$B$-sure I: Minkowski functionals as robustness test for tensor-to-scalar ratio detection from CMB observations

Abstract

The detection of primordial $B$-mode polarisation of the Cosmic Microwave Background (CMB) is a major observational goal in modern Cosmology, offering a potential window into inflationary physics through the measurement of the tensor-to-scalar ratio $r$. However, the presence of Galactic foregrounds poses significant challenges, possibly biasing the $r$ estimate. In this study we explore the viability of using Minkowski functionals (MFs) as a robustness test to validate a potential $r$ detection by identifying non-Gaussian features associated with foregrounds contamination. To do so, we simulate sky maps as observed by a LiteBIRD-like CMB experiment, with realistic instrumental and foregrounds modelling. The CMB $B$-mode signal is recovered through blind component separation algorithms, and the obtained (biased) value of $r$ is used to generate Gaussian realisation of CMB signal. Their MFs are then compared with those computed on maps contaminated by foreground residual left by component separation, looking for a detection of non-Gaussianity. Our results demonstrate that, with the experimental configuration considered here, MFs can not be reliably adopted as a robustness test of an eventual $r$ detection, as we find that in the majority of the cases MFs are not able to raise significant warnings about the non-Gaussianity induced by the presence of foreground residuals. In the most realistic and refined scenario we adopted, the test is able to flag non-Gaussianity in $\sim 26\%$ of the simulations, meaning that there is no warning on the biased tensor-to-scalar ratio in $\sim 74\%$ of cases. These results suggest that more advanced statistics than MFs must be considered to look for non-Gaussian signatures of foregrounds, in order to be able to perform reliable null tests in future CMB missions.

Figures (14)

• Figure 1: Overview of the steps adopted to build the MFs robustness test. Squares represent pipeline stages, while ovals indicate data products (input in yellow, intermediate in light blue). This procedure is then repeated for 300 "data" simulations.
• Figure 2: Left panel: needlet bands configuration adopted in this work, where the first bands have been merged. Right panel: full-sky angular power spectra evaluated on foreground (red) and noise (blue) residuals, for NILC (dashed lines) and MC-NILC (solid lines), applied to the d10s5 model. Black dotted line is the input CMB spectrum (lensing-only).
• Figure 3: Sky partitions adopted within MC-NILC component separation for d1s1 (left) and d10s5 (right) foreground models.
• Figure 4: Component separation outputs, for one simulation. Left column: CMB solution. Middle column: noise residuals. Right column: foreground residuals. Outputs are shown for NILC (upper row) and MC-NILC (lower row) methods, applied on the d10s5 model. Units are $\mu \mathrm{K_{CMB}}$.
• Figure 5: Output of the likelihood evaluation for a single simulation, for the NILC - d1s1 (left) and MC-NILC - d10s5 (right) scenarios, considering all the multipoles. Main plot: power spectra, with $C_\ell^\text{th} (r = 0)$ in dashed blue, $C_\ell^\text{obs}$ in red solid, $C_\ell^\text{lensing}$ in dotted black, and best fit spectrum in black solid. The shaded area represents the standard deviation of $C_\ell^\text{obs}$ across 300 realisations. Inset: normalised likelihood on the tensor-to-scalar ratio, with the peak value indicated by the dashed line.