While the evolution of linear initial conditions present in the early universe into extended halos of dark matter at late times can be computed using cosmological simulations, a theoretical understanding of this complex process remains elusive. Here, we build a deep learning framework to learn this non-linear relationship, and develop techniques to physically interpret the learnt mapping. A three-dimensional convolutional neural network (CNN) is trained to predict the mass of dark matter halos from the initial conditions. We find no change in the predictive accuracy of the model if we retrain the model removing anisotropic information from the inputs. This suggests that the features learnt by the CNN are equivalent to spherical averages over the initial conditions. Our results indicate that interpretable deep learning frameworks can provide a powerful tool for extracting insight into cosmological structure formation.
We search for evidence of parity-violating physics in the Planck 2018 polarization data, and report on a new measurement of the cosmic birefringence angle, $\beta$. The previous measurements are limited by the systematic uncertainty in the absolute polarization angles of the Planck detectors. We mitigate this systematic uncertainty completely by simultaneously determining $\beta$ and the angle miscalibration using the observed cross-correlation of the $E$- and $B$-mode polarization of the cosmic microwave background and the Galactic foreground emission. We show that the systematic errors are effectively mitigated and achieve a factor-of-$2$ smaller uncertainty than the previous measurement, finding $\beta=0.35 \pm 0.14\,\deg$ (68% C.L.), which excludes $\beta = 0$ at $99.2$% C.L. This corresponds to the statistical significance of $2.4\sigma$.