Suppression of the long-wavelength CMB spectrum from the Hartle–Hawking wave function in the Starobinsky-type inflation model

Abstract

Abstract The lack of correlations on the large scale cosmic microwave background (CMB) anisotropy provides a potential window to probe beyond the standard inflationary scenario. In this paper, we investigate the primordial power spectrum based on the Hartle–Hawking (HH) no-boundary proposal for a homogeneous, isotropic, and spatially-closed universe that leads to Starobinsky-type inflation after the classicalization. While we found that there is no suppression at large scales in the standard R + R 2 theory, we also found that it is possible to sufficiently suppress the large-scale power spectrum if a pre-inflationary stage is introduced to the Starobinsky-type model. In addition, such a pre-inflationary stage will be helpful to explain the preference of large e -foldings of the HH proposal. We calculate the C l T T correlation function and show that our proposal gives a better fit to the Planck CMB data. This suggests that our universe might have begun with a compact HH state with a small positive curvature.