Constraints on natural inflation from cosmic microwave background

We study constraints on the natural inflation model from the cosmic microwave background radiation (CMBR). Inflaton φ for the natural inflation has a potential of the form V=Λ4[1−cos(φ/2 fφ)], which is parametrized by two parameters fφ and Λ. Various cosmological quantities, like the primordial curvature perturbation and the CMBR anisotropy, are determined as functions of these two parameters. Using recent observations of the CMBR anisotropy by BOOMERANG and MAXIMA (as well as those from COBE), constraints on the parameters fφ and Λ are derived. The model with fφ lower than 8.5×1018 (5.4×1018, 4.5×1018) GeV predicts a power spectrum with index nS smaller than 0.95 (0.9, 0.85) which suppresses the CMBR anisotropy for smaller angular scale. With such a small nS, height of the second acoustic peak can become significantly lower than the case of the scale-invariant Harrison–Zeldovich spectrum.