so-called inhomogeneous or patchy reionization. We have investigated the effect on the CMB anisotropies when the reionization (starting at redshift 12 and completed at 5.5) is due to quasars of different luminosities for two different lifetimes. The angular power spectrum of induced anisotropies depends on the nature and formation of first ionizing sources. Predictions therefore span a large range of values.

The Sunyaev-Zel'dovich (SZ) effects:
The SZ effect is the inverse Compton interaction between cold CMB photons and free hot electrons in the intra-cluster gas. The number of photons is conserved but the energy distribution of the CMB photons is modified. We distinguish between two terms: The thermal effect (TSZ) (inverse Compton effect) which amplitude is given by the Compton parameter, and the kinetic effect (KSZ) (Doppler shift) due to the bulk motion of the electrons when the cluster is moving with respect to the CMB rest frame.
TSZ and KSZ anisotropies can be computed for a population of galaxy clusters using N-body or hydrodynamical simulations or using analytic methods based on Press-Schechter or modified Press-Schechter number counts combined with a cluster model . A useful information is the angular power spectrum of the SZ anisotropies which shows that the TSZ effects dominates all known sources of secondary fluctuations down to the arcminute scale.

As a result, SZ anisotropies are contributing in the signal observed in the CMB at arcminute scales (on top of primordial anisotropies). A coherent analysis taking into account the dependence in the cosmology of both signals at these scales should then be applied when one is looking for cosmological parameter estimations from CMB observations. We developped such a test and applied it to actual dataset.

Angular power spectra: large and small scale data compared with primordial, secondary and foregrounds theoretical spectra [from Douspis, Aghanim & Langer 2006]

 The secondary anisotropies, in particular the SZ effect, add a non-negligible contribution to the CMB signal at small scales. Such a component,  if not properly removed,  affects the cosmological parameter estimation. We have estimated such effects in the context of small scale CMB experiments. We have developped the first method which properly takes into account both primary and secondary anisotropies in the parameter estimation.

Beyond the power spectrum: Non-Gaussian signatures from secondaries

Non-Gaussian signatures that might be left in the primary density perturbations and thus in the CMB anisotropies are now being proposed as new probes for testing inflationary models. Several statistical estimators are developped for this purpose. However, the primary cosmological signal is not the only source of non-Gaussian signature. Secondary anisotropies are indeed highly non-Gaussian distributed. This is particularly the case for the TSZ and KSZ fluctuations. It is therefore essential to explore the higher order statistics of the induced anisotropies. In our group, we have used multi-scale analysis (wavelet, curvelet) to study the nature, the amplitude and the detectability of SZ non-Gaussian signatures. We have shown, that the Planck satellite might be able to detect the secondary non-Gaussian signatures at scales of about 12 arcminutes with a 96 % confidence level.