Nearly universal CMB TT spectrum from pre-inflationary dynamics in a closed universe: KICI scenario, bouncing universe, and emergent universe

Abstract

We utilize the phase space analysis method to study the early evolution of the spatially closed universe and find that there exists an attractor denoting the de Sitter expansion phase, and that the universe has three distinct evolutionary paths, which correspond to the kinetic initial conditions for inflation (KICI) scenario, bouncing universe, and emergent universe. Based on the results of the phase space analysis, we calculate the primordial power spectrum and CMB TT spectrum for these models. We find that, for these models, the primordial power spectrum and CMB TT spectrum are suppressed at large scales. The suppression originates from the pre-inflationary dynamics, while the common suppression trend is a consequence of the positive spatial curvature shared by all three models. The oscillation amplitude, in contrast, is determined by the details of the transition, with a smoother transition yielding a smaller amplitude. Moreover, the CMB TT spectra for these models overlap completely, indicating that these models are indistinguishable via their CMB TT spectra, and that the suppression and the detailed shape of the CMB TT spectrum are independent of the specific pre-inflationary dynamics or the presence of a transition stage in a closed universe.