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

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(TT) 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. (C) 2019 Elsevier B.V. All rights reserved.