From CFT Spectra to CMB Multipoles in Quantum Gravity Cosmology

We study the inflation process of universe based on the renormalizable quantum gravity formulated as a conformal field theory (CFT). We show that the power-law CFT spectrum approaches to that of the Harrison-Zel'dovich-Peebles type as the amplitude of gravitational potential gradually reduces during the inflation. The non-Gaussanity parameter is preserved within order of unity due to the diffeomorphism invariance. Sharp fall-off of the angular power spectrum of cosmic microwave background (CMB) at large scale is understood as a consequence of the existence of dynamical scale of the quantum gravity \Lambda_QG (\simeq 10^{17})GeV. The angular power spectra are computed and compared with the WMAP5 and ACBAR data with a quality of \chi^2/dof \simeq 1.1.