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Register a new userBayesian Inference of Polarized CMB Power Spectra from Interferometric Data
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Detection of B-mode polarization of the cosmic microwave background (CMB) radiation is one of the frontiers of observational cosmology. Because they are an order of magnitude fainter than E-modes, it is quite a challenge to detect B-modes. Having more manageable systematics, interferometers prove to have a substantial advantage over imagers in detecting such faint signals. Here, we present a method for Bayesian inference of power spectra and signal reconstruction from interferometric data of the CMB polarization signal by using the technique of Gibbs sampling. We demonstrate the validity of the method in the flat-sky approximation for a simulation of an interferometric observation on a finite patch with incomplete uv-plane coverage, a finite beam size and a realistic noise model. With a computational complexity of O(n^{3/2}), n being the data size, Gibbs sampling provides an efficient method for analyzing upcoming cosmology observations.
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The Epoch of Reionization (EoR) depends on the complex astrophysics governing the birth and evolution of the first galaxies and structures in the intergalactic medium. EoR models rely on cosmic microwave background (CMB) observations, and in particular the large-scale E-mode polarization power spectra (EE PS), to help constrain their highly uncertain parameters. However, rather than directly forward-modelling the EE PS, most EoR models are constrained using a summary statistic -- the Thompson scattering optical depth, $tau_e$. Compressing CMB observations to $tau_e$ requires adopting a basis set for the EoR history. The common choice is the unphysical, redshift-symmetric hyperbolic tangent (Tanh) function, which differs in shape from physical EoR models based on hierarchical structure formation. Combining public EoR and CMB codes, 21cmFAST and CLASS, here we quantify how inference using the $tau_e$ summary statistic impacts the resulting constraints on galaxy properties and EoR histories. Using the last Planck 2018 data release, we show that the marginalized constraints on the EoR history are more sensitive to the choice of the basis set (Tanh vs physical model) than to the CMB likelihood statistic ($tau_e$ vs PS). For example, EoR histories implied by the growth of structure show a small tail of partial reionization extending to higher redshifts. However, biases in inference using $tau_e$ are negligible for the Planck 2018 data. Using EoR constraints from high-redshift observations including the quasar dark fraction, galaxy UV luminosity functions and CMB EE PS, our physical model recovers $tau_e=0.0569^{+0.0081}_{-0.0066}$.
We briefly review our work about the polarized foreground contamination of the Cosmic Microwave Background maps. We start by summarizing the main properties of the polarized cosmological signal, resulting in electric (E) and magnetic (B) components of the polarization tensor field on the sky. Then we describe our present understanding of sub-degree anisotropies from Galactic synchrotron and from extra-Galactic point sources. We discuss their contamination of the cosmological E and B modes.
We present $it{CosmoPower}$, a suite of neural cosmological power spectrum emulators providing orders-of-magnitude acceleration for parameter estimation from two-point statistics analyses of Large-Scale Structure (LSS) and Cosmic Microwave Background (CMB) surveys. The emulators replace the computation of matter and CMB power spectra from Boltzmann codes; thus, they do not need to be re-trained for different choices of astrophysical nuisance parameters or redshift distributions. The matter power spectrum emulation error is less than $0.4%$ in the wavenumber range $k in [10^{-5}, 10] , mathrm{Mpc}^{-1}$, for redshift $z in [0, 5]$. $it{CosmoPower}$ emulates CMB temperature, polarisation and lensing potential power spectra in the $5sigma$ region of parameter space around the $it{Planck}$ best fit values with an error $lesssim 20%$ of the expected shot noise for the forthcoming Simons Observatory. $it{CosmoPower}$ is showcased on a joint cosmic shear and galaxy clustering analysis from the Kilo-Degree Survey, as well as on a Stage IV $it{Euclid}$-like simulated cosmic shear analysis. For the CMB case, $it{CosmoPower}$ is tested on a $it{Planck}$ 2018 CMB temperature and polarisation analysis. The emulators always recover the fiducial cosmological constraints with differences in the posteriors smaller than sampling noise, while providing a speed-up factor up to $O(10^4)$ to the complete inference pipeline. This acceleration allows posterior distributions to be recovered in just a few seconds, as we demonstrate in the $it{Planck}$ likelihood case. $it{CosmoPower}$ is written entirely in Python, can be interfaced with all commonly used cosmological samplers and is publicly available https://github.com/alessiospuriomancini/cosmopower .
We develop an analytic model for the power spectra of polarized filamentary structures as a way to study the Galactic polarization foreground to the Cosmic Microwave Background. Our approach is akin to the cosmological halo-model framework, and reproduces the main features of the Planck 353 GHz power spectra. We model the foreground as randomly-oriented, three-dimensional, spheroidal filaments, accounting for their projection onto the sky. The main tunable parameters are the distribution of filament sizes, the filament physical aspect ratio, and the dispersion of the filament axis around the local magnetic field direction. The abundance and properties of filaments as a function of size determine the slopes of the foreground power spectra, as we show via scaling arguments. The filament aspect ratio determines the ratio of $B$-mode power to $E$-mode power, and specifically reproduces the Planck-observed dust ratio of one-half when the short axis is roughly one-fourth the length of the long axis. Filament misalignment to the local magnetic field determines the $TE$ cross-correlation, and to reproduce Planck measurements, we need a (three-dimensional) misalignment angle with a root mean squared dispersion of about 50 degrees. These parameters are not sensitive to the particular filament density profile. By artificially skewing the distribution of the misalignment angle, this model can reproduce the Planck-observed (and parity-violating) $TB$ correlation. The skewing of the misalignment angle necessary to explain $TB$ will cause a yet-unobserved, positive $EB$ dust correlation, a possible target for future experiments.
Upcoming measurements of the small-scale primary cosmic microwave background (CMB) temperature and polarization power spectra ($TT$/$TE$/$EE$) are anticipated to yield transformative constraints on new physics, including the effective number of relativistic species in the early universe ($N_{rm eff}$). However, at multipoles $ell gtrsim 3000$, the primary CMB power spectra receive significant contributions from gravitational lensing. While these modes still carry primordial information, their theoretical modeling requires knowledge of the CMB lensing convergence power spectrum, $C_L^{kappakappa}$, including on small scales where it is affected by nonlinear gravitational evolution and baryonic feedback processes. Thus, the high-$ell$ primary CMB is sensitive to these late-time, nonlinear effects. Here, we show that inaccuracies in the modeling of $C_L^{kappakappa}$ can yield surprisingly large biases on cosmological parameters inferred from the primary CMB power spectra measured by the upcoming Simons Observatory and CMB-S4 experiments. For CMB-S4, the biases can be as large as $1.6sigma$ on the Hubble constant $H_0$ in a fit to $Lambda$CDM and $1.2sigma$ on $N_{rm eff}$ in a fit to $Lambda$CDM+$N_{rm eff}$. We show that these biases can be mitigated by explicitly discarding all $TT$ data at $ell>3000$ or by marginalizing over parameters describing baryonic feedback processes, both at the cost of slightly larger error bars. We also discuss an alternative, data-driven mitigation strategy based on delensing the CMB $T$ and $E$-mode maps. Finally, we show that analyses of upcoming data will require Einstein-Boltzmann codes to be run with much higher numerical precision settings than is currently standard, so as to avoid similar -- or larger -- parameter biases due to inaccurate theoretical predictions.
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