Cosmic Microwave Background with Planck (since 2012)

In my latest postdoctoral scholarship, I expanded my scientific horizons as a member of the Planck Collaboration and pursued studies of the cosmic microwave background (CMB). The Planck Mission endeavored to produce highly-reliable determinations of the CMB temperature and polarization across the sky, which act as powerful constraints of the cosmological parameters. To achieve these goals of Planck, a robust likelihood function must be developed that considers a variety of factors: the correlation of the temperature and polarization fields, the correlation of angular power spectrum estimators at different multipoles (ℓ) due to partial sky coverage, unresolved astrophysical foregrounds, and instrumental factors. The likelihood function is key as it can serve as the prime CMB analysis tool. A variety of likelihood functions, using different approaches, have been produced within the Collaboration. I led the development of the HiLLiPOP likelihood function. It is based on a Gaussian approximation to compare ℓ-by-ℓ the estimated temperature and polarization cross-power spectra with models.

The data consist of two sets of half-mission (I,Q,U Stokes parameters) maps at 100, 143 and 217 GHz. Frequency dependent apodized masks are applied to these maps in order to limit contamination from emission of diffuse Galactic dust, Galactic CO lines, nearby galaxies and extragalactic point sources. We ultimately retain 72, 62 and 48% of the sky at 100, 143 and 217 GHz, respectively, and use the same set of masks in temperature and polarization. Mask-deconvolved and beam-corrected cross-half-mission angular power spectra (first order a_ℓm correlation) are computed. From the six above maps, three sets of six band-averaged angular cross-power spectra are derived for TT, EE and TE. We select the multipole ranges to limit contamination from diffuse Galactic dust emission at low-ℓ and noise at high-ℓ in each power spectrum.

As the angular power spectra are highly correlated, we developed a semi-analytical estimation of the covariance matrix, which encompassed the anticipated (ℓ-by-ℓ) correlations. The method employs data estimates only, with no reliance upon Monte-Carlo simulations. We worked intensively to achieve an accurate calculation of the 4-alm correlations, which involves products of 4 spherical harmonics. We tested the approximations used in the calculation with Monte-Carlo simulations and we found that a precision better than a few percents was achieved.

In addition to the CMB component, our model considers foreground residuals and calibration differences among maps. We use different models for the foreground’s angular power spectra in temperature and polarization. Our model includes contributions from CIB, Galactic dust, thermal and kinetic SZ effects, Poisson point sources, and cross-correlation between infrared galaxies and the temperature SZ effect. I was heavily involved in the modeling of the astrophysical foreground’s angular power spectra in HiLLiPOP. For model construction, we employed the Planck HFI measurements of the millimeter sky (the 9 frequency band data from Planck permits a highly-accurate estimate of the angular power spectra and SED of the different astrophysical emission). Specifically, my colleagues and I worked on the estimation of the temperature and polarization angular power spectra of the Galactic dust emission. We built a model based on the 353 GHz frequency band, where the sky is mainly dominated by Galactic dust emission. Using the measured SED of the dust, we then extrapolated the model at lower frequency. In addition to the use of the derived Galactic dust templates in HiLLiPOP, our measurements shed new light upon interstellar dust physics and allowed for a precise determination of the level of contamination in CMB polarization experiments.

Finally, I worked on the statistical methodology used to infer the cosmological parameters from the likelihood function. In cosmology, the estimation of the parameters is predominantly performed in the Bayesian framework using Markov Chain Monte Carlo techniques sampling. My colleagues and I have proposed the employment of a different methodology, namely the multi-dimensional minimization and the construction of frequentist confidence intervals using profile likelihoods.

Today, I am continuing my research on the CMB as a Visiting Scholar at the Department of Astronomy at the University of Virginia. Most of my work is focused on the testing of the likelihood function and the improvement of the model of the estimated Planck angular power spectra. Recently, we investigated with my colleague at Laboratoire de l’Accélérateur Linéaire (LAL) the deviation from unity of the A_L parameter (control parameter that aims at measuring the degree of lensing of the CMB power spectra) found with the Planck public likelihoods.