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

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 ∼ 26% of the simulations, meaning that there is no warning on the biased tensor-to-scalar ratio in ∼ 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.