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The lack of correlations on the large scale cosmic microwave background (CMB)anisotropy provides a potential window to probe beyond the standardinflationary scenario. In this paper, we investigate the primordial powerspectrum based on the Hartle-Hawking (HH) no-boundary proposal for ahomogeneous, isotropic, and spatially-closed universe that leads to aStarobinsky-type inflation after the classicalization. While we found thatthere is no suppression at large scales in the standard R + R^2 theory, we alsofound that it is possible to sufficiently suppress the large-scale powerspectrum if a pre-inflation stage is introduced to the Starobinsky-type model.We calculate the C^TT_l correlation function and show that our proposal gives abetter fit to the Planck CMB data. l This suggests that our universe might havebegun with a compact HH state with a small positive curvature.

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