Improved solution to CMB quadrupole problem using ellipsoidal Universes with Chaplygin gas

Abstract: A Universe containing uniform magnetic fields, strings, or domain walls is shown to have an ellipsoidal expansion. This case has motivations from observational cosmology especially the anomaly concerning the low quadrupole amplitude compared to the best-fit $\Lambda$CDM prediction in Planck data. It is shown that a Universe with eccentricity at decoupling of order $10^{-2}$ can reduce the quadrupole amplitude without affecting higher multipoles of the angular power spectrum of the temperature anisotropy. We study the evolution of ellipsoidal Universes using dynamical system techniques for the first time. The determined critical points vary between saddle and past attractors depending on dark energy state equation parameter $w_{\Lambda}$, with no future attractors. Important results are shown with numerical integrations of this dynamical system done using several initial conditions. For instance, a tendency for high expansion differences between planar and perpendicular axes is observed which contradicts previous assumption on the evolution behaviour of ellipsoid Universes. Considering dark energy as a Chaplygin gas solves this contradiction by controlling cosmic shear evolution.