Temperature and Polarization CMB Maps from Primordial non-Gaussianities of the Local Type

TL;DR

This work develops and validates a polarization-inclusive framework for generating high-resolution, non-Gaussian CMB maps of local-type primordial perturbations, enabling robust calibration of non-Gaussian estimators. It extends a real-space, shell-based approach with pre-computed filter functions $W_\ell(r,r_1)$ and real-space transfer functions $\Delta_\ell^X(r)$ to produce $a_{\ell m}^X$ via $a_{\ell m}^X = \int dr\, r^2 \Delta_\ell^X(r) \Phi_{\ell m}(r)$ and to generate the associated curvature perturbation multipoles $\Phi_{\ell m}(r)$. Applying the fast cubic statistic to 300 simulations confirms unbiased recovery of $f_{\rm NL}$ and reveals $f_{\rm NL}$-dependent corrections to estimator variance, consistent with theoretical expectations, within full-sky, radiative-transfer calculations. The results demonstrate the feasibility of Planck-scale non-Gaussian analyses, provide a calibrated toolset for estimator validation, and open pathways to tomography and alternative estimators using polarization data.

Abstract

The forthcoming Planck experiment will provide high sensitivity polarization measurements that will allow us to further tighten the f_NL bounds from the temperature data. Monte Carlo simulations of non-Gaussian CMB maps have been used as a fundamental tool to characterize non-Gaussian signatures in the data, as they allow us to calibrate any statistical estimators and understand the effect of systematics, foregrounds and other contaminants. We describe an algorithm to generate high-angular resolution simulations of non-Gaussian CMB maps in temperature and polarization. We consider non-Gaussianities of the local type, for which the level of non-Gaussianity is defined by the dimensionless parameter, f_NL. We then apply the temperature and polarization fast cubic statistics recently developed by Yadav et al. to a set of non-Gaussian temperature and polarization simulations. We compare our results to theoretical expectations based on a Fisher matrix analysis, test the unbiasedness of the estimator, and study the dependence of the error bars on f_NL. All our results are in very good agreement with theoretical predictions, thus confirming the reliability of both the simulation algorithm and the fast cubic temperature and polarization estimator.

Figures (9)

• Figure 1: CMB angular power spectra extracted from $10$ simulations (triangles) are compared to the theoretical ones computed with CMBfast for the same model (solid black lines) . The cosmological parameters are $\Omega_b = 0.042$, $\Omega_{cdm} = 0.239$, $\Omega_L = 0.719$, $h = 0.73$$n = 1$, and $\tau = 0.09$ (same for all the following figures, unless otherwise stated).
• Figure 2: Temperature (bottom panel) and polarization (upper panel) transfer functions at high $\ell$ at last scattering.
• Figure 3: Temperature (bottom panel) and polarization (upper panel) transfer functions at low $\ell$ (reionization and late ISW contributions are visible). The oscillations visible in the plots are little numerical artifacts which have negligible impact on the final results. We have explicitly checked this by increasing the resolution in the k and r-grid by factors of $2$ and $4$ without noticing any improvement in the accuracy of the final $C_\ell$, that can be already reconstructed well using the sampling chosen in the paper (see fig. \ref{['fig:cl']})
• Figure 4: Temperature transfer functions at high $\ell$ and $r$ corresponding to the epoch of reionization. Polarization transfer functions at large $\ell$ are zero in this range.
• Figure 5: Angular power spectrum of the Gaussian curvature perturbation multipoles $\Phi_{\ell m}^{\rm L}(r)$ obtained by averaging over all the spherical shells of a given simulation. In this example we consider a spectral index $n = 0.95$ and divide $|\Phi_{\ell m}^{\rm L}(r)|$ by $\sqrt{r^{(1-n)}}$ in order to make the normalization of the spectrum independent of the shell radius before averaging. We compare the results extracted from our simulations (red triangles) to the expected shell power spectrum obtained from formula (\ref{['eqn:shellnormgamma']}), (blue line)