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, 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 GUT epoch, subject to mixed Neumann/Dirichlet boundary conditions at fixed points. As a consequence, a set of infrared cutoffs emerges in both the scalar and tensor spectra, leading to observable consequences in the CMB. We examine in detail the possible signatures of such a topology, particularly in relation to the even-odd parity imbalance already reported by the WMAP and Planck missions in the temperature angular correlations. Furthermore, we extend our study to the high-precision B-mode polarization data expected from the forthcoming LiteBIRD mission.