Probing the Topology of the Early Universe Using CMB Temperature and Polarization Anisotropies

The temperature and polarization anisotropies of the cosmic microwave background (CMB) as measured today can offer key insights into the topology of the early universe prior to inflation, for example by discriminating between flat and warped geometries. In this paper, we focus on a Kaluza–Klein model with an extra spatial dimension that compactifies at the Grand Unified Theory (GUT) epoch, subject to mixed Neumann/Dirichlet boundary conditions at fixed points. As a consequence, a set of Infrared (IR) cutoffs emerges in both the scalar and tensor spectra, leading to observable consequences in the CMB. We examine the possible signatures of such a topology in detail, particularly in relation to the even–odd parity imbalance already reported by the COBE, WMAP and Planck missions in the temperature angular correlations. Furthermore, we extend our analysis to the existing Planck E-mode polarization data and to the high-precision B-mode polarization measurements expected from the forthcoming LiteBIRD mission.